SLAC- 143
UC-34
(EXP)
A STUDY OF NON-STRANGE
BOSON RESONANCES
QUASI-MONOCHROMATIC
BETWEEN
MICHAEL
LINEAR
Stanford,
COMMISSION
BUBBLE
CHAMBER
M. MENKE
ACCELERATOR
STANFORD
PREPARED
BY
PHOTON BEAMS OF ENERGIES
4.3 AND 7.5 GeV IN A HYDROGEN
STANFORD
PRODUCED
CENTER
UNIVERSITY
California
94305
FOR THE U. S. ATOMIC
UNDER CONTRACT
December
ENERGY
NO. AT(O4-3)-515
‘3
1971
.
‘,
Printed in the United
Information
Service,
Springfield,
Virginia
Price:
Printed Copy
States of America.
Available from National Technical
U. S. Department of Commerce,
5285 -,JJort Royal Road,
.:
22151.
$3.00; microfiche
$0.95.
ABSTRACT
The photoproduction
of resonances
of a hydrogen bubble chamber
and 7.5 CeV nominal
on the three-prong
yp -p*‘r-
reactions
yp +
pl~+x-x’
The general analysis
and yp *
x+r+x-n
Using various
cross section decreases
to about .tOO~b/CeV2 at 7.5 CeV.
vector
The cross
part,
I t= o is then 9.4i2.3
meson production
of 4.3,
procedure
5.25
and results
We study the highly
at the annihilation
con-
energies.
found is 7.OkO.4
p” photoCeV
from about 130pb/GeV2
composed into an OPE and a diffractive
(du(p)/dt)/(du(w)/dt)
radiation
models to parameterize
pa+=- , the mean t-slope
in yp --t
in three exposures
over the energy range 2-8 CeV and the
are given.
the p” forward
annihilation
event topology are presented.
reaction
production
to positron
energies.
strained
Cross sections
has been siudied
-2
, while
at 3.3 CeV
section for yp ---f wp is dewhich is found to be 1.5*0.3pb.
at 7.5 C&V.
In comparing
with that of Compton scattering
da/dt for
via VDM for photon
n
energies
above 4 CeV, we find that for yi/41r
agreement
cross
at all s and t.
sections
to cT(yp)
the 90% confidence
width,
Inelastic
be associated
This same value of ~;/47r
at all our energies.
level,
ap,(1250)<0.3pb
peripheral
neutron channels,
co production
but with present
with it.
and Al n are observed,
= 0.32*0.03
The quasi-two
with cross
statistics
relates
our forward
A search for p’-+
and uc,(1650)<0.
co
217finds,
at
lpb per 100 MeV
is seen in both the proton and the
specific
body reactions
sections
there is good
decreasing
nucleon isobars
yp -
a-A’+,
cannot
p-A++,
with photon energy
For the first two a=l. 74kO.16 and 0.6iO.2 respectively,
indicating
like E-“.
Y
It follows that
that they are unlikely to have the same production mechanism.
if the reaction
yp -+p
tive decay width (-0.5
- ++.
A
1s due to an OPE process,
the required
MeV) is much in excess of the value predicted
rho radiaby SU(3).
ACKNOWLEDGEMENTS
It is a pleasure
to acknowledge
who made this experiment
the general direction
The experiment
possible.
of Dr.
the contributions
George Chadwick,
of help and understanding
both in matter
details
analysis.
of bubble chamber
operation
were Drs.
members
of the collaboration
was carried
Other major
sources of advice and co-
Peter Seyboth and Arie
which carried
Drs.
Zaven Guiragossian,
Skillicorn,
Joseph Ballam,
in matters
and criticisms
William
Paul Klein,
and Tai Ho Tan.
Professor
aid
Others who made material
contributions
all
Much help
Aahron Levy and
at various
William
stages are
Podolsky,
Ian
Special thanks are due to my thesis supervisor,
for his patience,
not only of physics
constantly
but of personal
of this work have been received
receptive
life.
attitude
Valuable
and
comments
from the co-signers,
Profs.
Bardeen and Mason Yearian.
The hospitality
several
and support of my research
years has been greatly
ductive atmosphere
received
from
Schwimmer.
Profs.
Group.
Helpful
Fred Gilman,
Also I appreciate
the Stanford Physics
appreciated.
by SLAC for the past
I especially
appreciate
the con-
created by the many people of SLAC, particularly
in Group B and the Theory
Department
The help and cooperation
Haim
goes to all the scanners
advice and consultations
Harari,
the continual
...
- 111 -
c
have been
support and encouragement
of the SLAC Accelerator
at SLAC,
those
David Leith and Adam
during my graduate career
and of Bob Watt and the 40” bubble chamber
credit
Shapira,
out the experiment.
Ken Moffeit,
source
and in the many technical
and advice in the early phases of the work came from Drs.
Gunter Wolf.
out under
who has been a major
of physics
Yehuda Eisenberg,
of the many people
here.
Operations
crew were superb.
the Weizman
of
Institute
Group
Special
and Tel Aviv
University
hadronic
(see Fig.
who diligently
events in a nearly
II. 1).
and Madge Tartar
operation
performed
the task of locating
overwhelming
The help in data reduction
is also greatly
background
of uninteresting
and management
appreciated.
from the staff of our SLAC computation
- iv -
and measuring
events
from Ken Eyeman
I also received
facility.
the
friendly
co-
TABLE
OF CONTENTS
page
I.
Introduction
It.
Experimental
HI.
Iv.
Apparatus
1.
The Hydrogen
2.
The Annihilation
3.
Determination
4.
Scanning Procedures
5.
Measuring
and Procedures
of Annihilation
Beam Parameters
...
and Kinematic
35
.......
Reconstruction
45
45
Flux Determinations
3.
3-C Channel Cross Section ...............
4.
Calculation
Photoproduction
60
Sections for 1-C Channels ....
of Neutral
The Channel yp -
Vector
p=+n-
Mesons
83
...............
84
...................
p” Production
B.
Nucleon Resonances
................
C.
Higher
Meson Production
Mass Vector
2.
Omega Meson Production
3.
Vector
Dominance
Vector
Meson Couplings
109
(p’) . . . .
. . . . . . . . . . . . . . . .
114
114
Model Tests and the Photon-
Photoproduction
State pr+r-r’
67
82
.........
A.
Associated
46
for Cross Sections ........
of Cross
29
33
..................
2.
2.
14
Beam ............
Radiation
General Method .....................
1.
8
.............
Bubble Chamber
1.
Resonance
8
..........
of the Cross Sections ............
Determination
1.
V.
1
..........................
. . . . . . . . . . . . . . . . .
in Four Body Final States . . .
Rho and Delta Production
. . . . . . . . . . . . . . . . . . .
-V-
135
in the Final
. . , . . . . . . . . . . . . . . . . . . s .
A2 Meson Production
125
139
147
r
page
3.
VI.
Inelastic
Conclusions
References
Rho Production
................
.........................
156
166
169
.............................
- vi -
LIST OF TABLES
page_
I.
parameters
and statistics
..............
36
in SLAC data ..........
38
II. 1.
Scannedevents
on SLAC rolls.
lI.2.
Fits to various
hypotheses
sections
47
...............
III. 1.
Fair cross
of Knasel.
m. 2.
Summary
III. 3.
Microbarn
III. 4.
Sample 3-C cross section calculation
III. 5.
Scan-to-measure
III. 6.
3-C cross section calculations
m. 7.
Combined
50
...........
of pair scans on SLAC rolls
equivalents
7
....
of the three exposures.
from pair spectra
56
.........
58
...........
61
................
correction
3-C cross sections
63
.......
at all energies
from 5.25 and 7.5 GeV
65
data .............................
III. 8.
Cross sections
for
Iv. 1.
Fitted
widths,
masses,
YP ‘pop
IV.2.
Forward
yp -cpr’r-x”
and total cross
sections
...
cross
sections
93
and d2g/dtdm
t=O for
98
..........................
Iv. 3.
Standard method for du/dt,
IV.4.
Total cross
sections
(0.715,
v. 1.
Fits to the channels px’x-x0
V.2.
A
to yp 4 pa+n-x0.
0.815) GeV ......
105
wp ......
120
for the reaction
A
P slopes> P;~, pll>
79
for
..........................
yp-pop.
ff
++and yp -7rxrn
and r’r”n-n
yp .
and shaping parameters
.....................
- vii -
137
.........
for fits
142
FIGURE CAPTIONS
Page
It. 1.
A bubble chamber
prong hadronic
II. 2.
Horizontal
picture
of a photoproduced
three
9
event . . . . . . . . . . . . . . . . . . . .
cross-section
of the SLAC 40-inch
bubble
12
chamber...........................
II. 3.
Schematic
layout of a positron
annihilation
radiation
15
beam............................
II. 4.
Noise to signal ratio
of positron
energy
for annihilation
Predicted
R.6.
Layout of the positron
II. 7.
photon intensity
Measured electron
annihilation
21
. . . . .
beam in end
23
collision
pair spectra
at the three annihilation
24
. . . . . . . . . . . . . . . . . . . . . . . . . .
Theoretical
spectrum
for a positron-hydrogen
at fixed angle.
II. 9.
E(gamma)
II. 10.
Photon spectra
reaction
in the bubble chamber
B . . . . . , . . . . . . . . . . . . . . . . . . . .
energies.
II. 8.
18
. . . . . . . . . . . . . . . . . . . . ..
II. 5.
station
beam as a function
atom
26
. . . . . . . . . . . . . . . . . .
- E(calculated)
for 1-C pairs
27
at 7.5 GeV . . . .
as deduced from measurements
of the
yp dpr+a-.
R. 11.
Bubble chamber
II. 12.
Relation
.
30
. . . . . . . , . . . . . , . , . . . . , , .
32
coordinate
system viewed in two planes.
between photon beam and projected
beam direction.
for 3-C events . . . . . .
40
for 3-C events . . . . . . . . . .
41
II. 13.
Gamma mass squared calculated
II. 14.
Chi-squared
distributions
positron
. ..
- Vlll -
III. 1.
Pair production
(Ref. 44).
III.2.
cross
sections
according
to Knasel
. . . . . . . . . . . . . . . . . . . . . . . . .
Spectra of PHONY generated
pairs
at 5.25 and
7.5Gev...........................
III. 3.
52
Spectra of PHONY generated
pairs on a percentage
scale...........................
III.4.
Cumulative
.
probability
III. 5.
to a pair with 1-C energy <E . . . . . . . .
Y
Cross sections for the reaction yp - pr+~- . . . . . . .
HI. 6.
Missing
mass squared for all events consistent
with the reactions
III. 7.
Missing
III. 8.
Missing
HI. 9.
Cross sections
mass of 5 body events treated as 3 prongs
for 4-body reaction
Iv. 1.
5 energy intervals.
IV.2.
IV. 3.
(0.60<m<O.
IV.4.
6.8-8.2
I t 1 distributions
Forward
yp-
pr’~-
for
77
81
in the first
yp - pnf-
85
in the photon
GeV. . . . . . . . . . . . . . . . .
86
for events in the o” region
85 CeV). . . . . . . . . . . . . . . . . . . .
double differential
as a function
for
73
channels with
. . . . . . . . . . . . . . . . . . . .
Dipion mass distributions
energyrange
. . .
in the final state . . . . . . . . . . . . .
Dipion mass distributions
71
for PHONY events
yp - ~?;‘T-TT’ . . . . . . . . . . . . . .
a single neutral
66
by
. . . . . . . . . . . . .
mass squared distributions
of the reaction
54
yp - pn+~- plus neutrals
T’A+T- plus neutrals
and yp -
53
that a pair of energy E6 will
reconstruct
ionization
48
90
cross section and slopes
of dipion mass . . . . . . . . . . . . . . .
91
Iv.5.
Mass skewing mechanisms
in the ading
phenomenological
. . . . . . . . . . . . . . . .
lV.6.
Summary
Iv. 7.
Spin one density
frame
N.8.
models.
of results
on p” production
matrix
elements
for the dipion system
(Mp”+) and (b) M(pr-)
and
at six energies
. ,
94
107
in the helicity
in the o” region
distributions
. . . . . . .
110
for yp 4 pr+n-
events with m(7i.+n-)(l
111
Iv. 9.
Cross sections
113
Iv. 10.
Angular
GeV . . . . . . . . . . . . . . . .
++ for yp -+ A 7~ . . . . . . . . . . . . . .
distributions
of the K+ in the helicity
the dipion system for events with rn(r’T-)<l
Iv.ll.
Iv.12.
Iv.13.
N.14.
lV.16.
. . . . . . . . . . . . . . . . . . . . . .
115
nfn-xo
mass distributions
ll?
invariant
yp -+ op total cross sections
v.2.
for yp -+ pn’x-?r’.
measured
.
in this
experiment
. . . . . . . . . . . . . . . . . . . . . . . . .
Differential
cross sections
do/dt
yp’op..
. . . . . . *.
. . . . . . . . . . . . . . . .
The spin density
Comparison
matrix
system
elements
yp -op.
yp total cross sections
. . . .
Model predictions
present
data using
$ /4n=O. 32. . . . . . . . . . . . . .
dt for Compton scattering
data.
Scatter plot of M(pr’)
- ++
cross
P--+P A
126
with
Dominance
UI
124
poo, Re10 and plel
Vector
d
122
for the reaction
for the reaction
of measured
photoproduction
v. 1.
GeV for the
7.5GeVdata..
in the helicity
Iv.15.
frame of
based upon the
calculated
129
from the present
. . . . . . . . . . . . . , . . . . .
132
versus
sections
M(x’n-)
for 7.5 GeV . . . .
141
determined
in this experiment.
146
-x-
v. 3.
M(pn) in all charge states for 1-C fits in the 7.5 GeV
data............................
148
v. 4.
M(nn) for all 1-C fits to yp --r A+r+r-n
v.5.
M(x*a+n-)
distribution
. . . . . . . , .
iiyp -+3r A 71 n
in the reaction
at (a) 4.3 CeV, (b) 5.25 CeV and (c) 7.5 C&V . . . . . .
V. 6.
M(~+?r+a-) distribution
for
yp d a+r+a-n,
datafrom4.3and5.25GeV.
M(r+s-?r”)
v. 8.
Dipion masses in all charge combinations
v. 9.
37r)l< 0.5 GeV2 . . . . .
in the 7.5 CeVdata.
M(xa) distributions
4.3,
v. 10.
YP dpa+a-x0
(t(y,
for the reaction
5.25and7.5CeVcombined.
M(a+x-)
155
. . . . . . . . . .
yp -) pr+a-r”
158
at
. . . . . . . . . . . .
159
for all 1-C fits to yp 4 x+=+=-n in the 7.5 GeV
Peripheral
161
M(aa) distribution
at all energies.
v. 12.
153
for 1-C fits
data............................
v. 11.
151
combined
. . . . . . . . . . . . . . .
v. 7.
to
at 7.5 GeV for
149
( 1 t(y,?w)l
. . . . . . . . . . . . . . . . . . . . . .
M(p?p) and M(nn+) distribution
yp -+ ~T+T-T’
i 0.5 GeV2)
and nn+r+r-
162
in the reactions
respectively.
- xi -
. . . . e . . . .
164
CHAPTER
I
INTRODUCTION
Photoproduction
and strong
interaction
lated since the beginning of systematic
From unitarity
accelerators.
physics
have been closely
experimentation
and time reversal
using high energy
invariance
shown that the phases of the single pion photoproduction
pion nucleon elastic
scattering
for two pion production.
sufficient
to calculate
nucleon scattering,
trates
This result,
but it serves
in the spin-isospin
such as whether
may be essential
the (3/2,
amplitude
in terms
ambiguities
3/2).
of multi-pion
duction proved a valuable
interactions
tum numbers
vector
Therefore
it is not
evidence of the pion
Moreover,
photopro-
of nucleon isobar
and
states above
3/2) resonance.
numbers
multi-pion
and illus-
or the Yang sign convention,
the complex
pion
in the pion nucleon phase
When photon beams of energy and intensity
nificant
is not
of elastic
solution
gave the first
state (3/2,
to use the Fermi
in disentangling
and the
agree modulo pi below the threshold
between these two processes.
duction data has helped to resolve
shifts,
amplitude
as a guide to the possible
that low energy photoproduction
nucleon resonance
alone it has been
known as the Watson theorem,
the photoproduction
the close connection
surprising
amplitude
re-
method to examine
and resonances,
Their dominant
ent with the experiments
to produce
final state events became available,
as the photon itself.
mesons.
sufficient
the properties
especially
Such resonant
-l-
photopro-
of pion-pion
and
those with the same quanstates are called neutral
role in photoproduction
at the Cambridge
sig-
Electron
first
Accelerator
became appar(CEA) and
the Deutsches
periments
Electronen-Synchotron
revealed
px+~- while
that the neutral
rho meson dominated
the omega meson was the most significant
state pn+r -*O.
final states,
limited
(DESY) in the mid-1960’s.
These same resonances
respectively.
were present
The utility
by their use of bremsstrahlung
ton energy determination
and produce
the final state
effect seen in the final
in the five and six body
of these experiments,
however,
beams which provide
no -a priori
mostly
low energy events.
new type of photon beam was needed to extend these results
gies and to obtain the higher statistics
Therefore
the first
Stanford
Linear
Accelerator
duction
exposures
l-7
photoproduction
uid hydrogen.
chamber
the neutral
complicated
were limited
11
vector
annihilation
monochromatic
bubble chamber
interesting
photoproduction
only bremsstrahlung
experiments
of photopro-
radiation
the energy of the annihilation
filled
9,lO
with liq-
and streamer
on the photoproduction
energy events relative
experiments
photons increased
to the bremsstrahlung
much lower energy photons.
-2-
particles
which had
Furthermore,
First,
constrained
in the final state.
the yield of interesting
induced events,
but
The pre-
to produce high energy photons.
photons was known to *2%, allowing
of
of more
photon energy.
over previous
fits to be made to events with one or more neutral
Second, the monochromatic
8
beam.
in 4, 5, and 6 body final states,
of the incoming
advantages
as a technique
ener-
gamma rays to be used for
information
reactions
by lack of knowledge
a
at the
mesons p” , W, and 4, as well as some glimpses
sent work had two distinct
come from
performed
in the SLAC 40” bubble chamber
.
yielded
pho-
Clearly,
to higher
was in fact a series
using the SLAC positron
The previous
studies
experiment
Center (SIAC)
experiments
was
necessary.
bubble chamber
This beam produced high energy,
These ex-
high
most of which
the annihilation
energy allowed the calculation
intheunconstrained
(rather
fit) of a missing
allowed a clean separation
picture
production,
of resonance
One of the outstanding
the mechanism
chamber
of numerous
duction
of neutral
counter
12
rho, however,
tion,
explanation
in photoproduction
a relatively
mechanisms.
resonances
physics
resonances,
cross section
The shape of the
The omega cross
the rho cross
in the first
sec-
with energy in a way consis-
plus one pion exchange (OPE) production
For example,
of other
the associated
to decrease
decay width of the rho into a pion and a gamma.
which had been expected with cross
Other
sections
range were not observed.
The main problems
this experiment
in the
thought to proceed via OPE and was used to
like the A2 meson,
in the microbarn
to the track
some evidence was seen for production
It was therefore
the radiative
has been
skewed toward low dipion masses,
in 4 and higher body final states.
with energy.
a
that o” photopro-
of p-A+ ’ in the four body final states was observed
production
estimate
constant
for this was known.
of diffractive
In addition,
yielded
In addition
for ItI up to 0.5 GeV2.
on the other hand, was found to be falling
tent with a combination
in the
above, this topic has been the subject
was found to be strongly
and no fundamental
This then
particle
These studies all indicated
maintaining
s channel center of mass system
system.
which has subsequently
meson production.
mentioned
studies.
is diffractive,
for the neutral
that is necessary
photoproduction.
questions
vector
9-11
experiments
mass
of events with a single neutral
final state from multineutral
more complete
than the assumption
existing
was performed
section remain
photoproduction
in the physics
can be summarized
constant
experiments,
-3-
of photoproduction
as follows.
at higher energies
First,
when
does
than those observed
and is there continued
indication
for s-channel
helicity
conservation?
skewed shape of the neutral
from
Second, what is the reason for the
rho, how shouldp’
the raw data on the reaction
models
imply for the forward
dominance
coupling
yp--pn’?r-,
constant
describe
there higher
.12
annihilation
implications
of the neutral
by the Veneziano
OPE parts of the omega production
diction
model?
with at least one neutral
production
particle,
mechanisms?
to improved
15
Fifth,
correspond
posed by using bremsstrahlung
This experiment
questions,
unsolved.
in some detail
because of the serious
questions
in photoproduction
in final states
about their
was tied
limitations
im-
the new contributions
are summarized
in the conclusion,
great number of other experimental
briefly
-4-
in
skewed shape remain
of this experiment
in the abstract
where our results
observations
like the differences
and that observed
and the reason for its apparently
physics
produced
to many of these problems
basic theoretical
More specifically,
photoproduction
decay width of the omega
has been able to shed some light on most of the above
although certain
production
and
beams.
between the rho meson observed
hadronic
are
to the SU(3) pre-
and if so what can be learned
techniques,
Fourth,
do the diffractive
boson resonances
The solution
experimental
14
me-
rho in the dipion mass spec-
mechanism
Sixth, are there additional
meson
into vector
for VDM?
and that expected from the known radiative
meson?
of vector
when obtained by photoproduc-
and by electron-positron
mass recurrences
trum as predicted
does the vector
and if so, what is the value of the photon-vector
and what are the subsequent
sons13),
Third,
the photoproduction
(which appears to disagree
tion in heavy nuclei
be derived
and what do these various
p” cross sections?
model (VDM) accurately
mesons on hydrogen,
cross sections
and reviewed
are compared
and theoretical
to
to a
16-24
predictions.
The SLAC annihilation
trons from electrons
resulting
positrons
celerator
and finally
resulting
annihilation
determined
energy.
sulting
were then accelerated
allowed
A residual
to annihilate
by their production
bremsstrahlung
photons were collimated
5.25,
all three groups.
background
The experiment
photoproduction,
discussed
present,
but the re-
the monochro-
photon energies,
was performed
Institute
Since close collaboration
as a collaboration
of Science and Tel Aviv Uni-
and analyzed
by the Weizmann
was maintained
phases of the experiment,
permits
an analysis
giving important
during both the
all the data are presented
This not only enhances the statistical
accu-
of the energy dependence of resonance
clues to the production
mechanisms
as
above.
Since this beam was developed,
available
was still
positron
the 5.25 GeV film by the SLAC group and the ‘7.5 CeV film by
as if from a single experiment.
but further
The
and have an energy
at an angle chosen to,enhance
the Weizmann
data taking and analysis
racy,
target.
to this background.
and 7.5 CeV.
group,
The
in a liquid hydrogen
angle and the incident
The 4.3 CeV film was measured
Institute
posi-
2/3 of the ac-
were made at three mean annihilation
of groups from SLAC,
versity.
by creating
along the remaining
photons obey two body kinematics
uniquely
Exposures
beam was produced
at a point l/3 of the way along the accelerator.
matic photons relative
4.3,
radiation
for producing
high energy photon beams.
ploys laser photons which both receive
tain a high degree of polarization
energy electron
beam.
other new techniques
25
One such method em-
a large amount of energy and main-
when they are backscattered
This method gives a high degree of
-5-
have become
off a high
monochromaticity
and polarization,
tion rate of current
tectors
lasers.
Hence,
like the bubble chamber
more complete
but is limited
information.
this technique
is most suitable
which also have a slow period
for de-
but obtain
Such a beam has been developed at SLAC26 and
used in the 82 inch hydrogen bubble chamber.
work have been published
by the power and repeti-
27-32
Preliminary
and have provided
data from this
a great deal of stimulation
to our own work.
The number of Pictures
electron
energies,
beam, and the number of events measured
The experimental
details
cedures
are discussed
sections
and corrections
The subsequent chapters
tion,
at various
explaining
in Chapter
II.
for various
describe
The determination
backgrounds
were derived
data as well as various
-6-
and analysis
of resonance
and comparing
theoretical
pro-
of the channel cross
is discussed
the investigation
of the
are given in Table I.
of the beam, the bubble chamber,
how these results
other experimental
the parameters
models.
in Chapter
III.
photoproducour data with
TABLE
Parameters
Central
Central
(%)
energy (GeV)
production
Photons/frame,
Total pairs/frame
volume
of the three exposures.
4.3
photon energy (GeV)
Resolution
Positron
and statistics
I
angle (mrad)
in scanning
Total frames
Total events measured
-7-
7.5
F2.0
12.0
i2.0
8.5
10.0
12.0
11.9
9.4
-54
k > 0.9 kA
5.25
-70
7.15
-30
15.8
16.2
11.7
300K
252K
-940K
10178
9153
-24000
CHAPTER
EXPERIMENTAL
The Hydrogen
II. 1
The first
Cambridge
Electron
Synchotron”
AND PROCEDURES
Bubble Chamber
studies of multibody,
Accelerator’
(CEA) and the Deutsches
The bubble chamber
secondary
interactions
allows
on hadronic
and the decay of many strange particles.
tively
to separate
further
to classify
bubble chamber
shown in Fig.
ionization
hadronic
picture
II. 1.
containing
stricted
a hadronic
vertices
Therefore
of the
it is rela-
ones and
A
event from this experiment
along hadronic
protons
but very useful momentum
of all
to the number of hadrons produced.
The bubble density
to be used to separate
tracks,
events from electromagnetic
events according
at the
Electronen-
the observation
interactions,
simple
high energy photopro-
out in 1964-1966 using hydrogen bubble chambers
(DESY).
charged tracks,
APPARATUS
comprehensive
duction were carried
II
tracks
allows
is
the
from kaons and pions in certain
ranges,
according
re-
to the approximate
relation
I(p) = I(min)
where m is the particle
chamber
mass and p is its momentum.
views a 4a geometry,
therefore
no complicated
in order
acceptances
the bubble chamber
periments
bubble chamber
technique.
P.
and angular
is particularly
disadvangages
First,
distributions.
biases and
-8-
data
For all these
well suited to exploratory
ex-
is to be studied.
in studying
a photograph
1)
Because the bubble
to be folded into the experimental
in which a wide range of properties
There are several
,
there are no severe geometrical
to obtain cross sections
reasons,
(1 + m2/p2)
photoproduction
with the
must be taken on each beam
FIG. II. l--A
bubble chamber picture of a photoproduced three-prong
hadronic event,
which illustrates
the copious background of electromagnetic
events and
the subsequent difficulty
in isolating events with short proton tracks.
The
hadronic event originates just before the first of the three obvious lines
crossing the bubble chamber in about the center of the chamber.
The proton track is very short and highly ionized, whereas the pion tracks are
minimum ionizing like the electromagnetic
background and form a characteristic l’fishtail”
pattern which usually indicates a high energy, low momentum transfer event, a likely candidate for the reaction yp -•, pop.
-9-
pulse,
whether
extremely
or not it contains
difficult
to trigger
Meres ting photoproduced
netic processes
photons irradiate
dronic
reactions.
hydrogen.
hadronic
the purely
electromag-
hadrons when high energy
Since only a limited
number of positron-electron
and delta ray tracks
can be tolerated
it has proved necessary
This increases
before the ha-
to reduce the flux
in ten contains
both the number of pictures
them.
the difficulty
Second, and related
in observing
with three charged hadronic
momentum
(140 MeV/c
is easily overlooked
nant background
to this large electromagnetic
corresponds
by scanners
to a range of 1 cm in liquid
pairs.
which has been the subject of several
correct
pletely
From counter
the forward
understood.
experiments
experiments,
experience
12
protons
counter
occured
for
to forward
p”
studies covering
the most significant
scanning
there is some evidence on how to
losses in the bubble chamber
data, but it is still
not com-
The method adopted in this and all other bubble chamber
to date has been to make a linear
d a/dt in the forward
hydrogen),
In both the CEA and DESY experi-
Most of these events correspond
the region where bubble chambers
losses.
An event
one of which is a proton of very low
ments these scanning losses due to the ‘Tinvisible’
production,
is
who can confuse these events with the domi-
of electron-positron
It (p,p) I CO. 04 (Gf3v/c)2.
to ex-
background,
events with very short proton tracks.
tracks,
a
needed to ob-
tain a useful sample of events and the amount of scanning necessary
tract
on
occur with a much higher probability
to a level where less than one picture
event.
construction
involving
events become obscured,
in such exposures
of standard
Furthermore,
than photoproduction
Compton electron
event, because it has proved
a bubble chamber
such as pair production
(200 times higher)
pair,
a hadronic
direction.
- 10 -
exponential
extrapolation
of
The SLAC 40” hydrogen
bubble chamber
diameter
of 1 meter and a depth of 50 cm.
chamber
is shown in Fig.
surface
providing
from circular
feature
bright
II. 2.
pair production
the hydrogen
each camera
in allowing
windows
illuminated
from
lens.
A very important
thin alumi-
is 6.5” x 28” with total thicklengths,
which limits
to less than l/9 of those made in
a useful flux of photons into the chamber,
was approximately
The central
magnetic
spread out
field setting for
26 Kg and the field was uniform
volume to 4Y0. The repetition
over the
rate in this experiment
varied
1 to 1.5 pulses per second.
The chamber
triangle
cm
The light comes
The large area of the beam windows was in-
so that events would not be obscured.
this exposure
system has a reflective
to less than 0.01 radiation
of the chamber.
of this
is the pair of large,
The area of these windows
from the chamber
with a visible
diagram
in the chamber.
for photoproduction
ness OX&‘, corresponding
strumental
The piston expansion
flash lamps surrounding
num beam windows.
A schematic
field illumination
of this chamber
is cyclindrical
is viewed by three camera
about 70 cm on a side.
thick,
assuring
quartz
viewing
ber is illuminated
reflected
in space,
by flash tubes which surround
piston.
a retrodirective
lens is bent by a 45 degree mirror
- 11 -
in a
path to vary
BK 7) and the
of 1:17.
the lenses.
The reflected
the camera
resulting
window (Schottglass
The lenses gave a demagnification
back to the camera by Scotchlite,
the camera
from
which cause the optical
are the chamber
to a dish attached to the chamber
through
The distance
was 245.5 cm
The materials
distance
ports.
position.
of the chamber
17 degree stereo angle.
from the physical
The lenses are mounted on a steel plate 10
a fixed relative
lens to the mid-plane
lenses set on an equilateral
The cham-
The light is
material
glued
light after passing
and focussed
on the
-.
L
FIG. II. 2--Horizontal
cross-section
of the SLAC 40-inch
- 12 -
bubble chamber.
film
The film format
plane.
forated
three view,
on 70 mm per-
film.
In addition
chamber
to the problems
discussed
further
serious
but rather
of studying photoproduction
above, the CEA and DESY experiments
handicap since their bremsstrahlung
This is not a problem
of unknown momentum.
a problem
charged particles,
rators
was single strip,
in using bremsstrahlung
momentum
analyzing
and neutral
created
crossed
the bremsstrahlung
spectrum
that of the total reactions
studied,
Because of these problems,
bremsstrahlung
relatively
for bremsstrahfurthermore,
so
few are at high energy.
photoproduction
produced were visible,
or those containing
experiments
using
very narrow
so the 3-constraint
and prominent
and their statistics
interactions.
For events with one or more missing
with only a single neutral
were strongly
weighted
fits were
resonances
like the
toward low energy
neutrals,
Hence it was very difficult
ments to do detailed
studies of channels
observed.
events at the tip of the bremsstrahlung
Although
in
the hypothesis
in the final state can always be fit by adjusting
energy in the O-C fit.
very narrow
after it is
toward low energies,
omega meson,
incident
For
can give information
In particular,
weighted
sepa-
content.
beams were able to study in detail only those channels
which all the particles
possible,
and particle
on the photon energy is known;
is strongly
For
field and radio frequency
techniques
and massless.
lung beams only an upper limit
photons
unique to bubble chambers,
but a photon beam can not be analyzed
since it is both neutral
from a
to produce photon beams.
K mesons time of flight
on the beam momentum,
suffered
beams delivered
can produce beams of very pure momentum
neutrons
in a bubble
and well separated
in these experi-
in which any of the particles
resonances
- 13 -
the
like the omega
spectrum
are not
and
could be studied in more detail,
creation
of photon beams.
new approaches
One possible
at the time of the bremsstrahlung
ments. 21 Other approaches
beams themselves,
tic beam.
marized
involve
II. 2
The Annihilation
polarized
Radiation
In I960 D. M. Binnie
bremsstrahlung
to construct
decreases
33
observed
the characteristic
ly excludes
photons,
with great success
For the annihilation
annihilation
in flight,
positron
angle
it would be feasible
photon beam by impinging
a well defined
through a collimator
the inner angle of which would greatly
forward-peaked
of a positron
process.
bremsstrahlung
exceed
This effective(see Fig.
of energy E and mass m into two
one of which has energy K and laboratory
the incident
beam to produce high
with photon production
angle m/E of the bremsstrahlung
most of the strongly
is the
that since the cross section for
beam on a liquid hydrogen target and accepting
shell of photons,
method,
26
much more rapidly
a quasi-monochromatic
only a conical
II. 3).
experiments
is sum-
Beam
than the cross section for positron
positron
and even more versatile
photons.
experi-
the photon
which was used for this experiment,
A recent,
electron.
the ideal of a monochromn-
of a laser beam from the SLAC electron
monochromatic,
the scattered
total cross section
in such a way as to approach
in the next section.
needed for the
tagging the photons
novel methods of creating
which has been used in photoproduction
energy,
by observing
in doing several
One such approach,
backscattering
method involves
process
This has been used successfully
were clearly
angle 0 with respect
beam, one obtains the energy-angle
relationship
to
(for
E >>m)
K=
E
1 + E02/2m
- 14 -
(II. 2)
W
Thus defining
the production
energy constraint
angle t3 determines
to be applied
high energy component
in the fitting
the energy K and a1Iows an
of photoproduction
of such a beam is approximately
equivalent
to a charged beam of well defined energy and decidedly
bremsstrahlung
aids in the identification
in particular
the discrimination
This ability
to isolate
corresponding
neutral
at SLAC in 1967. 8 This additional
of reactions
with missing
neutral
between single and multi-neutral
relatively
reactions
of several
background
pure reaction
samples
hanced relative
boson resonances
particles,
events.
for the photoproducfrom the
has indeed allowed
which had been obscured
the
by multi-
experiments.
how the intensity
to the background
is orders
ous processes
with two or more neutrals
in previous
To understand
strahlung
in utility
more useful than the
4-+--o
++tion channels pn+n-x0 , A T T n, pa r T T x , and x’=‘x’x-n-n
observation
The
beams which were the only high energy photon beams avail-
able until this beam was implemented
constraint
events.
of annihilation
photons can be en-
when the total cross section for brems-
of magnitude
larger,
by which positrons
it is necessary
passing through matter
to look at the varican produce photons
at an angle theta:
e+i-e--2y
(4
e+ + em-
e+ + e- + y
(b)
e+i-Z-e++Z
(c)
(II. 3)
e++e--mmy
In addition
m>2
to the two photon annihilation
there are the multi-photon
annihilations
tions to the two photon process,
nucleus bremsstrahlung
section
is proportional
34
(c and d).
to Z
2
process
f-y
(d) .
(a) under consideration.
(b), which are the radiative
as well as positron-electron
Since the nuclear
, it is clear
- 16 -
and positron-
bremsstrahlung
that the radiator
correc-
cross
should be hydrogen.
Furthermore,
there are two types of bremsstrahlung
main background:
direct
and indirect.
wide angle bremsstrahlung
than the characteristic
a positron
scattering,
angle followed
angle.
elastically
are strongly
with angle approximately
.
nihilation
Indirect
process
from positron
or inelastically,
implies
is a two step process,
the characteristic
the photon beam
angle.
direction,
decreasing
to bremsstrahlung
For a typical
photons increases
signal to noise ratio,
SLAC positron
energy,
E = 10 GeV, x = 200
photon energy of 5 GeV and an angle of 10.1 mrad.
sections
for positron
annihilation
36
lung have been evaluated numerically,
conditions,
>O. 02 GeV, with the indirect
For photon energies
ly as E increases
little
further
energy
estimated
improvement.
However,
bremsstrah-
shown in Fig. II.4.
photons to annihilation
E(brems)
to be 100/oof the direct
photons
bremsstrah-
above 2.5 GeV the signal to noise improves
Hence to optimize
The condition
- 17 -
signal one
to as symmetric
energy for a reliable
beam at SLAC is about 12 GeV, to obtain photon energies
rapid-
level off with
the monochromatic
K = E/2 is referred
since the maximum
37
> 1 GeV and E(brems)
until E = 2K, beyond which point the curves
should run with K< E/2.
annihilation.
positron
and direct
with the results
II. 4 shows the ratio of bremsstrahlung
expected for two interesting
lung.
It
below.
The cross
Fig.
as x2,
x must be in the
The choice to run with photon energy just half of the incoming
is explained
Both of
(x = Ee/m), whereas the two body an35
only as dx/x.
Therefore the ratio of photons
decreases
an annihilation
larger
dx/x3
will be shown that for a reasonable
range 200-300.
is simply
of magnitude
through
peaked in the forward
as
annihilation
bremsstrahlung
within
which give the
bremsstrahlung
at angles one or more orders
by bremsstrahlung
these processes
Direct
effects
higher
positron
than 6 GeV
I
I
I
I
I
9
\
8.
Ey=2
I
I
I
IO BeV
BeV
I
2
I
4
I
6
I
8
I
IO
I
12
I
I4
I
I
I
I
I
I
I
I
10 BeV
%6-
W
i
24i-2
2
2
z2
Ey= I BeV
b
O-
I
2
I
4
I
I
6
E+
8
( BeV )
I
10
FIG. IL 4-- Noise to signal ratio for annihilation
positron energy.
- 18 -
I
12
I
14
I
492-6-L
beam as a function
of
it was necessary
CeV spectrum
to run at slightly
suffered
less than optimal
conditions.
The 7.5
from this as will be seen in the beam spectra
for the
three exposures.
The limits
on the resolution
to either angular or momentum
-dK
K
e
For symmetric
minimum
-dK
K
=- 1
2
il%
which give the highest energy obtainable
-dE
E
comes from:
uncertainty
the photon interaction,
scattering
(11.5)
.
is dominated
The contribution
in production
ce2>
lengths.
to be about 10
-4
in position
of
angle in the inciplus the multiple
before annihilation.
=
15 MeV
E
2
>
Since the divergence
radians,
in 0
The
in hydrogen behaves as
(
with t in radiation
have
of the H2 target where
of the positron
in the target material
scattering
uncer-
to the uncertainty
angle due to errors
in the position
and 3) uncertainty
of the positron
it
by the angular
The last is composed of the beam divergence
mean square multiple
timated
e
beam (0 = 0.01 rad. ), the beam will
2) uncertainty
the photon was created,
dent ef beam.
d0
=_-
beam can easily obtain a full width dE/E cl%,
for de = f 0. 1 mrad.
I)
for
reduce to
-dK
KE
and
For the 10 GeV positron
resolution
(II. 2),
E
out that the beam energy resolution
tainty de.
Differentiating
F
these equations
Since the SLAC positron
works
and
conditions,
e
uncertainties.
=-- K dE
E E
background,
of the photon beam energy K may be due
implying
- 19 -
t
z )
(11.6)
of the positron
a minimum
beam is es-
energy spread of at
least *l%,
it is clear that each independent
to this magnitude
if possible.
It has been shown
where the resolution
37
should be kept down
Thus t must be about 0. 02 radiation
that the intensity
is dominated
get is proportional
uncertainty
lengths.
of the photon beam in the region
by multiple
scattering
to the cube of the allowable
in the hydrogen
resolution
dK/K,
tar-
according
to
the expression
I
Y
-8
and symmetric
or about 1000 monochromatic
In order
to suppress
conditions
hadronic
in the beam direction.
tons while reducing
a factor
of three.
chamber
into account,
In addition,
one radiation
was
electromagnetic
bremsstrahlung
nearly
particles
emission
re-
all the low energy pho-
of high energy photons by approximately
the finite
the intensity
azimuthal
acceptance
by a similar
Fig. II. 5 shows the predicted
bubble chamber
positrons.
This beam hardener
This removed
the intensity
window decreases
incident
events,
field which swept the resulting
out of the beam line to reduce the secondary
radiated
10
= 9.6
photons below 20 MeV, which cause a significant
hydride was put in the beam.
placed in a magnetic
tn. 7)
this says that Ir/I+
photons for 10
scanning annoyance but yield no interesting
length of lithium
dK 3
K
.
(E - K)
For a net 1% resolution
x 10
I(>
K2
= 0. 024 I+ ;
factor.
of the bubble
Taking all these
high energy photon intensity
for a photon beam of 1% net energy resolution
per 10
in the
10
inci-
dent positrons.
The flux used in the experiment
,production
cross
was still
section of about 20 millibarns
fifteen photons to interact
gen.
However,
limit
on the tolerable
electromagnetically
the number of pairs produced
photon flux,
lower
causes approximately
in one meter
in each frame
since too many pairs
- 20 -
than this since the pair
of liquid
one in
hydro-
places an upper
can drastically
reduce
I
r I
I
I
!\ I
-7
I
-
Photon
Swathe
FL-
Chamber
Window
1
I
2
I
4
I
6
I
I
8
E+
10
(BeV)
I
12
I
14
I
16
492-e-A
10
FIG. II. 5-- Predicted photon kensity
in the bubble chamber per 10
Beam window
positrons of 1% energy resolution incident.
acceptance and attenuation in 1.0 radiation length of
hardener are included (see Ref. 37).
-bl-
J
the efficiency
determined
of scanning for hadronic
events.
by the constant monitoring
experimental
bubble chamber
meant that it was possible
but this did require
run.
The operating
of test strips
The high positron
opening the collimators
beam direction
ing the toroid
The positron
position
strahlung
entering
monitors
magnets,
by CO, Cl,
hardener.
the first
The beam arriving
with approximate
dimensions
Three exposures
symmetric
the maximum
ting.
with a
spot with a beam di-
target
15 cm
of 0.1 milliradians
long.
The
by checkby 35 m.
mass while the photon beam
and C2 (140 radiation
Charged particles
of which contained
lengths in total) before
were removed
the lithium
by three
hydride
at the bubble chamber was crescent
beam
shaped
6.4 cm. x 45 cm.
were made at conditions
discussed
as close as possible
above.
energy of 12 GeV necessitated
Table I shows the beam conditions
II. 7a, b, c show the energy spectrum
sures.
exposures)
than m/E which bounds the brems-
photon productiongeometry
positron
beam of
P36 and 2Pl which were separated
much larger
the bubble chamber.
sweeping
at a liquid hydrogen
was kept to a tolerance
at an angle
emission
A positron
of the various
beam was dumped into a shielding
was collimated
II. 6.
of <0.5Y’ is focussed to a 3 mm
of <O. 1 milliradians
positron
at SLAC
energy as defined below.
energy E (see Table I for the parameters
vergence
currents
during the
and using the event vertex posi-
The actual beam layout is shown in Fig.
resolution
by physicists
to get an adequate flux of photons into the chamber,
tion to define the annihilation
momentum
flux was finally
For the 7.5 GeV run
a slightly
asymmetric
and the size of each exposure.
of measured
The high energy peaks are obviously
- 22 -
present
pairs
to the
SetFigs.
in the three expo-
but they are significantly
BEAM POSITION
INDICATOR
DUMP MAGNET
\
STEERING \
CURVED
COLLIMATOR
Cl
/
II
SWEEP M2
I
40 ”
HBC
BEAM POSITION
8 HARDENER
0
I
IO
I
SCALE, meters
FIG. II. 6-- Layout of the positron
annihilation
beam in end station
B.
20
I
800
-
>
(5 600
-
14.250 PAtRS
4.3 GeV
012345678
400
>
LT 300
-7
0
25 200
w
2
100
0
012345678
0
I
2
3
4
5
Ey
6
7
(GeW
8
9
IO II
12
I89501
FIG. II. 7-- Measured electron pair spectra at the three annihilation
energies.
The larger degree of spreading apparent in the annihilation peak
of the 7.5 GeV data is because this exposure was made at less than
optimal conditions (see Section II. 2).
- 24 -
wider
than the resolutions
First,
claimed
there is the ultimate
produced
by the radiative
transfonrs
in Table I.
resolution
This is due to three factors.
of the annihilation
tail of multi-photon
the two photon annihilation
annihilation
When this and the resolution
due to the energy and angular
uncertainties
from
each individual
the production
with a net resolution
event still
processes,
spike at K into the cusp-like
tion peak shown in Fig. II. 8.
gether,
photon spectrum
discussed
which
annihila-
of the photon beam
above are folded to-
can be assigned a monochromatic
angle determined
by its vertex position
Because of this,
of about *2%.
energy
in the chamber
the collimators
were
opened to obtain an adequate flux of photons in the bubble chamber.
sulted in a superposition
These spectra
about 10%.
energies,
of monochromatic
therefore
about *2% from the calculated
high energy peaks in Fig.
of E(fit)
II. 9.
- E(calculated)
This removes
discrepancy
suring
multiple
the measured
the cross
photons known to
This is the second effect spreading
by plotting
as has been done for the data of Fig.
II. 7c in Fig.
and the true photon spectra
The correction
sections
A third
is due to meaplus normal
This tends to spread out the ideal cusp in both directions,
This leads us to use the energy spectrum
This is illustrated
pair
the
the spectrum
the effect of the finite width of the collimator.
to obtain the Ey spectrum,
no bremsstrahlung.
II. 10.
monochromatic
II. 7; it can be eliminated
toward lower energies.
of 3-C events
large spread of photon
with undetected energy losses due to bremsstrahlung
scattering.
but primarily
in Fig.
angle.
between these spectra
tracks
photons over an energy range of
show a fairly
but with the energy of individual
This re-
spectrum
for
tracks
suffer
almost
for the 3-C events by the inset graphs
these bremsstrahlung
is a very
in the experiment
since hadronic
important
and will
- 25 -
distortions
of
feature
for obtaining
be discussed
in detail
in
.-
-+k
d&
di;ldk
;_
I
I
I
I
i
I
I
y
I
e++-es-2 y
--3Y
I
e++p-e++p+y j.
e++g+e++e+y ; I
j / )
(e++e-+3 y
e'+p---e+tpty
A
K,
..
E
309-l-A
FIG. II. 8-- Theoretica!
spectrnm for a positron’-hydrogen
atom collision
at fixed angle.~ k:is the,photon.energy,
ka is the 2 photon
annihilation energy, and the upper limit to the bremmsstrahlung
background is the-incident, positron energy, E.
- 26 -
800
10304
PAIRS AT 7.5 GeV
150
r
100
50
0
-6.0
-4.0
2.0
Ey- Ecalc (GeV)
FIG. II. 9-- E(gamma) - E(calculated)
for 1-C pairs at 7.5 GeV. Inset graph
These
shows an enlargement of the annihilation peak region.
measurements
are not corrected for the distortions
introduced by
bremsstrahlung
and multiple scattering.
0
Section III. 2.
A summary
is given in Fig.
II. 10 in addition
note the resemblance
II. 8.
of the photon spectra
The small
to E(gamma)
of this spectrum
hitting
than expected,
the collimators
ducing indirect
II. 3
The bremsstrahlung
probably
the bubble chamber
coordinate
with the coordiiptites
rately
ef-p
was about
beam particles
scattering
maintained
gen target and the system
magnet were moved.
marks
beam direction
of the liquid
pro-
This,
its value in space,
of the incident
from x=0 was
and could be accu-
runs because of the fixed nature of the hydro-
of rails
small
of the target
on which the bubble chamber
housing and
for runs in between which the bubble chamber
shifts
in the vertical
(nearly
Therefore
systems.
or horizontal
alignment
changes in the values of the
60 meters
were obtained separately
the resulting
target in
together
defined the direction
away) as measured
in the
the y and z values of the
for each run by projecting
obtained in 1-C pair fits back to the x distance
A slightly
the photon
hydrogen
(See Fig. II. 11).
could produce substantial
coordinate
target coordinates
system
However,
was moved for servicing,
bubble chamber
the location
to determine
for different
y and z coordinates
were not only used to determine
(along the photon beam line of the target
very accurately
and averaging
background
II. 10
Beam Parameters
of the event vertex,
The x distance
of the fiducial
of Fig.
peak in Fig.
because of stray positron
of the Annihilation
but also to determine
surveyed
spectrum
Also
bremsstrahlung.8
The pair measurements
beam.
for 3-C events.
to the theoretical
and the large amount of inelastic
Determination
spectra,
- E(calc)
tail of events above the monochromatic
is due to e+-p bremsstrahlung.
50% higher
obtained at all three energies
the
of the target
distributions.
more complicated
calculation
- 29 -
is necessary
to be able to
(a) VIEW OF THE x-z
(HORIZONTAL)
PLANE
X
t
(b) VIEW OF x=0
(VERTICAL)
PLANE
PHO TON BEAM
\
\
\
\
\
\
\i
LIQUID H2 TARGET
(-5989,yt,zt)
r2 i(ye-yo)z+(ze-zoJ2
e+ BEAM
\
FIG. II. ll--
Bubble chamber coordinate
are the coordinates of event
coordinates of the projected
coordinates of the projected
plane. The liquid hydrogen
I’s,;
sys tern viewed in two planes.
(x, y , Z)
vertex, while (yo , zo) are the
photon direction and (ye ,ze) are the
positron beam direction in the x=0
target was located at (-5989, yt, zt).
- 30 -
determine
the angle of the incident
tron beam from the vertex
and z coordinates,
photon with respect
The technique
position.
called ye and ze , the positron
plane x=0, i.e., at the bubble chamber,
beam dump.
Then the incident
the event vertex
if it had not been deflected
photon direction
into the
can also be projected
and the photon direction
is to find the correct
This is done by adjusting
the presumed
so that the quantity
can be calculated
does not exceed 20 cm, whereas
from
peak, since if ye is incorrectly
plotted
(see Fig.
B(Y) = r(yO)/xt
= [r + (ye-m)
as a function
exposure
in order
of y.
to center
Due to the possibility
Ize-zol
is 40-60cm.
the width of the annihiliation
angles as a function
is plotted
photons
of y accord-
Such di-plots
E(fit)-E(calculated)
- 31 -
in different
y
have been made for each
its actual value.
of bremsstrahlung
(II. 8)
.
versus y on a two dimension-
of energy differences
to adjust ye toward
of ze have been adjusted
(See Fig. II. 11)
@-(ye + Yye)/2)/rl/xt
al plot the center of the distributions
shifts
a case of adjust-
II. 12):
This means that if E(fit)-E(calculated)
intervals
beam.
II. 10 is center-
set, events produced by annihilation
of the same energy will be assigned different
ing to the relation
lye-yol
z separation
minimize
The only subtle
in Fig.
This is primarily
the typical
at a known
ye and ze of the positron
y separation
value of ye will
angle.
for the positron
coordinates
as possible.
ing the value of ze, since the typical
the proper
direction
E(fit)-E(calculated)
ed at zero and is as narrow
However
which y
beam would have had in the
from the target to give the photon production
part of the process
beam,
is to ascertain
posi-
into the x=0 plane to give yo and zo, and hence the distance
between the ef direction
distance
to the original
Similarly
the values
at zero.
along the leptonic
tracks,
AY
(J=
r(yo)
xt
(ye-y ye)(yo- ye+2YYe )
WHERE r(yo) z r +
r
1895A15
FIG. II. 12-- Diagram illustrating
how an incorrect value (yye) of the projected
positron beam coordinate ye can influence the calculation of the
photon beam angle (and hence the annihilation energy), making the
calculated photon energy a function of the projected y vertex
position instead of just the distance from the projected positron
beam direction in the x= 0 plane.
- 32 -
care was taken to select high energy pairs with long, well measured
for the determinations
of target positions
sults from pair measurements
3-C fits so that the visible
direction
and project
been determined
and beam projections.
were then rechecked
particles
using events which gave
for the target positions
In this way consistent
and positron
the beam
values have
beam parameters.
Scanning Procedures
II.4
The purpose of the scan was two-fold:
to determine
strongly
the photon flux.
interacting
positive
charge,
work) leaving
of charge.
Infrequent
vertex
scattering,
ly with low energy;
zero net visible
(also called
one unit of
“prongs”
in this
odd with one net positive
momentum).
Strange particles
unit
are identified
2) electron-positron
can be confused with hadronic
pair is produced
or when a negative
background
is identified
resulting
as single negative
pairs,
Ton) before
can often be identified
1) Compton electrons,
charge and usually
the electromagnetic
state contains
proton (e. g. , ~-p +
The electromagnetic
characteristics:
resulting
occur when the outgoing proton has a range
on a neighboring
distance.
decay.
photon-electron
is normally
(i. e. , less than 80 MeV/c
a visible
the following
event is defined as a number of
Because the initial
exceptions
prong charge-exchanges
events and
such as pions , kaons , and protons,
collision.
the primary
characteristic
to find all hadronic
the number of charged tracks
of less than lmm
traveling
A hadronic
particles,
from a photon-proton
pairs
These re-
could be used to determine
back to the target.
tracks
by their
by one of
from elastic
tracks,
general-
produced off nuclei,
have
zero opening angle (the rare wide angle
two prong events);
off an electron,
of minus one.
- 33 -
and 3) triplets,
where
have total visible
charge
The hadronic
within
a fiducial
events were recorded
only if their
volume defined in view 2.
This fiducial
so that a sufficient
mine accurately
determined
within
length (a minimum
the momentum
whether
without
on the momentum
of fast forward
ionizing
could not be made, the event was recorded
on a track that an accurate
the same fiducial
that the statistical
in the flux determination
views,
In practice
views,
areas were recorded
as bad frames
light
Frames
tracks,
in a pre-scan
where a combination
made accurate
scanning impossible
Two independent
results
of poor film quality
were removed
Pairs
would be greater
This comparison
by computer
poor contrast
or blank
and were subsequently
In addition,
and abnormally
from
certain
high flux
the experiment.
and all discrepancies
scan.
efficiency
had been shown to be among the most reliable.
The
resolved
scan was conducted only by scanners
in a third
- 34 -
than
although in some
scans were made for events and pair counting.
of these were compared
so
which had missing
deleted in scanning for events or in flux determination.
regions
the electron-
on enough frames
this was every 200 frames,
abnormally
deter-
as unmeasurable.
the experiment
pairs were counted more frequently.
overlapping
interaction
volume defined for the events.
throughout
accuracy
to check
momentum
of photon flux was made by counting
were counted systematically
regions
a proton track.
If a secondary
mination
that of the events.
stopped
the end point of the track was measured
so close to the vertex
pairs within
tracks
indicating
occurred
positron
to deter-
Also the scanners
hadronic
of the short stopping protons.
The determination
volume was limited
tracks.
decay or annihilation,
For such stopping protons,
occurred
of 25 cm) could be measured
any of the strongly
the chamber
vertices
The combined
whose
scan
efficiency
can then be computed
from
N(nl + n2 - N)
E =
(II. 9)
“1 . n2
where n1 and n2 are the numbers
of events found in the first
respectively,
and N is the net number found in the two scans.
events found,
the scanning efficiency
bers are presented
The corrected
Furthermore,
has been applied to the flux,
error
It. 5
numbers
100%.
the
Therefore
although the possibility
no specific
of a small
correction
systematic
has been considered.
Measuring
machines
measured
and Kinematic
Reconstruction
reference
points for subsequent
spatial
However,
tion of factors,
the accuracy
including
due to turbulence
finite
by the measuring
gradients
in certain
The latter
problem
by using different
only one of which had been used to measure
constants.
The net result
unit
stage was about 1
distorting
and some non-linearities
optical
The smallest
apparent bubble displacements
chamber,
was aggravated
on
was much less due to a combina-
bubble size,
or temperature
marks
in each view to serve as
reconstruction.
obtainable
mea-
Six to ten points were
on each track in each of three views and four fiducial
on the film which could be digitized
micron.
on conventional
put on-line to an AS1 6020 computer.
the inside of the chamber window were measured
mining
scanned at
of pair scanning has been ex-
The events analyzed at SLAC were measured
suring
num-
have been used to determine
the efficiency
amined and found to be essentially
The number of
by event type, and the corrected
for 3 prong and 5 prong events in the film
SLAC in Table II. 1.
cross sections.
and second scan
regions
the original
optical
path in the
of the measuring
measuring
fiducials
machines,
for deter-
is that a more honest estimate
- 35 -
stage.
of
TABLE
II. 1
Number of events found in two independent scans of the film, scanning efficiencies
by event type, and corrected number of events on the film for those portions of the 5.25 and 7.5 GeV data scanned at SLAC and used for
The second digit of the event type indicates the number of charged tracks seen (3 and
cross section calculations.
5 prong events), while the last digit gives ionization in formation:
0 for all tracks minimum ionizing,
l-9 otherwise.
All efficiencies
except for type 130 are consistently
above 99%. The corrected numbers of this table have
been compared to the numbers actually measured and on the SLJMX tape to determine the scan-to-measure
corrections of Table RI. 5. Also note that those scanning efficiencies
only correct for random scanning losses and
not the systematic
losses of low momentum transfer events with short range protons,
5.25 Gev Data
Event type
130
Rolls 218-282
( 131-9 1 150 1 151-9
Events seen on film
I------
I
130
Rolls
131-9
‘732-830
150
930
3352
222
151-9
270
Scanning Efficiency
0.975
0.993
0.994
0.998
Events on film
953.8
3375.6
223.2
270.5
7.5 GeV Data
I
T
Rolls 3’71-578
Rolls
1240-1531
I
Rolls
1685-1762
151-9
130
131-9
150
399
1534
1336
114
Scanning Efficiency
0.999
0.988
0.993
0.998
Events on film
399.4
1553
1345.4
114.2
Event type
Events seen on film
the accuracy
of measurements
20 microns,
corresponding
to 150-300 microns
as the one by Levy and Wolf
suring
accuracies
microns
in the film plane would be in the range of IO-
38
discussed
below have typically
in space in the range of 50 microns
Studies such
obtained mea-
in the x-y plane and 250
in the z direction.
The geometrical
the programs
reconstruction
and hypothesis
TVPG and SQUAW. 3g The particle
three and five prong events are listed
attempted
incident
for each possible
in Table II. 2.
final state,
The former
is designated
are attempted
to final states with no missing
fits are attempted
particles.
In addition,
ent assignment
Therefore,
mass calculation
of masses to tracks,
magnitudes
matic chi-square
The 3 and 0 constraint
of these quantities
surement
than 30.
were then compared
mine which fits were compatible
for incorrect
event types,
measurements.
fits
and both 0 and
was made for each differannihilation
fits listed
give some feeling
fits.
The
for the percentage
photons.
The successful
constrained
fits with kine-
hypotheses
for each mea-
to the events on film by physicists
with ionization.
overlooked
photon
in Table II. 2
4 and 1 constraint
of fits was done by rejecting
greater
particles
using the calculated
of events produced by the monochromatic
The selection
A for annihilation
both 3 and 4 constraint
neutral
exclude those that also made the corresponding
relative
according
to final states with one (or more) neutral
a missing
energy and heam direction.
placed on the
energy calculated
by the mnemonic
B for bremsstrahlung.
were done by
Two types of fits were
one with no constraint
and the latter
1 constraint
fittings
states fitted by SQUAW for
gamma energy and one with the incident
to Eq. lI.2.
quality
in the chamber.
Also the physicists
strange particle
All events whose original
- 37 -
to deter-
decays,
checked
and poor
event type was incorrect
TABLE
Reaction
Reaction
hypotheses
n. 2
tested for 3 prong events.
No. fits at:
Notation
Source
4.3 GeV
(1)
+ YP-+P” ?I
(2)
5.25 GeV
7.5 GeV
Annih.
Brems.
P+-A
P+-B
823
3917
519
4020
810
11868
)/p -+,7r+71-7p
Annih.
Brems.
p+-OA
p+-OB
832
1571
943
2058
1689
5608
(3) yp --+nn+n+n-
Annih.
Brems.
n++-A
n++-B
479
1313
339
1384
592
3809
(4)
Annih.
p-+-MM
2403
3001
7397
++-MM
1792
1723
4401
yp --t ~+a-MM
(5) ‘yp-.
T+r+r-MM
Annih.
ti
or which were badly measured
was continued by physicists
of events either poorly
were sent for remeasurement.
This check
at each stage of remeasurement
measured
or unmeasurable
until the number
was reduced to a very
small percentage.
The calculated
photon mass for all 3-C fits to events in the 5.25 and
7.5 GeV monochromatic
peak region is given in Fig.
distribution
is due to the errors
distribution
depends on the knowledge
field.
of measurement,
In both aspects our measuring
production
40
experiments,
especially
The width of the
while the centering
of the central
quality
II, 13.
value for the magnetic
is comparable
considering
of the
to previous
photo-
energies
of these
the higher
exposures.
The chi-square
Fig.
II. 14.
ments,
distribution
is shown for these same 3-C events in
The usual phenomenon
namely that the chi-square
41
encountered
distribution
in bubble chamber
is loo wide,
is evident here.
There are about 7-14s too many events in the high chi-square
theoretical
factor
shape is off by a scale factor
can be fit in either
level distribution.
be generalized
the chi-square
The chi-square
in the remaining
distribution
distribution
in which case Q! = 1 corresponds
experimenters
generally
1-2, which means that the errors
factor
tail and the
events.
This scale
or the confidence
for 3 degrees of freedom
can
to
PjY2)K($)1’2.
chamber
itself
experi-
(II. 10)
exp(.$)
to the theoretical
distribution.
find that the scale factor
Bubble
2
CY is in the range
in TVGP output are underestimated
by a
of o.
The exact causes of these deviations
- 39 -
from the theoretical
distribution
120
“>
100
’
:
9
80
60
P
z
40
20
I
nr I
F
I-
I
PI
I I
100
a
z
0
518 EVENTS
5.25 GeV
I
120
“>
I
I
641 EVENTS
7.50
GeV
80
.
q
60
u-l
2
2
40
20
0
0
MF (GeV*>
0.2
189582
FIG. II. 13-- Gamma mass squared calculated for 3-C events at the
annihilation energies from the geometry values for the
visible tracks.
-40
-
120
I
518 3-C EVENTS
5.25 GeV
80
40
2
c!3
0
0
2; 160
641 3-C EVENTS
z
z 120
80
40
0
0
2
4
6
IO
8
X2
FIG. II. 14-- Chi-squared
3 -C events.
I4
16 I8
119,116
distributions
-4-l
I2
-
at 5.25 and 7.5 GeV for
Poorly
are elusive.
understood
tortion
corrections
and liquid
effects
in Coulomb scattering
that the chi-square
strongly
viation
and the generally
corrections
revealed
may well be responsible.
of the 5.25 GeV data deviates
diffuse
(see Chapter V), the optical
film was processed.
ence in chamber
was the initial
characteristics
understood
Another
liquid
however,
improved
greatly
possible
turbulence
difference
at SLAC,
and dis-
of these data
which re-
and the overall
by the time that the 7.5 GeV
systematic
difference
between the two runs.
is the differ-
The 5.25 GeV film
and the particular
stability
of the chamber were perhaps not as well
as they were after many months of operating
both sets of data have greatly
parameters
constants
is that the 5.25 GeV film was
film measured
and idiosyncracies
for scaling
mass plots
reprocessing
One systematic
output from a new bubble chamber
of their differences,
tributions
A complete
improvement.
of the measurements
Because of this de-
redone for the 5.25 GeV data to see if
had been made originally.
batch of photoproduction
We note
much more
nature of some of the invariant
mains between the two exposures,
the first
dis-
corrections
were completely
no significant
constants,
as well as real non-Gaussian
from the expected shape than the 7.5 GeV data.
some error
quality
in the optical
turbulence,
distribution
studied in the 1-C channels
tortion
uncertainties
o well within
experience.
improved
In spite
chi-square
dis-
the usual range of l-2.
We
2
find LY2 = 1.4 for the 5.25 GeV data and CY = 1.2 for the 7.5 GeV data.
Since these numbers
a quite reasonable
are reasonably
chi-squared
tortion
of the errors
rather
the conspiracy
close to 1 and since this scaling produces
distribution,
one concludes
is not due to a small
of all the poorly
set of poorly
understood
-42
-
that the basic dis-
measured
features
rolls,
mentioned
but
above.
As noted above, there are many sources
tortions
in a bubble chamber
and its geometrical
among them turbulence
in the chamber
determination
parameters
of optical
the measurement
photograph
and geometrical
charged particles
deviations
in the chamber
to
field off.
measuring
machines
and a search
lines expected.
in
It is possible
with the magnetic
and
made for
Any such deviations
effect of one or more of the potential
sources
for dis-
listed above.
A. Levy and G. Wolf 38 have performed
bubble chamber
measuring
analysis
machines,
the TVGP optical
photographed
consisting
such a study for the SLAC
of the 40” chamber,
and the TVGP geometrical
determined
fast muons in the chamber
of many tracks
distortions
system,
constants
tions due to multiple
tions.
process,
and errors
process.
programs,
dis-
or incomplete
constants,
by conventional
from the straight
would be the combined
an incorrect
or distortion
by the usual reconstruction
systematic
tortion
liquid,
systematic
reconstruction
reconstruction
Their paths may then be measured
reconstructed
for possible
scattering
reconstruction
by fiducial
The upper limits
plane (y direction)
of the directions
for such distortions
and 250 microns
From a fit to the curvature
normal
a maximum
42
field off.
by adding together
in the same region of the chamber.
were found in either
program
measurements.
with the magnetic
were eliminated
the NRI
with
They
Distor-
the effect
In this way no systematic
normal
to the beam direc-
were 50 microns
in the visual
to the visual plane (z direction).
detectable
1600 (+2400, -600) GeV/c was found by assuming
momentum
a magnetic
of P(MDM)
=
field of 26 kG
and 100 cm. of track length.
In many instances
we have checked our programs
and studied the ef-
fect of our cuts on the data using the track and event simulation
-43
-
program
PHONY. 43 This program
produces
fake events,
then digitizes
a fixed num-
ber of points along each charged track with a Gaussian distributed
finally
projects
PHONY seemed to imitate
exact relationship
nature quite well,
between PHONY setting errors
was never fully understood.
It was necessary
in PHONY than that used in TVGP in order
ties.
chi-squared
However,
and missing
the PHONY missing
so we are confident
our losses due to cuts.
-44
-
setting error
the physical
FRMS
mass squared proper-
these errors
routines
should be
worked
mass and invariant
seem to be a very good representation
obtained experimentally.
studying
and TVGP setting errors
to reproduce
and the Coulomb scattering
In all cases,
butions obtained
distributions,
except that the
to use a different
at least for the lower energies
Coulomb dominated
sistently.
and
these into the three camera planes as if they were a real
measurement.
distributions,
error,
very conmass distri-
of their counterparts
that they are a valid way of
CHAPTER
DETERMINATION
OF THE CROSS SECTIONS
General Method
HI. 1
Since the bubble chamber
magnetic
terms
rately.
III
pairs,
By instructing
volume,
energy interval
(El,
u (events,
The quantity
both hadronic
the cross section for the hadronic
of the pair-production
same fiducial
observes
cross section,
the scanners
it follows
which is known extremely
to record
events and pairs
that the cross section
Er)
Number of events (E ,AE
YY
= Number of pairs (Ey,AEy)
N(pair)/u(pair)
the beam is not purely
monochromatic
to the same energy interval,
should be considered
(El,
equivalent
in order
considered,
for the expo-
it can be com-
First,
this equation.
should correspond
is large,
to equal
the cross section
at the median energy rather
than the mean,
should be averaged over the interval.
or multiple
the measurement
scattering
microbarn
-45
-
Third,
of electrons
of the true pair spectrum,
to obtain the photon spectrum.
accurate
if
(and our beam with its bremsstrahlung
such as the bremsstrahlung
which distort
Er).
E2), or at least be normalized
as calculated
and energy dependent quantities
are carefully
the
cross sections.
Second, if the energy interval
must be corrected
in exactly
o@air,
was not), the pairs and the events considered
and positrons,
accu-
for events in the
and once it has been determined
Several points should be noted regarding
energy intervals.
in
)
is called the microbarn
pared to any set of events to determine
any effects
events can be evaluated
E2) may be deduced from the formula
sure in that energy interval
background
events and electro-
equivalents
If all these effects
can be determined.
The methods to be described
here were applied to the best film of the
5.25 C&V data and that part of the 7.5 GeV film analyzed at SLAC.
The main
problem
this was
was to determine
done, these cross
the cross section for “/p----- pa+n-;
sections
were used to determine
exposure which could be extracted
Similar
procedures
The cross sections
deduced agreed well within
The 3-C cross
vious experiments.
the flux for the entire
using the numbers
were used by the Weizmann
sections
after
of 3-C events found.
group for their 4.3 CeV data.
errors
calculated
with the results
of pre-
in this chapter
are
from the SLAC data only.
Several earlier
the cross
experiments
on photoproduction
section for pair production
about 3-590.
40
However,
uations of theoretical
are accurate
in 1970 T. M. Knasel
formulae
to better
on hydrogen
due to Jost,
46
published
Luttinger,
sections
of Knasel which have been used for this work are listed
III. 2
in Fig.
counting all pairs
of curvature
as events,
factor
was ascertained
in order
with energy greater
eight frames
average of about 50 events.
and all discrepancies
by counting
that the statistical
approximately
accuracy
in the cross section computations.
of the two tracks
on approximately
in Table
for Cross Sections
The number of e+e- pairs
flux not be a limiting
of 1%. The cross
III. 1.
Flux Determination
twice as many pairs
which
have been
by recent experiments
to an accuracy
eval-
45
and Slotnick
These results
of
to only
numerical
verified
III. 1 and plotted
at DESY
that were reliable
44
than 0.5% above 20 MeV.
used calculations
This involved
than 100 MeV (by requiring
to sum to more than I4 cm ).
per roll,
yielding
of the
the radii
This was done
about 100 pairs
versus
Two independent pair scans were performed,
were resolved
in a third scan by one of the most
-46
-
an
TABLE
Cross sections
III.1
for pair production
to Knasel (Ref. 44), as a function
on hydrogen,
according
of photon energy,
EyS
EyWW
u (mb)
Ey l&V)
u (mb)
0.10
11.66
1.0
18.29
0.15
13.15
1.25
18.65
0.175
13.69
1.5
18.91
0.20
14.15
1.75
19.11
0.30
15.45
2.0
19.26
0.40
16.28
3.0
19.65
0.50
16.85
4.0
19.87
0.60
17.28
5.0
20.02
0.70
17.62
8.0
20.25
0.80
17.88
10.0
20.33
0. so
18.10
-47-
20
E
0
“a
2
E
-
II?
19
b’- I9
17
15
I
I
I
0.2
I8
I
I
0.4
I
I
0.6
I
I
I
/
0.8
I
13
1.0
I
5
Ey (GeV)
FIG. III. l--
Pair production
cross
-48
-
sections
according
to Knasel
(Ref. 44).
reliable
scanners.
set of film,
pairs
This procedure,
resulted
present.
in getting within
Since errors
errors
1% of perfect
could introduce
ones, it was decided to neglect
statistical
when checked by physicists
false pairs
these corrections
on the events.
The results
poor film quality
as well as miss real
as being much less than the
in Table IfI. 2.
pair scans were conducted uniformly
ment with the exception
in the number of
of the pair scanning
tions of the work done at SLAC are presented
from this table,
accuracy
on a sample
for the por-
As can be seen
throughout
the experi-
of one set of the 5.25 CeV data, which because of
and excess flux was not used for cross
section
measure-
ments.
In order
to know the energy distribution
of photons in the annihiliation
beam, about 50% of the scanned pairs were measured
These spectra
spectrum.
posures.
error
have been presented
culate the cross
section for reactions
the total pairs produced
complicated
tron pairs actually
belonging
events.
near the annihilation
to annihilation
These effects
tracks.
the strongly
bremsstrahlung
depopulate
interacting
distortions
since many elec-
and bremsstrahlung
energies
on the
enhance the regions
just above and
can only reduce the measured
in either direction).
are all much heavier
are negligible
-4s
must be known.
peaks of the mea-
can cause errors
particles
of
the annihilation
bremsstrahlung
scattering
peaks,
to cal-
the fraction
photons yield measured
scattering
and correspondingly
below the peaks (whereas
multiple
For a given exposure,
in some energy interval
the peak region due to multiple
sured pair spectra
energy,
II. 7 for the three ex-
by photons in that energy interval
This is especially
leptonic
in Fig,
the pair
In each case the sample is large enough to reduce the statistical
well below that due to hadronic
outside
to determine
on hadronic
-
pair
Because
than the electrons,
tracks,
making the
the
TABLE
Statistics
Pair Scanning and Pair
III. 2
Frames
for Rolls Scanned at SI,AC
This is the raw data as tabulated by the program INDEX which was used to record and compare the results
of scanning.
Note that rolls 600-730 were the best 52 of 130 rolls which suffered from high flux and poor
development.
Since the criteria
for acceptable film had been considerably
relaxed, no pairs were scanned nor
were they used for cross section determinations.
The flux for rolls 1063-66 has been estimated using the pair
flux from rolls 1083-1146.
5.25 GeV Data
Bad
Good
Frames
Frames
#Rolls
Total
Frames
59282
70369
11015
48267
600-730
49
52
4801
65568
1654
--
732-830
- 94
132226
13803
118423
1128
Total
195
261877
29619
232258
2782
#Rolls
Total
Frames
7.5 Gev
Bad
Frames
117
169781
1063-1066
4
1083-1146
Rolls
218-282
Pair
Frames
Pair
Frames
5664
164117
5667
650
64
93833
1240-1531
262
1685-1762
51
, Total
498
18762
Z Flux
586086
)ata
Good
Frames
Rolls
381-578
#Pairs
#Pairs
I: Flux
10394
2072337
5017
824
--
17644
76189
670
9317
1054731
372291
5966
366325
1906
21001
4021964
74015
865
73150
378
4121
794868
715587
30789
684798
3778
44833
8013100
--
(69200)
3-C event spectrum
shape much closer
iterative
procedure
was used:
timated
3-C cross
then corrections
bremsstrahlung
obtained from
and multiple
PHONY generated pairs
scattering
weighted
an
by the es-
and finally
pair spectra
pair spectrum.
spectrum
the corrections
of Fig.
were applied for
to produce a distorted
the measured
between the distorted
trum were obtained,
measured
the 3-C event spectrum
Therefore
section gave the shape of the assumed photon spectrum,
which should approximate
the differences
to that of the photons.
spectrum
In each energy bin
and the assumed photon specfound were applied to the
II. 7 to see how many pairs
actually
belong
in each energy interval.
The program
tiple scattering
PHONY (see Section II. 5) was used to simulate
and bremsstrahlung
on leptonic
Fig. III. 2 shows the outcomes
corrections.
5.25 and 7.5 GeV after simulation
programs
above.
by PHONY and reconstruction
give energies
If in fact these two curves
in the cumulative
ratio
tortion,
pairs
within
Em/Ep.
(Fig.
form,
each energy bin of the measured
the bin limits,
but whose energies
been organized
into an iterative
III. 3).
E/E (produc-
These data are very use-
namely the probability
that a pair
Because of this dis-
pair spectrum
contains : (a) those
from photons outside
because of measurement
matrix
-5l-
of the
in Fig. III.4.
in that bin whose measured
and (b) those pairs
fall within
by the same
energy less than Em as a function
These data are presented
due to photons with energies
at
the actual measurements.
are plotted on a scale versus
of energy Ep will yield a measured
generated
less than their exact energy and l/3 go
tion) they are seen to be very similar
fully presented
to obtain the necessary
of 3000 fake pairs
(TVGP and SQUAW) used to process
About 2/3 of the pairs
tracks
the mul-
calculation
errors.
which,
energy lies
the bin limits
This has
given the
1200
2731 PHONY PAIRS
MADE AT 5.25 GeV
1000
800
600
400
200
0
800
I
I
I
I
I
I
I
I
5.0
6.0
7.0
8.0
2754 PHONY PAIRS
600
400
200
0
0
1.0 2.0
3.0
4.0
E,(I-C)
FIG. III. 2--
GeV
Spectra of PHONY generated pairs
- 52 -
9.0
at 5.25 and 7.5 GeV.
r
I
I
I
I
I
I
I
I
I
I
I
1.2
1.4
1.6
2731 PHONY PAIRS
1000
800
600
400
200
0
1000
I
I
I
I
I
I
2754 PHONY PAIRS
MADE AT 7.5 GeV
800
600
400
200
0
0
I-
0.2
1
0.4
0.6
0.8
1.0
Ev (I-Cl/En
FIG. III. 3--
Spectra of PHONY generated pairs
- 53 -
1.8
189586
on a percentage
scale.
I
1.0
0.8
I
I
I
I
I
I
2731 PHONY PAIRS
MADE AT 5.25 GeV
0.6
0.4
0.2
0
1.0
I
I
I
I
I
I
I
I
1
I
I
I
2754 PHONY PAIRS
MADE AT 7.5 GeV
0.8
0.6
0.4
0.2
I
0
0
0.8
0.4
I.2
E, (I-C)/E,
I
FIG. III.4--
I
I
I
I
1.6
”
Cumulative probability
that a pair of energy E,-, will reconstruct
to a pair with 1-C energy <Ey , deduced from the PHONY spectra
of the previous figure for EO =5.25 and ‘7.5 GeV.
-54-
cumulative
effect of bremsstrahlung
on the pair measurements,
an original
photon spectrum
energies.
From this and the original
into the resulting
function
of energy and interval
various
energy intervals
spectrum
spectrum
can be found.
of measured
a correction
of the measured pair spectra
factors
were evaluated
7.5 GeV data, in each instance
event spectrum
differed
This was necessary
which is needed to
for the 5.25 GeV data and for those rolls
tions of the typical
flux error
of 7.5 GeV data that were
independent
For maximum
calculations
The important
sources
will be presented
calculations
of error
applied
Table HI. 3 shows these
energy ranges and found to be consistent
These independent calculations
and the 3-C
since the appropriate
section calculations.
in the high energy cross sections,
done over different
for the 5.25 and
and the correction
under consideration.
analyzed by SLAG and used for cross
marized
to the
gives the actua1 num-
separately
for the two exposures
depended upon the interval
errors.
as a
applied
using both the PHONY results
for that energy.
energy intervals
accuracy
pair
the cross sections.
The correction
results
factor
This correction
ber of pairs produced by photons in that energy interval,
compute
transforms
were
well within
the
below as illustra-
(see Table IH.4).
in the flux determination
by looking at the equation which defines the microbarn
can be sumequivalent
for a given energy interval:
NP(E1 > E2).
Microbarn
equivalent
BC . NSCT - NGF
(El, E2) =
CT* NPT * NPF
where NP(El,E2)
is the number of pairs
sured pair spectrum,
in the interval
NPT the total number of measured
pair cross section in microbarns
for the interval,
- 55 -
(El, E2) of the meapairs,
u the mean
BC the correction
for
TABLE
III. 3a
5.25 GeV Flux Determination
True Flux
2 18-282,
732-830
#Pairs
732-830
Correction
Factor
.4-o. 5
715
1.00
1.30
.5-O. 6
575
1.01
1434
Ey t&V)
.6-l.
0
1. o-1.2
a(Pair)
in mb.
lo5
Events/$
218-282
732-830
16.8
7.75
1. 06
17.1
6.18
1.01
2.64
17.8
14.82
467
1.02
0.87
18 5
4.69
1.2-l.
5
515
1.02
0.96
18.8
5.09
1.5-2.
0
614
1.01
1.13
19.1
5.91
2.0-2.5
438
1.00
0.80
19.35
4.12
2.5-3.0
320
0.95
0.55
19.6
2.81
3. o-3.5
281
0.94
0.48
19.75
2.44
3.5-4.0
237
0.88
0.38
19.85
1.91
4. o-1.5
285
0.68
0.35
19.9
1.77
2485
1.11
5.02
20.0
25.11
6. O-7.0
85
0.83
0.13
20.2
0.636
7.0-8.0
56
0.85
0.09
20.3
0.427
8.0-10.0
64
1.12
0.13
20.4
0.640
--
--
--
1.703
4.5-6.
0
6. O-10. 0
--
Total 1-C measured
Total flwr,
rolls
pairs on rolls
218-282,
732-830,
732-830,
14096.
2.567X 106.
- 56 -
TABLE III. 3b
7.5 GeV Flux Determination
EyW’)
0.4-O. 5
0.5-O. 6
0.6-l. 0
1.0-1.2
1.2-l. 5
l-5-2.0
2.0-2.5
2.5-3.0
3. o-3.5
3.54.0
4.04.5
4.5-5.0
5. o-5.5
5.5-G. 0
6.0-6.5
6.5-7.0
7.0-a. 0
8.0-10.0
0.2-12.0
1-C
measured
pairs
btal pair
flux from
scanners
canned/
measured
--zd
578
273
212
555
167
163
218
164
108
88
65
63
47
61
40
52
100
386
87
19
12401530
532
413
984
351
358
444
230
231
176
131
148
107
88
104
126
215
844
138
37
16851762
112
78
195
59
65
78
55
50
39
27
26
25
20
20'
35
40
133
32
19
b&l
4957
9902
1976
2072337
402 1964
794868
418.06
406. II
402.26
Total
917
703
1734
577
586
740
499
389
303
223
237
179
169
164
213
355
1363
257
75
Correction
J?actm
1.0
1.0
1.01
1.01
1.01
1.01
1.01
1.01
0.99
0.97
0.95
0.93
0.91
0.83
0.55
0.68
1.314
0.62
1.00
apair)
in mb.
16.8
17. 1
17. 8
18.5
18.8
19.1
19.35
19.6
19.75
19.85
19.9
20.0
20.05
20.1
20.15
20.2
20.25
20.3
20.4
381578
6.79
5.18
13.17
3.81
3.66
4.82
3.58
2.33.
1.84
1.33
1.26
0.92
1.16
0.69
0.59
1.41
10.45
1.11
0.39
Events/fib
12401530
12.86
9.81
22.68
7.78
7.81
9.54
5.94
4.83
3.58
2.60
2.87
2.03
1.63
1.75
1.40
2.94
22.19
1.70
0.73
16851762
2.68
1.83
4.45
1.30
1.40
1.66
1.14
1.04
0.79
0.53
0.50
0.47
0.37
0.33
0.39
0.54
3.46
0.39
0.37
TOtIll
22.33
16.84
40.30
12.89
12.87
16.02
10.68
8.20
6.21
4.28
4.63
3.57
3.16
2.77
2.38
4.89
36.1
3.2
1.5
TABLE
III.4
5 GeV 3-C Cross Section Calculation
Experimental
(Ey=4. O-6.0 GeV)
Data
Values
2770
Pairs with Ey=4. O-6.0 GeV (1-C Fits)
6% correction
for bremsstrahlung
losses
Pairs created
by photons with Ey=4. O-6.0 GeV
Total number of 1-C fits to measured
Fraction
pairs
2.0%
14096
1.0%
2940 =o* 209
14096
2.2%
218-282)
0. 586X106
Scanned pair flux (rolls
732-830)
1. 981x106
Total flux in 218-282 + 732-830
Equivalent
O-6.0 GeV
0.209 * =5. 35x105
F =20 mb
(218-282 + 732-830)
3-C events (218-282 + 732-830),
8% scan to measure correction
Ey’4.
26.8 events/pb
O-6.0 GeV
(Table III. 5)
3-C events on film with Ey=4. O-6.0 CeV
%isible
(3-C,
3 prong,
Ey=4. O-6.0 GeV)= iF8
13% Forward
cbtal
1.0%
2. 567x106 = 4~
Pair Cross Section Ey=4. O-6.0 GeV
Microbarn
0.
2940
Scanned pair flux (rolls
with Er=4.
1.9%
170
of all pairs with Ey=4. O-6.0 GeV
Number of pairs
Errors
loss correction
(yp ----t pa+?r+, Ey=4. O-6.0 GeV)
- 58 -
=
2.5%
1%
2.7%
418
4.9%
- 34
452
1.4%
5.1%
16.9 pb
5.7%
2.2 pb
1.5%
19.1~1.15
pb
6.0%
bremsstrahlung
distortions
to the actual pair spectrum
NSCT the total number of pairs
good frames
in the experiment
but all the other factors
the microbarn
contribute
equivalent.
and possibly
cross section
definition
a small
either systematic
systematic
contributes
or statistical
errors
and do not
they are a source of statisti-
error
for pair counting.
The number NP(El,E2)
the largest
to
statistical
The pair
is the smallest
error;
also it is by
interval-dependent.
The most difficult
strahlung
correction
error
BC.
this error
the corrected
number.
in NP.
(e. g. intervals
statistical
sideration,
with the bremsis ultimately
For each bin of the spectrum,
smaller
are adjusted
NP(E1, E2) to obtain
is then ( IBC-1 I /NP(El,
than (NP(E1, E2))- li2,
E2))
in the microbarn
correction
are small
from the peak by measuring
equivalent
in the number of measured pairs
the statistical
However,
error
in the correction
it is incorporated
- 59 -
m
the percen-
in the bremsstrahlung
so that the corrections
most of those displaced
Since the error
I BC-1 I < < 1.
error
pairs
which
which are wide enough around the center of the annihilation
encompass
error
from the observed
This shows that the error
is least when the intervals
errors).
part of this error
at one energy.
The percentage
I BC-11 < 1, this is clearly
peak to
is that associated
is taken to be the square root of the net number of pairs
must be added to or subtracted
tage error
to estimate
The statistical
based on 3000 Monte Carlo pairs
For
are exact and hence have no error,
being considered;
is known to <O. 5%.
number and therefore
on which pairs
Both NPT and NSCT are large numbers
depend on the energy interval
above),
NGF the total number of
and NPF the number of frames
These last two numbers
were counted.
cal error
counted in scanning,
(as discussed
is dominated
by the
in the interval
under con-
is unimportant
if
in any case by multiplying
the
.
statistical
percentage
under consideration
error
in the number of measured
by the factor
This procedure
which were used to determine
in the interval
I 1 - BC 1 ) l/2 .
(1 +
can fruitfully
pairs
be illustrated
the cross sections
for the two intervals
in the region of the annihi-
lation peaks: 4.0-6.0
GeV for the 5.25 data and 6.8-8.2 GeV for the 7.5
*
GeV data. A sample calculation is presented in Table III. 4.
III. 3
3-C Channel Cross Section
In order
rections
to obtain cross
must be introduced
sections
worth retrieving.
the number
successfully
these into one number,
ed are also listed
energies.
owing to scatters
cf events which failed
considered
channels,
cor-
in the double scan,
or short fast tracks,
all measurements
and
or were lost and not
The number of events found in the scans and
measured
are shown in Table III. 5.
the “scan to measure”
correction,
in Table III. 5 for three and five-prong
This boost was applied equally
theses of Table II. 2, assuming
Combining
the results
to all of the various
The numbers
are large enough that the statistical
error
obtain-
events at both SLAC
physical
that losses other than short protons
dependent of the event configuration.
rection
reaction
for events that were missed
events that were not measurable
a small fraction
for various
hype-
are in-
which make up this corin the correction
is quite
small.
In addition
there is a significant
and therefore
to this t’scan to measure”
loss in the p7r’r-
very short protons,
pair to the scanner.
This forward
correction,
for 3-C events
channel of events with small
t(p,p)
+which can make the event look like an e e
loss correction
- 60 -
is also quite significant
TABLE
Ran-to-measure
corrections
III. 5
for events used to determine
3-C cross sections.
These corrections
do not include energy-dependent
effects like the forward losses which must be corrected separately,
but do account for all random
losses in the processes of scanning and bookkeeping, including losses for unThe events “on SUMX’
measurable events and events never remeasured.
have been counted directly from our SUMX tapes, while the events “on film”
are corrected for scanning losses as in Table II. 1.
5.25 GeV Data
Three Prong Events
Rolls
On Film
218-282
1386.3
1289
178.5
147
732-830
4329.4
3993
493.7
426
_
Sum of above
5715.7
5282
672.2
573
Correction
Factor
On SUMX
Five Prong Events
On Film
1.032
on SUMX
1.173
7.5 CeV Data
Three Prong Events
On Film
Rolls
on SUMX
Five Prong Events
On Film
On SUM1
381-578
4445.1
4212
605.2
545
1240-1531
8742.6
8143
1137.6
1019
1685-1762
1651.5
1571
236.6
__217
14839.2
13926
1979.4
1781
Sum of above
Correction
Factor
1.065
1.111
1
I
- 61 -
for the channel pw but less so for other events in the channel pa’x-~’
the proton seems to be less peripherally
nel x’r+a-n
which generally
ward loss corrections
study of forward
has 3 clearly
visible
above,
can be obtained directly
correction
events on film and divided by the microbarn
loss corrections
lation are then applied where applicable
III. 6.
It is clear from
uncertainty
events.
in the cross sections
perimental
and Fig.
exponential
to give the results
results
are
to give the visible
using a linear
of the cross section
to have maximum
intervals
tive to the calculated
“catch”
These numbers
equivalent
is dominated
accuracy
by high energy annihilation
made in wider
are not dis-
3-C
extrapo-
shown in Table
by the statistics
that the
of the hadronic
from the 5.25 and 7.5 GeV
compared
with other ex-
for three-constraint,
three -
9,10,16
In order
produced
IV. 1.
to give the number of visible
El. 5 shows these SLAC results
determinations
prong events.
in section
the number of events in each energy interval
Table III. 7 shows the combined
exposures
The
the number of 3-C events in any ener-
from a histogram.
then boosted by the scan to measure
the for-
separately.
the 3-C event energy spectra
pair spectra,
Forward
in the chan-
Therefore
losses in the channel pp” will be discussed
torted like the measured
cross section.
tracks.
must be studied for each reaction
Since, as discussed
gy interval
produced and of course
where
in the cross
photons,
sections
independent
for events
calculations
were
than those in Table III. 7 so that they are less sensi-
correction
function
more of the pairs whose energies
(i.e.
, the intervals
are mismeasured).
- 62 -
being larger
This check
TABLE
5.25 GeV 3-C,
III. 6a
3 Prong Cross Section Calculation
---
Ey (C+eV)
Events/p b
3-Z Events
- 01 suM.x
3-C Events
on film
0.4-0.5
7.15
69
74.5
9.6 pb
9.6 pb
0.5-0.6
6.18
249
268.9
43.5 pb
43.5 vb
14.82
LO24
1105.9
74.6 pb
74.6 pb
1. o-1.2
4.69
299
322.9
68.9 pb
68.9 pb
1.2-1.5
5.09
259
279.7
55.0 pb
55.0 pb
5.91
261
281.9
47.7 pb
47.7 pb
2.0-2.5
4.12
139
150.1
36.4 pb
36.4 pb
2.5-3.0
2.81
80
86.4
30.7 pb
30.7 pb
3.0-3.5
2.44
62
67.0
27.5 pb
f-V&
29.2 pb
3.54.0
1.91
49
52.9
27.6 pb
8%
23.8 pb
i.o-4.5
1.77
36
38.9
22.0 pb
10%
24.2 pb
25.11
382
16.4 pb
13%
18.5 pb
1.70
19
12.0 pb
14%
13.7pb
0.6-l.
1.5-2.
0
0
L.5-6.0
5. O-10. 0
4.2.6
20.5
C&3-C)
Forward loss
correction
U(3-C)
TABLE
7.5 GeV 3-C,
ItI.6b
3 Prong Cross Section Calculation
-
Ey(-V)
Events/pb
3-C Events
- 01.1SIJMX
3-C Events
on film
*y (3-C)
Forward Loss
correction
0(3-C)
o-4-0.5
22.33
131
192.8
8.61J.b
8.6IJ.b
0.5-0.6
16.82
777
827.5
49.2 pb
49.2 pb
0.6-1.0
40.30
2962
3154.5
78.3 pb
78.3 pb
1.0-1.2
12.89
855
910.6
40.6pb
70.6 pb
1.2-1.5
12.87
744
792.4
61.6 pb
61.6 pb
l-5-2.0
16.02
754
803.0
50.2pb
50.2pb
2.0-2.5
10.66
367
390.9
36.7 pb
36.7pb
2.5-3.0
8.20
244
259.9
31.7 pb
31.7 pb
3.0-3.5
6.21
142
151.2
24.3 ,ub
3.5-4.0
4.28
88
93.7
21.8pb
7%
23.4pb
4.0-4.5
4.63
83
88.4
19.1pb
8%
20.6pb
4.5-5.0
3.57
67
71.4
20.opb
9%
21.8pb
5.0-5.5
3.16
56
59.6
18.9pb
10%
20.8pb
5.5-6.0,
2.77
45
47.9
17.3,ub
11%
19.2 pb
6.0-6.5
2.38
29
30.9
12.3 pb
12%
13.8 pb
6.5-7.0
4.89
64
68.2
13.9 pb
13%
15.7 pb
7.0-8.0
36.10
469
499.5
13.8 pb
3.20
38
40.5
12.7 pb
8.0-10.0
6.5%
13.4%
14%
25.9pb
15.7 pb
14.4 pb
TABLE
Cross
sections
for the 3C fit reactions
found in this experiment,
III.7
yp -+pn'~-
averaged
and
Y~,~I?T+IT-R-
in the energy intervals
shown.
EyGW u(yvp~+d(N-4
I
0.4-0.5
9.0+
1.0
0.5-0.6
47.6~3.0
0.6-1.0
7'7.2 * 3.5
1.0-1.2
70.2~4.0
1.2-1.5
60.023.5
1.2-1.5
0.035rto.04
1.5-2.0
49.5L3.0
1.5-2.0
0.8LO.2
2.0-2.5
36.5 k2.0
2.0-2.5
1.9 LO.3
2.5-3.0
31.222.2
2.5-3.0
3.lLO.5
3.0-3.5
26.8~2.0
3.0-4.0
5.5kO.7
3.5-4.0
25.3~2.5
4.0-5.0
4.4LO.7
4.0-4.5
20.7rt2.0
5.0-5.5
4.9LO.7
4.5-6.0
19.0&1.0
5.5-6.0
6.Okl.O
6.0-7.0
15.8 ~2.0
6.0-7.0
4.6rt0.9
7.0-8.0
16.011.2
7.0-8.0
4.6ItO.4
8.0-10.0
14.5 ~2.5
8.0-10.0
5.4Ll.O
- 65 -
,....
;..A+&
I
I
I
.....I.....4,
A+.....&--:I
-+
I
- 66 -
I
I
+
I
produced
quite consistent
results:
c(3-C,
3-prong) = 19.1 f 1.2 microbarns
Ey =4.0-6.0
GeV
c(3-C,
3-prong)
Ey =6.8-8.2
GeV
= 15.7 f 1.0 microbarns
which are the values used to normalize
other cross
sections
in the rest of
this study.
III.4
Calculation
of Cross Sections for 1-C Channels
Constrained
fits can be made to events of the reactions
-!--0
YP -plT?TT
++T 77n
-YIP ---7~
if these are produced
determines
tested by comparing
events,
constraints
The remaining
from diverse
the confidence
since the location
of the vertex
uniform
constraint
scatter
plot.
Three of the four energy-
the three neutral
can act as a filter
This is the standard
with charged beams,
to isolate
procedure
where the incident
In our case there are a number of backgrounds
As in the charged case, there are the multi-neutral
YP -ppn+T-?PP.
,
YP -
was
levels of 3-C and 4-C fits for the same
are used to determine
backgrounds.
ber experiments
photons,
(III. 2)
photon energy to about *l. 50/O. This precision
which gave a fairly
momentum
ables .
by annihilation
the incident
(III. 1)
particle
vari-
these events
for bubble chamenergy is well known.
which are troublesome.
reactions
. -
(I& 3)
.IT+T+B-flPn. . .
(III. 4)
- 67 -
where the dots represent
more,
reactions
1-C hypotheses
additional
under consideration
let the notation
wise for reactions
(2) - (4).
can be contaminated
(LA) denote reaction
from bremsstrahlung
Thenfor
example,the
if one of the pions in reaction
reaction
photons may fit the
or unfavorable
(1) from annihi-
photons,
sec-
and like-
events of reaction
(1A)
by the events from (1B) and events of (3A) and (3B).
can not be distinguished
larly,
Further-
the energy cuts used in the previous
(1B) denote the same reaction
Moreover,
particles.
due to poor measurement
lation photons (i.e. , photons within
tion):
neutral
(1) to (4) produced by bremsstrahlung
Therefore
kinematics.
possible
from a proton,
(2) or (4) is fast enough so that it
it may simulate
(2) may be contaminated
reaction
(1).
Simi-
by fits from events of (1) or (3) with
fast protons.
The independent determination
of the gamma energy allows
ing mass of the fit to be used as a criterion
to isolate
of reactions
backgrounds
Therefore
(1A) and (2A) from the various
a missing
pure samples
discussed
mass approach has been adopted to determine
number of events to be assigned to these reactions.
annihilation
relatively
peak and perfect
Assume
The calculated
measurements.
the miss-
above.
the true
a very narrow
missing
mass,
m, is defined by
m2 = (KA+
mp - Evis)2
- (rA -rvis)
where kA and kA are the energy and momentum
the proton mass,
photon, m P
and Evis and Fvis are the sum of energy and momentum
or visible,
peak sharply
at the mass squared of the missing
the background
tracks.
Then if the hypothesis
the charged,
from
of an annihilation
m2 will be more uniformly
- 68 -
is correct,
particle,
distributed.
for
m2, will
while for events
In practice,
the
distinction
is less precise,
since the annihilation
and the spread in measurements
peak is not a perfect
is non-negligible
(see Fig.
spike
II. 7).
For a number of reasons it is more useful to study distributions
missing
mass squared rather
is more closely
related
have an approximately
than missing
to the measured
normal
quantities,
distribution.
mass squared do appear to be normally
studying
reactions
is distorted
a single pi-zero,
To understand
criminatory
tion,
momentum,
the actual neutral
of an ambiguous
mass and production
system of particles.
track is measured
= (mf2 - mF)/2p,
track of momentum
off for good ionization
lated neutral
mass squared as a dis-
can not be identified
kinematics.
by ioniza-
In the labora-
angle with respect
In the bubble chamber
essentially
correctly,
Let f=(assumed
where mf is the mass assigned
p (p greater
in
an event,
k the
mass fit and let Eo, PO, m. and theta be the
assigned depends on the assumed mass.
energy)
in
The neutron mass is
but has been treated
to examine photoproduction
in the missing
of
mass distribution
let kt be the true energy of the photon producing
value assumed
histograms
Furthermore,
the missing
of missing
tool in the case that the particle
tory system,
to
for consistency.
the effectiveness
it is necessary
energy,
distributed.
this distortion,
the same way as the pi-zero
mass squared
which are presumed
because the pion mass is so close to zero.
far enough from zero not to suffer
exactly
Missing
Also experimental
missing
involving
47
mass.
of
to the beam of
the momentum
but the energy
energy minus true
to an ambiguous
than 1.4 GeV , which is the approximate
discrimination)
while mt is the true mass.
cut-
The calcu-
mass mc is then given by
rn: =m “,+2(kA-
kt)(Eo-PO
case ) -2f(E0
- 69 -
- kA + kt - f/2)
W. 6)
If the ambiguous
track is assigned
its correct
mass,
then f =0 and it is clear
that for true photon energy kt less than the expected annihilation
rn: is always greater
neutral
than the true missing
system will make the missing
energy.
For example,
an annihilation
between calculated
single neutral
proton bremsstrahlung
be seen from
hypothesis
events,
in the final state (f > 0) generally
represent
energy and the
events which will
be assigned
when f =0 are from the electronthan kA, and as may
contamination.
gave low enough E. and high enough m. to
hypothesis
(1) or (3), annihilation
a considerable
pion whose
it turns out that those with a true neutron
with the p=+?r-r’
reaction
annihilation
of Fig. II. 10, will make negligible
For ionization-ambiguous
proton from
neutral
photons with true energy greater
the spectra
make the overlap
events with 3-C fits will very often
The only multineutral
photon energy.
a fast forward
to assumed photon
(1A) by adding a fast forward
energy is just the difference
correct
mass insensitive
low energy pr’?r-
also give a fit to reaction
However,
mass.
energy,
small.
Those with a true fast
or bremsstrahlung,however,
overlap with reaction
(2A) and must be treated
more
carefully.
The separation
of a pure sample of four-body,
energy events for the three annihilation
mass squared plots.
After
mass squared of the neutral
applying
Fig.
the type Yp -
and Yp -
peak at MM2 = rni and MM2 = rnt . In order
reactions
criteria,
from
the missing
the annihilation
particles
mass squared distributions
~r+.rr+n-MM.
(1) and (2) in the monochromatic
by Eq.
for fits of
These distributions
to obtain the cross
peak regions,
- 70 -
high
was done using missing
momenta of the visible
III. 6 shows the missing
pr+n-MM
the ionization
system was calculated
photon energy and the measured
(Ill. 5).
experiments
single neutral,
clearly
sections
it is necessary
for
to
(4
(b)
yp-pn+a-
MM
yp-TT+T+K-
200
50
Ey=4.3 GeV
r
n
Ey=4.3 GeV
r
Ey=7.5 GeV
80
MM
Ey7.5
GeV
20
t
r
-0.5
0
I
I
0.5
1.0
-1.0
0
MISSING MASS SQUARED (GeV)2
FIG. ICI. 6--
1.0
2.0
3.0
1-1
(a) Missing mass squared, as defined in text, for all events
consistent by ionization with the reaction yp -px+aplus
neutrals at three photon energy settin f se9 (b) same for events
consistent by ionization with yp --t ?r i&r- plus neutrals.
Events with fast proton appear in both (a) and (b). The dotted
lines show the various background estimates as explained in
the text and Ref. 7.
- 71 -
determine
missing
the shape and magnitude
Exactly
mass plots.
the neutron channels.
before discussing
the specific
three main classes:
(i) contamination
contamination
photons,
(ii)
contamination
largely
reactions
below.
peaks fall into
by misidentified
by multineutral
Then PHONY calculations
according
5.25,
were used to estimate
and 7.5 CeV.
the generation
mass cuts could then be separately
the num-
Events of reactions
of the 3-C
as being a mono or brems
energy was within
energy cuts used for these exposures.
and
Each of these events was labelled
to the energy used in generation
depending on whether
All
The choice of these cuts is
(1) and (2) were generated by PHONY with the energy distributions
at 4.3,
events.
0.10) GeV2 for the pi-zero
ber of true events which had been excluded by this cut.
event spectra
by events
excluded by making cuts in the missing
1.2) GeV2 for the neutron distributions.
discussed
terms
events of pn+n-?P and vice versa,
The cuts used were (-0.18,
mass spectra.
here in general
of the high energy regions
of the four-body
of these backgroundswere
and
channels.
i. e. , fits to T+?r’x-n by ambiguous
and (iii)
to the
methods were used for the pi-zero
in the region of the single neutral
from nearby bremsstrahlung
(0.6,
parallel
contributions
These methods will be described
The backgrounds
events,
of the background
or outside the standard
The discrimination
determined
event,
of the missing
for brems
and mono events at
each energy.
The PHONY missing
mass squared distributions
Those events produced with energies
well defined signals
particle,
whereas
at the appropriate
III. 7.
inside the mono energy bands show very
missing
mass values for their neutral
the brems events give very distorted
most of which fall outside
appear in Fig.
the cuts used.
missing
mass spectra,
It is evident that most of the mono
- 72 -
YP 80
I
I
p-rr+-rr- TTOPHONY EVENTS
I
I
270 Events
4.3 GeV
I
I
252 Events
5.25 GeV
I
I
I
366 Events
7.5 GeV
(0)
1
1
1.
I
4
I
2470
5.25
Events
GeV
I
I
2877
Events
7.5 GeV
(b) -
I
-0.2
0
0.2
-0.2
0 0.2
‘I
MISSING MASS SQUARED (GeV)’
FIG. lTI. 7--
,soscil
Missing mass squared distributions
for PHONY events of the
reaction
yppn’ir-16’.
(a) 1-C fits to events with photon
energies in the bremsstrahlung
region for each exposure.
(b) 1-C fits to events with photon energies in the annihilation
The arrows in (a) show the cut used to define good
regions.
n0 events.
- 73 -
events will
survive
exact numbers
percentages
the cuts whereas
can be used to generate
of mono and brems
These can then be combined
N
ratios
observed
the missing
to relate
The
giving the
mass cuts.
the true number of
inside the cuts.
The necessary
are
obs
(mono) =f(mono)
Nobs(brems
N
true
(mono)
in mono) = f(brems
Ntrue (b rems)
in mono) Ntrue (brems)
Ntrue(mono)
=X
where X is a factor which combines
the relative
number of photons attributed
to the brems and mono regions with the different
these regions
known,
events will fail.
f(mono) and f(brems)
events which survive
for any exposure
mono events to events actually
equations
most of the brems
for the reaction
it can be adequately
at the cross
approximated
and by defining
Although
using first
sections
in
X is not perfectly
guesses (uncorrected)
the brems region
to extend far enough
in energy below the mono region that it is very unlikely
for any fits to come
from farther
sections
being studied.
average cross
away into the mono region.
bined to give a relation
served within
Then these equations
between those events--brems
the missing
can be com-
or mono--actually
ob-
mass cut and the number of true mono events--in
and out of the cut, namely
fibs
= Nobs(mono)
=(f(mono)
+ Nobs(brems)
+ X f(brems))
This equation has been used to correct
cuts above backgrounds
Ntrue (mono)
those events within
(ii) and (iii) into the total number
- 74 -
the missing
mass
of events produced
in the mono region.
from section
This number divided by the proper
III, 2 then yields
Backgrounds
protons
strained
the cross
of type (ii) in the neutron channel from events with fast
were estimated
by recalculating
the missing
of the opposite contamination
as s’r+r-MM.
the characteristic
bump
mass.
Very
(i. e. , true neutron events simulating
was found.
body events,
were estimated
namely 3-C fits to p~‘r”?r-x-.
is kinematically
equivalent
squared distribution
is concerned
(p” production
nn”.
it is possible
to simulate
px*a+x-7r-
is not important
Backgrounds
as two different
from p*+ir-r”xo
to the Pi-Zero
with ionization.
Simi-
events ?r+a’?r-MM by
and =‘rfr-rOn
In this way simulahave been obtained.
Channel
Fig. III. 6a shows the missing
prong events failing
when
likewise
events of the type pr+*-MM.
each negative pion with the proton for omission.
tions to the backgrounds
mass
in turn each 8’~~ pair from p*+n’r-a-,
four different
can be recalculated
that a B+T- pair
as the missing
and that px- combination
Then by omitting
approximates
by using the actual five-
It was assumed
to a mono pair insofar
averaged over all X+X- combinations)
pairing
protons
mass plots just below the true neutron
The type (iii) backgrounds
larly
mass squared of con-
fits to pa+a-~~’ with good MM2 and ambiguous
in the neutron missing
pr’r-x’)
equivalent
section.
Such events which also gave a neutron fit explained
little
microbarn
mass squared calculated
a 3-C fit but making a O-C fit to reaction
for all three
(1) consistent
The data for each energy appear to peak very close to m2
7To *
to fall off smoothly
to the left,
and to encounter
as one moves beyond the two pion threshold.
- 75 -
rapidly
increasing
Superimposing
background
on the data the
symmetric
Fig.
at m2+ , as predicted
curve centered
III. 7), determines
the point above which the background
bute more than the good single pion events.
Gev2 are suggested;
by a PHONY calculation
-0.18
The limits
the height of the tail of the symmetric
The primary
Whatever
effects
the missing
are neglected.
constraint
mass distributions
backgrounds
of the true signal,
events,
to reactions
events,
2
(1A).
the dominance
, estimated
Their
subtraction
distribution
tant for establishing
background
within
resulting
from 3-
using only the proton and two pions
Using the requirements
near a missing
we have not included
- 76 -
seen in five-prong
III. 6a.
For the pur-
the events of reaction
however,
background.
of the cut described
35 events at both energies.
mass squared
via PHONY in a more quantita-
as given by PHONY,
the level of multi pi-zero
the limits
xf7r-x0
as shown in Fig.
separately
of symmetry
shape by multi-pion
from the number of no -
since they can be corrected
tive way.
which result when two charged pions
of the background
one can draw the backgrounds
pose of background
by PHONY while the
from actual five prong events by
of some n ’ production
and the presence
of 0.3Gev
are from reactions
This is the shape that has been used for the multi-
are shown in Fig. III. 8.
neutral
to this reaction
mass squared distributions
events calculated
dis-
of true events.
The effect of (1B) has been simulated
The missing
five-prong
the PHONY simulations
for the exclusion
of (3 A & B) have been simulated
studying
(1B)
cut is chosen,
a correction
events is about twice
x0 peak, using the left side of the peak
sources of background
(1B) and (3 A & B).
of -0. 18 and i-0. 10
the Gaussian tail of the true T’ events and 0.10
GeV2 is the point where the height of all O-constraint
cussed above determine
events contri-
GeV2 is about the point where the flat background
under the ?p peak intersects
to define the shape.
(see.
has been imporIn this way the
above is seen to be about
50
I
I
I
I
I
I
I
I
4 COMBINATIONS OF I73
PRONGS AT 5.25 GeV
40
30
20
r
4 COMBINATIONS OF 203
3-C 5 PRONGS AT 7.5 GeV
20
IO
0
-0.5 -0.1
I
0.3
I
0.7
I.1
MM2
FIG.
1.5
(GeV2)
1.9 2.3
2.7
3.1
‘89518
III. 8--Missing mass of 5 body events treated as 3 prongs to simulate
the behavior of yp +pr+n-fl?r”
events.
The arrows show the
cut used to exclude multi-r’
events.
Backgrounds
to the Neutron Channel
Fig.
III. 6b shows the missing
making a O-C fit to reaction
considered
included
thesis n+?r+w-n.
One type, from reactions
events of p*‘r,-r’
and pa+n+n-r-.
events , included
a+?r+ir-mr”.
events to other &body charge states,
used.
and pnilr-4iro
Another
the isospin
The sum of these three backgrounds
but as in the pi-zero
but in the quantitative
ground within
which fit the hypoevents in
from pa+?r+~-n- 3-C
weights of Shapiro
48
were
gives the solid line in Fig.
shows estimated
case, these are not corrected
way discussed
the limits
fore estimated
with fast protons,
type, from multineutral
To transform
The broken line above the solid background
levels,
of background
These were studied using actual fits to ambiguous
the channels pn+a-r’
neutron
As can be seen, the sources
(2).
were very diverse.
misidentified
mass squared for all three prongs
above using PHONY.
III. 6b.
bremsstrahlung
from the graph,
The net back-
of the cut of events not of the type nfrTT+r-n is there-
to be 51 events for the 5.25 GeV data and 42 events for the
7.5 GeV data.
In Table III. 8 the net yields of O-C fits within
are given,
along with the microbarn
resulting,cross
sections
making the calculation
of the invariant
culation
section
and the
In
(1A) and (2A) at the three energies.
for the proton channel,
mass spectrum
for those samples
the events in the omega region
were removed,
a separate
cross section
cal-
made for those events (see section IV. 2), and the omega cross
(without
the cross
the 10% correction
section for non-omega
PHONY corrections
events,
for reaction
equivalents
the cuts at each energy
and forward
which was necessary
for neutral
events.
decay modes) was added to
This allowed
loss corrections
for omega and non-omega
since omega production
- ‘78 -
the use of separate
is much more
TABLE
Cross sections
yp--+nlrfnfir-
III. 8
found for the reactions
at the annihilation
over a photon energy interval
E
4.3
peak energies,
approximately
y p-Ppr+n-7P
Y
up--tpafn-7ro
yp-tns
and
averaged
1 GeV.
++-
H x
Gev
5.25 GeV
7.5
Gev
Raw SLAC data yp-~“+“-?pp
Unique O-C Events in Cut
Non-Omega
Omega
Background
in Cut (non-w)
Correction for
Excluded Events
Non-w Forward
Loss Correction
5.25 Gev
394
67
10
0.916
1.5%
7.5
408
78
8
1.019
1.5%
Gev
Raw SLAC data yp+s’nfa-n
O-C Fits
in Cut
Estimated Background
from Other Reaction
Net True
Events in Cut
Correction
for
Cuts and Brems
Estimated True
y p-+a+a+n-n
5.25 GeV
208
54
154
1.032
159
7.5
196
42
1,54
1.131
175
Gev
peripheral
than the rest of this channel.
cut (0.68 CeV<m(3r)<O.
sometimes
track as the proton) which introduced
counting has been corrected
Recent results
sample,
cussed extensively
weight
error
associated
tage error
The errors
is relatively
in the number of events,
is the percentage
straight
N
-l/2
change in N resulting
analogous
to the way the error
corporated
into the flux error
Table
for the
with the size of the
with the PHONY corrections
in the photon flux have been dis-
in section III. 2 and the statistical
calculation
in preparing
laser beam fit quite well
associated
root of the number of events in the sample.
the error
l/2
This double
here are the flux determination
errors
subtractions.
the
III. 9.
the statistical
and the systematic
and background
some double-counting.
from the SLAC backscattered
The main sourcesof error
equivalent,
whereas
gave two fits (one with each positive
for by assigning
with our data as shown in Fig.
microbarn
the omega mass
88 GeV) were assumed to be unique,
events of the channel p?r+a-*’
III. 8.
The events within
error
is the square
Also for the PHONY correction
forward,
multiplying
, by a factor
the percen-
(1 + IDI )
l/2
from the PHONY correction.
due to the bremsstrahlung
calculation
in section
- 80 -
III. 2.
correction
where D
This is
is in-
- 81 -
CHAPTER
PHOTOPRODUCTION
This chapter
OF NEUTRAL
begins the presentation
in this experiment
concerning
specific
stand the data in photoproduction
model (VDM). l4
IV
VECTOR
of the experimental
reactions.
are influenced
VDM is currently
the photoproduction
on the SU(3) behavior
of the photon as the IJ:
r-3- T-p O+
Bv is the mixing
phi.
dominance
theoretical
This approach
member
of the vector
apis based
(l-)
+ $cos ev) ,
angle which correctly
this relation
for diffractive
of hadrons.
$ (wsinBv
If it is assumed that vector
all mesons,
by the vector
to under-
49
as :
meson octet expressed
singlet.
data obtained
Most attempts
the most comprehensive
proach for explaining
where
MESONS
combines
meson-proton
may be interpreted
photoproduction
the SU(3) l- octet and
scattering
is the same for
as giving the relative
of the neutral
vector
Note>that the photon has both isovector
amplitudes
mesons rho, omega and
(rho) and isoscalar
(omega and
phi) components.
Experimentally,
rho production
the channel pr+r-
as the incident
This prominence
chapter
the photoproduction
and compared
11
above the background
to its extremely
reactions
narrow
yp-pop
in light of vector dominance
- 82 -
the
in the channel p=+a-n’,
fits are possible.
very complicated
width.
Therefore
and yp --+wp
predictions.
by neutral
Furthermore
regions where only unconstrained
of the omega meson in an otherwise
channel is due primarily
dominated
photon energy increases.
omega meson stands out clearly
even in the bremsstrahlung
is increasingly
in this
are studied
Unfortunately,
since
this experiment
not possible
vector
did not study the photoproduction
to make the relevant
comparisons
Because the neutral
mesons.
of strange particles,
of the phi meson to other
rho meson is so dominant
and because the small amount of nucleon resonances
accounted
duced to explain
mesons,
mass vector
together.
mesons as predicted
Therefore
nated by a single reaction.
presentation
This includes
being neither
exami-
a search
model. I5
Such
including
vector
inelastic
than protons),
nor so domi-
is singled out for
as a quasi-elastic,
diffractively
pro-
All other aspects of the C-body final states,
meson.
p’production
associated
so free of back-
are measured)
omega production
here due to its importance
duced neutral
(i. e. , rhos produced off particle
rho-delta
charged rho meson production,
production,
are presented
states other
charged A2 production
together
and
in the final chapter.
The Channel yp -+ p=+?rThis reaction
has been investigated
experiments,
9-12
dominates
the channel,
forward-peaked
parity
has a roughly
production
t-channel
led to the interpretation
in previous
track chamber
and
which showed that the reaction
YP +
natural
model) intro-
if they were found, would then also have to appear in Eq. (IV. 1).
ground as the 3-body channel (where all particles
counter
entirely
the entire
by the Veneziano
The channel pxf7r-7ro is quite different,
Iv. 1
seen is almost
the skewing of the H+K- mass distribution,
nation of the 3-body channel is presented
for higher
in the channel
models (e.g. , the Sb’ding interference
for by certain
it is
POP
w.
2)
constant cross section with a sharply
angular distribution
exchange mechanism.
of this reaction
and is consistent
16,50
as a diffractive
- 83 -
with a
These observations
process.
have
For squared
four-momentum
appears
lo,16
y-p vertex
to E
transfer
to the proton,
that s-channel
in the overall
helicity
CMS).
1 t 1 , less than 0.4 GeV2 it
is conserved
In addition
(i. e. , no spin-flip
a small
contribution
at the
proportional
-2
9,10,29,51
from the reaction
Y
-
YP is observed.
nA
Evidence has been sought,
than p” in the T’?T- mass system.
52
our data and shows that p” production
incident
A.
but not found, for resonances
This section confirms
increasingly
other
these features
dominates
in
the channel as
energy increases.
p” Production.
In Figs.
IV. l-2 the invariant
mass of the x’r-
six photon energy ranges.
The previously
invariant
with respect
mass distribution
comes especially
almost
++
dramatic
observed
system
skewing of the dipion
to the usual Breit-Wigner
in the 7.5 GeV data (Fig.
In Fig.
change of shape for the 7.5 GeV data with t is illustrated
form
but at small
even the s-wave
Breit-Wigner
the mass
prediction.
53
This distortion
model adopted.
phenomenological
below
means that a
The approaches
follow those taken by the SLAC-Berkeley-Tufts
in their studies of p” photoproduction.
To present
r ) as is shown by
1t 1 the high mass tail is significantly
depends upon the production
used here generally
collaboration
by plotting
the
seems to approach a relativistic
(i.e. , Eq. (IV. 5a) below with a fixed
the solid curve,
full analysis
IV.2(b,c)
near the rho mass for O< It 1 <O. 12 GeV2 and 0.12< 1t 1 <O. 40 GeV2.
At large 1t\ the mass distribution
Breit-Wigner
shape be-
IV. 2), there being
no sign of a high mass tail to the distribution.
distribution
is shown for
(SBT)
16,30,32
the raw data independent of models we begin with a purely
approach.
It is assumed that the double differential
- 84 -
cross
I ’
2.5-3.0
__d
’ ’ ’ ’ ’ ’
3.0 -3.7
GeV
0.4
0 .8
1.2
0.4
0.8
1.2
M (kr-1,
2.0
0.4
0.8
1.2
1.6
G eV
0.4
M Crr+rr-).GeV
FIG. N. l--
-
GeV
0.8
1101.1
Dipion mass distributions
for yp ----f pn’ir- in the first 5 energy
intervals as labelled.
The darkened areas of (d) and (e) represent events with pn+ mass in the A++ 1236) region (1.12<M(pa+)
Cl.35 GeV and t(p,plr+)l .<0.8 GeV 2’).
- 85 -
-
-
-
-
I
zi
I
0
-*
I
I
z
-
I
I
0
a0
I
I
0
0-
l70’0/s+uaA3
I
Aa9
I
0
CD
- 86 -
I
I
0
*
I
I
0
N
I
- T
0
I
I
FIG. IV. 2 (cont’d. )
I
AW bO’O/ SlNM3
- 87 -
I
(9
(u
l3.l
cu’
CD
.
FIG. IV. 2 (cont’d. )
PHENOMENOLOGICBL
FITS
6.8 < Ey < 8.2 GeV
TO yp-p-rr+r-
40
0.24
5 I tl 5 0.80
GeV2
<n(t)>=l.2*0.6
20
0
203
618 3-C EVENTS
0.06<ltl~t,,,GeV2
<n(t)> q 3.2 f 0.3
x2
3- C EVENTS
0.12 2 Itl 5 0.24
<n (tl>= 3.8f0.5
GeV2
= 13.5/22
0
0.06 5 Itl 5 0.12GeV’
<n (t)> q 4.3 20.4
) -
40
20
) -
0
4c 1 -
2C1 -
(1 L
0.2
0.6
1.0
1.4
1.8
M,+,-
2.2
(GeV)
2.6
3.0
3.4
3.8
I8PSCZZ
(e) Phenomenological
model fit curve superimposed on 3-C event data with
6.8<E (8.2
GeV for 0.06 GeV2< It 1 <t,,.
(f-h) Phenomenological
model
fits inlhree different t intervals,
each a subset of the data in (e). The variation of the exponent n(t) is illustrated
by these fits.
- 88 -
section
for dipion production
1t 1 < 0.4 GeV’ may be described
with
by the
form
2
dg
dtdm
with
A and B functions
the t distributions
represents
IV. 3 shows
(0.60<m<O.
this region well.
85 GeV),
A loss in scanning of
A and B have been determined
for fixed
in m for events with 0.06< 1t 1CO.4 GeV2 using the “average-t”
method as explained
below.
slopes are shown in Fig.
more marked
B=7.0*0.4
The resulting
IV.4.
interval
production
in the range from 4 to 8 GeV.
analysis
models.
fall into two classes:
the kinematic
other interference
of p” photoproduction,
The production
i) the interference
skewing or phenomenological
models differing
background;
matic factor,
which
17
it is neces-
models suggested in
model of sijding
models,
the second includes
class also includes
any modifications
and Uretsky
very accurate
- 89 -
of the
of the kine-
or Mannheim
exponent used with the Ross-Stodolsky
the data with such models,
17
such as the one
from that of Sb’ding in the details
such as the models of Kramer
or the variable
By fitting
This
collaboration
suggested by Ross and Stodolsky. 54 The first
interfering
815 GeV), namely
GeVs2 at a photon energy of 4.7 Gev.
sary to use specific
originally
and
with the same value
of the SLAC-Berkeley-Tufts
To make a more detailed
and ii)
sections
of slope with mass becomes
about the rho mass (0.715<m<O.
agrees well with the results
the literature
cross
but is consistent
GeV-2 for photon energies
found B=6.6*0.5
forward
The variation
at the highest energies
in a symmetric
16.
Fig.
mass.
for events with m in the rho region,
events at small t is evident here.
Maor,
,
of m, the dipion invariant
which show that Eq. (IV.4)
intervals
= AeBt
factor
determinations
and
in Ref.
of
&J
;
-
-
90 -
/
r
(0)
IOOO-
2.0-2.5
800.
E
M ( T+ TT- I. GeV
(b)
I
16
rlliT-Tw’
2.0-2.5
l
Gev
, ‘v----
_ -2 5-3.0
GeV
16N
t
’
d
8-
m
I
16 -
I /I
1
47-5.6
I, w-i
’
Cev
I
l---e+-6.8-8
2 G CV
8-LA
-11
0.4
I
0.6
0.8
M (T’T-),
FIG. IV.4--
(GeV)
11018
:
(a) Double differential
cross section d2a/dtdm (t=O). The curves
are the phenomenological
shapes described in text (Eq. IV. 5)
with r =O. 125 GeV, mp=O. 765 GeV). The exponent n=6 was
used a P all energies except Ey=2. O-2.5 GeV, where n=4 has been
used. (b) The slope B for the interval 0.06< 1t 1CO. 40 GeV2 as
a function of the dipion mass.
-91-
the quantities
polation
A(m) and B(m) can be made if the models provide
of the data points.
A particular
to provide
functional
been fitted
to obtain p” cross
the rho.
Applied
forms
describing
The results
shown in Table IV. 1. A third
A(mc) from the raw experimental
model independent as possible.
2)
kinematic
The true p” cross
these values.
fitting
of these two fitting
sections
Therefore
Siding
ference
Fits.
and 4. 7 GeV, including
produced
presumably
interference
background
amplitude
values,
procedures
are
from
in order
to be as
I) Sliding fit values,
and
lie somewhere
3)
“standardtl
within
values.
the range of
methods the cross
as for an “undistorted”
sections
rho, which should be most
Detailed
descriptions
of these three
It has been shown in Ref. 16 that the Siziding intermost of the characteristics
of co production
the shape of the dipion mass distribution
In this model the major
p” (Fig.
inherent
follow.
model explains
dependence.
uncertainty
three sets of photoproduction
These are
for making VDM comparisons.
1.
by small amounts
has been derived
dipion mass spectrum
In the Sijding and the standard
procedures
These have
near the rho mass by determining
(phenomenological)
quoted may be interpreted
relevant
of the theoretical
have been determined.
skewing
data.
and values for the mass and width of
set of cross sections
of dipion pair production
cross sections
the dipion production
sections
as a measure
in the choice of models.
the intensity
example of each class has been used
to the same data, these values differ
which may be regarded
a good inter-
IV5a) as in VDM.
of the diffractive
due to the Drell
rho amplitude
The distorted
amplitude
and its t
is from a diffractively
p” shape is due to the
with a p wave non-resonant
diagrams 56 (Figs.
IV. 5b, IV. 5~).
is assumed to have a nearly constant phase,
- 92 -
at 2.8
interfering
rfr-
The Drell
TABLE
IV. 1
Raw and corrected events and cross sections for the channel ~p-+pn+n-.
Fitted masses,
total cross sections for p” produced in yp--+o”p as obtained by the phenomenological
and &ding
Cross
sections
are
corrected
for
other
t
values
assuming
in the interval 0.06< 1t 1 CO. 4 CeV2.
exponential.
l-
Same1 Eve]
mcorrected
Ey(GeV
s and Cro
j Sections
:orrected
2.0-2.5
1001
1001
C@+T-)
---i&L36.5i2.0
2.5-3.0
642
642
3. o-3.7
552
3.7-4.7
-r
Phc 3menolo
ro(MeV;
lpWV)
-I-
:a1 Fits
jding Fits
npWeY
y$G)
widths and
fits made
a linear
TotMeW
y,bW
764*7
143*12
19.1*1.7
765*8
146h15
18.5*1.9
769=%
144-114
22.1*1.4
31.2*2.2
772=%
136*15
21.4&l.
588
26.3*2.0
772*7
141*18
18.7U.6
773*8
140*15
15.7&l.
775
852
21.5*1.2
‘769*6
134*10
16.2*1.7
774*5
142*10
14.7S.7
4.7-5.8
536
606
19.0*1..2
759+4
110*10
15.4&l. 4
75415
122*12
16.6*1.7
6.8-8.2
809
917
16.0*10
758%
151*11
13.7*1.3
771s
14 7*10
14.3*1.3
6
l.
7
(b)
I
I
(d)
0.2
0.4
Mhd
FIG. IV. 5--
0.6
I
I
----p
BREIT-WIGNER
--------DRELL
TERM
I\ -*---INTERF:
TERM
I
80
(cl
\\--n-r
0.8
(GeV)
DISTRIBUTIO
N
I.0
18OBA13
(a-c) The contributing
diagrams in the Sijding model.
(d) The contributions
of the Drell, interference
and p-wave Breit-Wigner
terms to the yp --+ pn+~are normalized to the number
cross sections at 7.5 GeV. The distributions
of Drell, interference
and p” events obtained with the Siding fit.
- 94 -
FIG. IV. 5 (cont’d.)
I
6
I
I
I
(e3
4.3 GeV
5.25 GeV
7.5 GeV
5
4
3
2
.
I
%O
3.0-3.7
6
5
2.5-3.0
GeV
2.0-2.5
GeV
GeV
\
4
3
2
I
0
0
0.2
0.4
0
I
I
0.2
0.4
Itl (GeV’)
0
0.2
0.4
0.6
MPJUO
(e) The variation of the phenomenological
exponent n(t) with t for all 6 energy
The data has
The lines are best fits of the data to straight lines.
intervals.
been fit in the t intervals O-O. 12, 0.12-o. 24, and 0.24-o. 80 GeV2 (e.g. , see
Figs. , IV.2f-h).
- 95 -
constructively
produce
below the central
the observed
cross-sections
mass of the p” and destructively
mass skewing.
we followed
closely
M2, and M3 are the matrix
the procedure
elements
and IV. 5c, then the cross-sections
term”
and the interference
2Re \M*~(M~+M~))
For the quantitative
evaluation
used in Ref.
for the diagrams
for diffractive
in Figs.
to 1Ml1 2,
In the calculations
were used with the following
t dependence of diffractive
Ml 0: exp(Bt/2).
changes (See footnote
production
p”
If Ml,
N. 5a, IV. 5b,
the “Drell-
, M2+M31 2, and
the explicit
given by Sijding for Ml, M2, and M3 as well as his computer
formulae
13 in Ref.
16).
First,
multiplying
Third,
The virtuality
the amplitudes
by
T,(s , t) which describe
the x N inter-
of the interacting
i6
T * (s , t) by a Ferrari-Selleri
p” in elastic
8x scattering,58
evaluate
which corrects
to form a p” indistinguishable
the rho cross-sections,
incoherent
(b) the reaction
yp -+
s-A++,
directly.
and (c) Lorentz-invariant
Practically
I
Ml
The cross-section
2
I
over the available
- 96 -
IV. 5 (a-c),
The
by the fitting
by the fit and most of the
term without
for
To
to an
phase space.
determined
no phase space was required
- ++
events were accounted for by the Drell
TA
mined by integrating
(IV. 2) were fitted
(a) the diagrams
program.
- ++
7~ A
events.
with the
from that produced
given by:
57
element
of the
width and slope were free parameters
yp -+
matrix
for the rescattering
rho mass,
tional
the Drell
events of reaction
sum of three distributions
for by
type form factor.
cosS, where 6 is the p-wave phase shift associated
e
dipion system
data for
pion was accounted
double counting was avoided by multiplying
by the factor
the
has been approximated
Second, the amplitudes
74 GeV.
17
program
action at the lower vertex were evaluated from the xN phase-shift
M(pr)<l.
of
16.
p” production,
term are proportional
respectively.
above it to
a need for addi-
yp -pop
was deter-
mass range while the
2
M2+“3
t
calculated
and interference
results,
shown in Fig.
of the diffractive
resulting
terms
p”
term,
were regarded
as background.
IV. 5d, illustrate
the relative
the, Drell
dipion mass distribution
term,
importance
and the interference
at 7.5 GeV.
Typical
term in the
The comparison
between the
raw data and the Siding fit shown in Fig. IV. 2d shows that this method gives
an excellent
representation
The parameters
of the experimental
mp, 5,
from a fit in the t region
section
results.
and B of the Sading model were determined
It11 =0.06<
for co events in this t range,
jt~<lt,l
=0.4
GeV2.
The cross
cp (t 1, t2), was then increased
by the
2
ratio of I Ml I integrated over the entire physical region of phase space to
2
portion of the physical region where
I Ml I integrated over the restricted
0.06</
t l(O.4
GeV2 in order
slope determined
physical
to obtain the total p” cross
for 0.06 <I t ‘1(0.4
region for dipion production
section.
GeV2 in the integral
is equivalent
Using the
over the entire
to the usual
forward
loss
correction.
The forward
extrapolation
p” cross section was also computed
to t=O using:
d,S”;d
a-
BE%d
0 (tl’t2)
(t=O) =
Sijd
tl) - exp(BSijdt2)
exp(B
’
This method avoids the effects of scanning losses at small
by the kinematic
resulting
c (t t ) by an
p 1’2
from
boundary at tmin,
fit parameters
and cross
the minimum
sections
IV.2.
- 97 -
momentum
t and the distortion
transfer.
are given in Tables
The
IV. 1 and
TABLE
IV.2
Forward cross sections and slopes for the p” as obtained by the three methods,
and double forward differential
~108s sections for mTr = ,715 - .815 GeV. Slopes
B were determined in the range 0.06 < 1t ( 5 0.4 GeV2.
$- (t = 0) (pb . C&V-~ )
<&(t=w>
B (W-2)
EyWV)
I
CD
co
I
m
Phenom.
&ding
Standard t
Phenom .
Siiding
2.0-2.5
138 f 20
143 f 14
180 f 20
5.9*
.7
5.4 *
2.5 - 3.0
179 * 27
170 * 17
184*25
7.7-t
.9
3.0 - 3.7
159 f 26
160 f 16
152 f 22
3.7 - 4.7
130 f 13
100*10
4.7 - 5.8
123 f 14
6.8 - 8.2
104 + 11
= .715 -. 815 Ge’
Standard?
(pb GeV-3)+
.5
6.7*
.s
770 *
6.4 *
.6
7.5 f
1.1
780 * 110
8.2 + 1.0
7.1*
.7
7.5 * 1.2
650 + 100
105 f 10
7.5*
.6
6.5-+
.5
6.8*
.7
450
132 + 13
117 l 12
7.6-t
.6
7.7*
.6
6.7*
.8
500 *
102 + 10
so f 10
7.5*
.6
7.1*
.6
7.0*
.8
380 + 40
t No incoherent background correction.
l
so
45
55
Phenomenological
2.
rho was parametrized
by:
Fits.
In this method,
the shape of the neutral
16
P(m) =
f@W4W
,
w.
5)
where5’
f(m) =
T(m)
2
(m
P
(IV. 5a)
- m2)2 + mir2(m)
and
(IV. 5b)
L(m) is a Lorentz-invariant
momenta
tively.
two-body
phase space factor,
in the dipion rest frame for dipion masses of m and mp respecEq. (IV. 5) is essentially
exponent is replaced
departure
the Ross-Stodolsky
by a t-dependent
from the procedure
modification,
introduced
used in our preliminary
in Ref. 16, describes
when the fit is repeated for distinct
of t, decreasing
similar
2,3
the experimental
at all energies.
at all energies,
is a relatively
the low ~-mass
energy-independent
enhancement
Fig.
data well.
However,
( It IN. 5
IV. 5e shows how the
It is
n(t), exhibits
that the true mass skewing
effect.
is presumed
- 99 -
This
of t at all energies.
skewing factor,
suggesting
a
n(t) is found to be a function
of Ref. 16.
as a function
to note that the exponential
behavior
mechanism
model,
with the results
shape changes strongly
interesting
t intervals,
reports.
from about 5.5 at t=O to about 0 at large t values
in agreement
distorted
form where the constant
exponent n(t), which represents
When fitted over the full range of t, < n(t)>=4
c,v2,,
q and qp are the T
In the Ross-Stodolsky
to originate
from genuine
co events.
ALthough this interpretation
which has a sin20 H distribution
distribution,
all mtl.
would explain the p” decay angular
0 GeV, in the sijding interference
distribution
is also provided
be used to provide
Lorentz-invariant
tions of p”, a-A’+
and <n(t)>.
term.
a smooth interpolation
As in the Sb’ding fits,
and from
interpretation
by the Drell
seen for the 7.5 GeV data in Figs.
in the dipion center of mass for
contributions
from the reaction
differential
cross
and fitting
together
cross sections
the resulting
Ittinl<ltl<
The frac-
0.06 GeV2.
with the mass,
were derived
width
by re-
sections
to the
This fit to the
GeV2.
section was also used to correct
- ++
x A
yp -+
p” cross
in the range 0.06< 1t I<&4
cal p” cross section for
as can be
have also been allowed.
The rho slope and forward
form (N.4)
fits can
N. 2(e-h).
and phase space were fitted
exponential
The parametrization
between raw data points,
phase-space
peating the fit in t-intervals
such an angular
the total phenomenologiTables
Iv.1
and N.2
list the values found.
Both of the above models suffer
phenomenological
developed
diffraction
model,
as is implied
dissociation
the high statistics
(mp/m)4
the exponent must be a function
Although
the
suggested
four-momentum
transfers,
l6 showed that to fit the data well
of t, which has no theoretical
underpinning.
of Ref. 16 does show evidence for an interference
which changes sign at the rho mass,
rho interfering
Sijding model,
only for small
of the SBT collaboration
The moment analysis
basis.
model of Ross and StodolskyB4 originally
factor
The
deficiencies.
by the name, has been empirically
to fit the data with almost no theoretical
using the kinematic
diffractive
from theoretical
however,
which supports
with a Drell background
has other problems,
- 100 -
the physical
(see Figs.
term
picture
of a
N. 5a-c).
The
despite the fact that it gives an
excellent
fit to all aspects of the experimental
in how the exchanged pion should be corrected
We used the Ferrari-Selleri
form factor
rho widths which were consistently
meson.
Fortunately,
factor
this ambiguity
to use.
underscores
diffractive
accurate
experimental
determination
Method.
Breit-Wigner
interference
resonance
model,
even the lfDrell”
introduced.
skewing
diagram
and
must be
at m’mp
vanishes
he suggests a very
These observations
at mp itself.
method.
A common feature
the interference
intensity
60
of the shape of the dipion mass distri-
of the two classes
incoherent
of
background,
is just that given by the peak of a
shape describing
For the kinematic
factor
besides the Drell
above is that, apart from a small
the value of A in equation (IV.4)
form
the use of any form factors
must vanish at the rho mass,
“Standard”
of the correct
but
that in any case a great deal of the non-
form the basis for the so called standard
models discussed
rho masses vary less,
as has been pointed out by Yennie
bution near the rho mass and especially
3.
expected for the rho
Yennie argues that these other contributions
but realizing
background
question
other diagrams
for gauge invariance.
could be significant,
and fitted
gives fitted
than the Ferrari-
than widths
our lack of knowledge
57 Furthermore,
even by Sliding himself,
considered
sections
Also some theoreticians
in photoproduction.
however,
about 20 MeV larger
and which were on the average larger
still
above, but Benecke and
The latter,
Selleri,
the cross
for its off mass shell behavior.
mentioned
have suggested another form factor.
Durr57
There is uncertainty
data.
an undistorted
rho meson.
In the
term goes through zero at m=mp and
because of the rescattering
explanations
of the skewed distribution,
in all cases becomes unity by definition
- 101 -
corrections
at the rho mass.
the
Hence,
by interpolating
the total forward
ent background)
the data shown in Fig. IV.4
cross section by multiplying
by a factor
p” is
no estimate
data at the higher energies
the previous
fitting
However,
usually
proportional
dependence of the cross sections
which can be substantial
Also it illustrates
can be easily
explicitly
because of the steep slope of the dipion
errors.
These uncertainties
are
Since VDM allows
a com-
(see Section IV. 3), the
form has been taken in which F=n rp/2,
60
The
cross section then becomes
rr
$P,t
the
made for the mass
rp=130 MeV and mp=765 MeV as suggested by D. R. Yennie.
forward
analo-
Because the number
all experiments
and Compton scattering
of the Breit-Wigner
the raw data
to the height of the best fit to the
in the region of the rho mass.
of photoproduction
“standard”
for
is found to be small by
obtained on the choices
above and beyond the usual experimental
with
,
Since
only be reliable
quoted as possible.
when analyzed by this method.
zero width limit
P
F is then given
(IV. 4) in a form as closely
raw data at the value adopted for the rho mass,
parison
resonance.
in the sense that it presents
cross section
in this way is directly
mass distribution
f
procedures.
gous to the p” cross sections
and width,
it will
where such background
from the double differential
compared
for incoher-
this method is not a fit and provides
therefore
background;
This method is standard
obtained
a p-wave
assumed to have the form (IV. 5a) above,
of incoherent
one could find
F which depends only on the o” meson width,
mp f(mp )).
by F = Jf(m)dm2/(2
P
A(mp) (corrected
assumed and on the exact form chosen to describe
the undistorted
to m=m
,=,=2
d&
(m=m p’ t=O) =
- 102 -
A(m
2
)
W.
6)
which merely
mentioned
counter
expresses
above, useful for comparing
results
of McClellan
This standard
determination
production
A(mp ) in a more ,recognizable
et. al.
12
method requires
way.
experiments;
It is, as
in particular,
the
have been obtained by this method.
an interpolation
function if an accurate
of the height of the data at the rho mass is desired.
models discussed
data with high accuracy,
above have been shown to reproduce
lo’ l6 one possible
fit to the raw data with the model,
t=O, and then multiply
procedure
Although
at m=mp and
a good interpolation
cross section data, the fit curves
in the region of the rho mass (see Fig. IV. 2d,e),
mass can cause a significant
change in A(m
).
the raw
is to obtain the best
use this to find d20/dtdm
by F as given above.
can be made to the forward
Since the
so a small
are very steep
error
in the rho
While these sensitivities
P
cannot be avoided,
from the data.
815) MeV,
form
it is possible
Numerical
symmetric
to calculate
calculations
A(mp ) in a more direct
have shown that for the interval
about the value of the rho mass used (765 MeV),
(IV. 5) has the same area to 20/oprecision
Breit-Wigner
under the distorted
interval
By numerical
integration
using m
rp =I30 MeV, the expected value of the double differential
this 100 MeV interval
has been related
the
under an
shape ((IV. 5) with n=O) is essentially
shape.
(715,
for any n between 0 and 6.
This means that the number of events in this symmetric
undistorted
way
the same as
P
-765 and
cross section
to the height of this cross
in
section at
the rho mass:
m=615
(m=m,)
= >
1.1
d%mdm
m=715
- 103 -
2
(IV. 7)
III particular,
this latter
method for finding
the amplitude
A(mp) has been
used for the data of Table IV. 2 and IV. 3.
Finally,
since in the Sb’ding model,
skewed rho mass shape roughly
the interference
cancels in a mass interval
tered at the p” mass (with other backgrounds
of about
turns out to be true of the phenomenological
possible
to relate
differential
numbers
the raw numbers
cross
energy settings,
the mean of d2c/dtdm
differential
cross
by 1.15 to obtain the
cross
rp taken as 130
sections
and slopes
do/dt(t=O)
and the
Ae
Bt
e-B I v
that this procedure
- (It21 + l/BP
average-t
which,
-B t2
I I
0-V. 8)
_ e-B I 31
1tll<
to the maximum
The slope B for events in a certain
by a numerical
815 GeV) are given
from the measured
for events with
is identical
by the stan-
is given by:
-B tl
I I
(It11 + l/B&
<t > was determined
derived
part of the rho (0.715<m<O.
distribution
<t>=
I I
cross section
section d2u/dtdm(t=0)
The slopes were derived
for an exponential
determined
above, by in-
by 711; /2, with
forward
given for the
t bin where scanning
are obtained as explained
the standard
the forward
double differential
in Table IV. 2.
slope.
815 GeV is
the forward
and them multiplying
dard method for the central
where
In Table IV. 3 the
below.
The slopes,
forward
0.715-o.
for the mass interval
These values determine
as discussed
form for all values of n(t), it is
omitting
The values of da/dt
value at the rho mass,
MeV.
100/O)and the same
section at all t values using Eq. (TV. 7).
three annihilation
creasing
of 100 MeV cen-
of events in this mass range to the p”
of events found in the interval
losses occur.
term causing the
solution
It I< 1t2 ( . It can be shown
likelihood
solution
dipion mass interval
for the
was thus
of (IV. 8) where <t > is the average
- 104 -
TABLE
Event distribution
M(*‘a-)
for the reaction
= 0.715 - 0.815 GeV.
are from the ltStandard”
described
T-
4.3 GeV
g
Yp -pn+a-
(@/GeV2)
in the mass range
The corresponding
method
t(GeV) 2
Events
IV. 3
sections
in the text.
I
5.25 GeV
:vents
cross
7.5 GeV
I
Events
g (@/GeV2)
------I
g
@b/GeV2)
.06-. 10
71
65 f 7
52
69 f 9
44
. lo-. 15
60
44* 5
48
51f7
55
44*6
. 15-.20
42
31 f 4
40
43 f6
31
25 f 4
.20-. 30
53
19f2.5
38
20 f 3
40
16 *2
.30-. 40
31
11 f 2
21
11 f2
19
7.7 l 1.7
.40-.80
32
18
1.8kO.4
2.9io.5
25
3.3*
0.6
45f 6
four-momentum
transfer
squared for that mass interval.
given by AB=(aB/at)A<t>
the error
where 8B/8t is derived
on the average four momentum
approach,
dddt(t=O)
P
transfer
Finally,
squared.
the extrapolated
is
For the standard
7rrp/2,
with
values for d20/dtdm
) are also given in the last column of Table IV. 2.
were obtained by assuming
on B is
(IV. 8) and Act>
was taken as d20/dtdm(t=0,m=mp)
rp =130 MeV as above.
(t=O,m=m
from
The error
at
These results
that the data of Table IV. 3 have the ideal shape
given by (IV. 4) and making a simple
exponential
extrapolation
form and the number of events with 0.715<m<O.
based on that
815 C&V and 0.06< I t I< 0.4
GeV2.
The results
IV.1,
obtained by the three methods are summarized
2, 3 and Fig. lV.6.
The fitted p” parameters
given in Table IV. 1 for all six energy intervals.
give the observed
cross section
menological
and corrected
The first
sections
are
three columns
number of events as well as the total channel
at each energy.
The fit results
models are also given.
there is substantial
and cross
in Tables
agreement
using the Sb’ding and the pheno-
Inspection
of Table IV. 1 indicates
between these two fitting
procedures.
that
The
rho mass is around 765-770 MeV and the fitted width about 135-140 MeV.
The cross
section seems to drop by about 30% between 2 and 8 GeV.
In Fig.
IV. 6 the forward
from the central
above are plotted
IV. 6d).
part of the p” as determined
(Figs.
The errors
are similar
differential
cross sections
by the three methods discussed
IV. 6a-c) as well as the total p” cross sections
in Figs.
IV. 6b-d are the phenomenological
to those of the other approaches.
From
IV. 1 and IV. 2 it appears that all three approaches
within
errors.
and slopes derived
Fig.
errors
which
TV. 6 and Tables
yield similar
results
The dipion slope at the rho region is consistent
with a
- 106 -
(Fig.
t- z
(,-Aag/qd)
(ch=u
-1
IO=+) 3
2
- 107 -
0
ad
constant
slope of about 7 GeV
-2
for 4< Eye 8 GeV, and similar
obtained from the Sb’ding and phenomenological
there is a slow drop of the fovard
that observed
by Alvensleben
ward cross sections
other than px+a-.
smaller
Compton scattering
free of possible
Also,
22
at very small
In this regard
t values,
energies.
that due to
is not sensitive
agree well with counare unbiased.
Total and forward
cross
to
cross
section agree at cor-
in Ref.
16.
The total cross sections
methods and indeed they agree.
determined
Thus the kinematic
in the p” matrix
The slope B
element,
it from a fit to the differential
cut off at large m(n’a-)
slopes found by the SBT (B
Since the siding
to the
The Sb’ding model is applied here in a way slightly
in the present work was fitted directly
data).
IV. 6c) is
model can be compared
lo,16
experiments.
from the SBT collaboration
the smaller
it must be admitted
but our results
as well as the slope of the differential
SBT collaboration
in
from channels
and closer
this experiment
from the phenomenological
were fitted by equivalent
tions.
experiments
in the t range where both techniques
those of other bubble chamber
responding
backgrounds
yp-pop
our average slope B (Fig.
in most counter
slopes.
The results
different
lower than those obtained in the counter
losses for short range protons
ter measurements
sections
of our for-
in the 4-body final states which might be hard to
than that observed
to any structure
the magnitude
with
As will be shown in Section V. 3 there is a considerable
with other techniques.
the scanning
However,
consistent
to point out here that the reaction
is essentially
amount of p” production
eliminate
12
are significantly
the bubble chamber
In this energy interval
cross section with energy,
et.al.
It is important
experiments.
fits.
slopes are
model describes
S6d
and small
- 108 -
while
the
p” cross
sec-
t brings
about
=5.9&O. 3 GeV for their
the data very well,
sd
E=4.7
our procedure
CeV
for deriving
standard
the forward
method,
distribution.
&ding
cross section is essentially
using a p” width which would fit the observed
However,
the Sb’ding model fits subtract
ground which is of increasing
importance
method are higher at low E
for the dipion system
appears
description
ReplO and plsl
reflections
lo,16
conservation
tem is valid for
indicate
B.
are displayed.
For most points,
hypothesis
elements
(0.6,
system
61
0. 85)
provides
of the photon
elements
poo,
Backgrounds fmm A
by analyzing
were negligible.
with and without
and in particular
++
cuts
the small
It is evident that the y-p
of no spin-flip
in the s-channel
helicity
sys-
1t 1 up to 0.4 GsV2, and the data from the 7.5 GeV exposure
that the hypothesis
may be good up to
1t 1 = 1.0 GeV2 (see Ref. 62).
Nucleon Resonances
In addition
reaction
to the p” production
discussed
above,
A”
production
via
Fig. IV. 8a shows the M@n+)
at all energies.
++
production is obvious.
Only those
for the 7.5 GeV data where A
(IV. 3) is observed
spectrum
events with rn(R+x-)>l
GeV are plotted.
I t@,Pa+)l< ItCP>P”-)l *
mechanism,
with it,
the helicity
IV. 7 the three measurable
system
the results.
these corrections
the standard
matrix
because the helicity
and phase space were subtracted
t regions,
helicity
In Fig.
in the helicity
and interpolating
back-
IV. 6b
from
in the mass interval
of the distribution
to be conserved.
sections
Fig.
the spin-one density
As has been observed previously,
the simplest
dipion mass
Y’
Using the method of moments,
have been evaluated
cross
to the
the incoherent
as Ey decreases.
indeed shows that the values of the forward
GeV.
equivalent
In black are those events for which
If the nucleon isobar
one would expect the smaller
as is clearly
true for the A’+(l236).
- 109 -
is produced by a peripheral
of these t values to be associated
Fig. IV. 8b shows the same
2.5-3.0
GeV
3.7-4.7
GeV
4.7-5.8
%eV
ltl,(GeV2)
FIG.
N. ‘7--Spin one density matrix elements in the helicity frame for the dipion system
(0.60<m<O. 85 GeV) with background subtraction.
,808Alb
in the p” region
II
x
w
4
5
1
2
w
lo
rc’
m .*
II
h
W
I
>
Q)
W
c
‘t
a
i
(3‘
.
>
0)
f
t
a
z
thing with r? replaced
4.3,
5.25,
In Figs.
by g-.
and 7.5 GeV regions
IV. 8c and d the combined
is shown for M(pn+) and M@a-) respectively,
using only those events with m(a+x-)>l
those with the lesser
pelling,
momentum
the accumulation
GeV.
transfer.
The solidly
blocked
events are
Although not statistically
com-
of events in the 1.9 GeV region for pnf and the
1.6 GeV region for pa- indicates
m(ni7r-) >l GeV are probably
Drell
data for the
that a substantial
accounted
fraction
of the events with
for by N* production
(e.g. , by the
process).
In Fig.
as determined
IV. 9 the cross sections
- f-b
for yp ---L A A
at the six energies
from the phenomenological
fits using a relativistic
delta shape5’ of the form given by (IV. 5a) are plotted.
dence of the delta cross section
with a slope a=l. 74tO.16,
hadron collisions
is well descrtid
One would expect nil=.
difficult
mechanism
involved
meson exchange.
5 (oi3=.
to draw decisive
and the reflections
the reflections
are minimal
with
~0.4
mechanism
63
The use of a
of the cross section,
0) in the Jackson system
for the delta
proceded by pure one pion exchange (OPE;).
from the density
1t@ ,pr+)l
ETa
29
not change the slope.
however,
a-A++)=
which is close to the slope for quasi-two-body
produced by non-strange
decay if delta production
The energy depen-
by U( yp -+
delta shape other than (IV. 5a) may reduce the magnitude
but will
p-wave
conclusions
matrix
elements
about the A’ ’ production
because of the small
from the o” events.
=0.21*0.10
other than pure OPE.
- 112 -
statistics
For the 7.5 GeV data, where
(see Fig. IV. 2), the matrix
GeV2 is &
It is,
element
which probably
for events
indicates
a
I0.C )-
I
I
I
I
III
8.CI6.C )-
\
T
5.c l4.c I-
-
2.0
5
‘k
t
“x
1.0
b
0.8
0.6
\
0.4
^ -
z .w
I
-
I I
6.0
4.0
E,(GeV)
FIG. IV. S-- Cross sections for yp -+ A’+ T- as obtained with a fit to a
relativistic
p-wave Breit-Wigner
for the delta.
The solid
line represents the best fit to the form A Eea.
Y
- 113 -
C.
terval
Higher
Mass Vector
Meson production
Vector
mesons with square of their
about 1 GeV are predicted
decay width,
crepancies
existence
but presumably
(p’)
mass forming
by the Veneziano
a series
15
model,
allowed to decay to two pions.
between VDM and experimental
with in-
with uncertain
Also,
some dis-
data could be reconciled
of higher mass vector mesons (see section IV. 3).
by the
No evidence for
such states is to be found in the spectra
of Fig. IV. l-2.
data the number of events with m(x’x-)
> 1 GeV turns out to be especially
small.
Furthermore,
as was shown in the last paragraph,
the events appear to correspond
angular distribution
to rN interactions.
of the T+ in the dipion helicity
two t ‘(Y , a~) intervals
transfer
(t’=t-t,m,
for the given mass).
If the p’ were diffractively
interaction
( sin20f
to occur with
In Fig.
system
Iv. 10 (a-b) the
is plotted
The shaded events represent
produced
distribution),
in a center-of-mass
helicity-conserving
= 11/16.
for events with lcosef;II
to events with momentum
transfer
Fig.
< 6.5.
squared to
These events with
lcoseH )<0.5 and
77
to 1 event/(O. 1 GeV) in the 1650 MeV region and
1 GeV) in the 1250 MeV region,
level that up (1600)<0.1
momentum
then one would expect most of the p’ events
the dipion system less than 0.4 GeV2.
GeV2 correspond
for the
the A++ events.
lcos @:I cO.5, i.e. , with N( lcos er? <0.5)/N(all)
The shaded areas correspond
4 events/(O.
a large number of
where tmin is the minimum
IV. 1Oc shows the dipion mass distribution
t’~O.4
For the 7.5 CkV
pb and up (1250)<0.3
indicating
with 90% confidence
pb per 100 MeV width of such
resonances.
IV.2
Omega Meson Production
The analysis
of the reaction
YP-+@P
- 114 -
0-v. 9)
YP---
((
,‘;r
p7f+x-,
M(~~%r-bl
I
(b) lt’l>0.4
1) It’1 CO.4 GeV
30
GeV, Ey=7.5
GeV
GeV
r---l
2c
ri
6
4
2
2.2
1.8
M(x+fl,
2.6
GeV
3.0
,*clB*i:
FIG. IV. 10--(a), (b) Angular distributions
of the ?r’ in the helicity frame
of the dipion system for events with m(n%-)>l
GeV for the
7.5 GeV data. Shaded area represents delta events.
(c) Dipion mass diskibutions
for those events with (cos e$< 0.5. 2
The shaded area represents events with It (y , a?r)l < 0.4 GeV .
-1 .5 -
is more complicated
than that of p” photoproduction
pn+n-a0 is much more complex
discussed
In addition
above.
and difficult
due to the presence
channel does not have a single resonance
does in the pn+lr- final state.
events,
saturating
for the 1-C channels
of the contamination
of the annihilation
to noise ratio by removing
Although
omega production
the narrow
over relatively
large backgrounds.
omega signal observed,
in section
necessarily
proof the
has given some
events by events
mass cut which optimizes
the
events,
leads to a neutral
It has therefore
is consistent
particle
been possible
in
to deterand brems-
mass distributions
with the reaction
pn+r-(mm)’
for eight intervals
of the reconstructed
energy intervals,
reaction
>O. 005.
(Iv. 10)
photon energy Ey . In the three higher
(IV. 10) is identified
with the missing
level
III.4
one pi-zero
Fig. IV. 11 shows the x+x-x0 invariant
yp -
cut on confidence
The discussion
for events induced by both annihilation
for fits where track ionization
photon energy,
but also significant
width of the w meson makes the signal detectable
mine omega cross sections
photons.
a missing
this
the channel as the rho
most of the contaminating
the final state,
s trahlung
of bremsstrahlung
and plr”po is observed.
of other channels and has determined
signal
particle
for about 15% of the events in this channel,
section determination
indication
by multi-neutral
Not only is a prominent
duction of the final states A++pcross
to analyze than the 3-body channel
,to the contamination
events and to complications
accounting
because the channel
by a 1-C fit to the annihilation
mass cut determined
The restriction
- 116 -
in section
III. 4 and a
to 1-C fits satisfying
the
(0)
I----
320
’
Ey=l.2-1.5 Ge\
280
’
’
(b)
Ey = 1.5-2.0
(1239
(742 Entries
GeV
Ey T 2.0 -2.5
Entries)
(978
GeV
EntrIes)
240
>
2 200
0
160
p
II /
/’
1111
-%&!kl
2
iTI
120
2
80
rll
0.6
1.0
0.8
I
0.6
I1
L
1.0 1.2
0.8
1.0
0.6
M (TT+TT- TO)
80
I
’
I
’
I
’
!e)
I
I
’
I
’
I
$ 60
w
(651
- 4.7
’
I
’
I
’
(9)
I
Ey=4.7-5.8
GeV
(453 Entries)
I II Ey’3.7
I .4
GeV
Ey = 3.0 - 3.7 GeV
(603 EntrIesi
k
1.0
0.6
1.4
nn
fl
(h)
(f)
I
GeV
Ey = 6.8 - 8.2
Entries)
(495
Entries)
I
40
20
0
0.8
1.2
I.6
2.0
0.8
1.2
M (TT+TT-TT~)
1.6
GeV
2.0
2.4
2.8
lWSC3
FIG. IV. ll--a+~-P
invariant mass distributions
for yp ----t p~+x-~’ with
photon energies in the rang= of 1.2-8.2 GeV. Dashed lines
indicate the phase space background assumed.
- 117 -
missing
mass and probability
bremsstrahlung
cuts removes
background.
Although
fits to events in the bremsstrahlung
clearly
identifiable
In order
to be considered:
tamination
no such cuts are possible
region,
and
for the O-C
in every case the w signal is
increasingly
over background,
to determine
most of the multi-neutral
so at higher
the w cross-sections
several
corrections
(a) loss of events with a short (invisible)
of the data by events not belonging
energies.
proton;
had
(b) con-
to the channel p?r+~-x’,
mainly
events in which more than one x0 was produced and which nevertheless
a good 1-C fit or a O-C reconstruction
(c) contamination
at lower
Ey according
of the data by events of reaction
photons outside each selected
gave
to Eq. III. 6;
(IV. 10) produced by
energy band, which gave acceptable
1-C or
O-C fit with Ey inside the selected energy band;
(d) loss of omega events
because of the cuts in the 3-pion mass spectrum
introduced
omega event or because of the cuts used to eliminate
These cuts were (i) 0. 68<m(n+n-so)<
(probability
cut).
cut) and (iii)
Since correction
estimated
(a) is essentially
for E<3 GeV, and 10-14s
study of corrections
has been used.
the missing-mass
w events significantly
removed
(effects
reactions.
P( X 2, >O. 005
mass squared
it can be best
It turned out to
yp -pop.
in the energy range 3-8 GeV.
Both pw and phase-space
Study of the fake events has indicated
imposing
a scanning loss,
(b)-(d) the track and event simulation
jected to the same geometry-kinematics
(ii)
10 GeV3 (missing
by using our more abundant reaction,
be negligible
background
0.88 CeV (w-cut),
0.18 < MM2<0.
to define an
program
events were generated
fitting
For the
PHONY
and sub-
and cuts as the real events.
that for the annihilation
(1-C) events
cut (-0. 18<MM2< 0.10 GeV2) did not affect real
whereas
contamination
(c) and (d) resulted
(b) above is almost
entirely
in a long low level tail on the expected w
- 118 -
mass distribution).
approximate
The net corrections
knowledge of them should give a good final cross-section.
the five lower energy intervals
of the fit was generally
overall
corrections
energy intervals
A further
Previous
The
in Table IV. 4 and for all
than the statistical
accuracy
9,lO
have shown that the cross
significantly
of a substantial
with increased
contribution
of the data.
w decay
(which has a cross section63
cross section from a diffractive
section
approximately
process.
for omega
photon energy,
from the one-pion
The data at high energy flatten out, indicating
constant
accuracy.
in the bubble chamber.
decreases
indicative
Ey-2 ).
measuring
(a)-(d) are specified
For
from the O-C nature
of 10% was applied to account for the neutral
experiments
photoproduction
uncertainty
by the better
they are smaller
modes which are not visible
(OPE) process
the increased
countered
for effects
correction
behavior
amounted to about 10% and thus even
a
exchange
proportional
in addition
to
a nearly
This work has extended
the upper range of photon energy to 8.2 CeV, as well as making independent
measurements
in the energy range 1.2-8.2
the cross-section
presented
is shown in Fig.
together
at SLAC.
for reaction
than the pry
more to reaction
In Fig.
IV. 12a our results
A more comprehensive
(IV. 9) is given in Fig.
From SU(3) it is expected
larger
IV. 12.
The energy dependence of
are
with the recent data at 2.8 and 4.7 GeV from the polarized-
photon (laser) experiment
cross-sections
CeV.
19
in the ratio 9:l.
of
IV. 12b.
that the WAY coupling
Thus one-pion
(IV. 9) than to co production
compilation
should be much
exchange can contribute
and in fact be a substantial
A fit has been made to the data of Fig. IV. 12a (for E>2.0
part.
CeV) by a curve of
the type
C(YP -wp)
= c
OPEEy
+1+
- 119 -
c
DIFFEy
-‘y2
(Iv. 11)
TABLE
Number of observed
chromatic
events,
corrected
total channel cross
sections
IV. 4
w events,
as a function
-
EyWV
Events(a)
Observed
No. of w” Events
Observed
w total cross
sections
of the incoming
l- crT(W)(C)
Corrected
04
and mono-
photon energy.
Total Channel
Cross Sections
W)
1.2 - 1.5
742
220
235
6.9 f 1.4
1.5 - 2.0
1239
180
194
6.7 f 1.2
2.0 - 2.5
978
141
150
6.9 * 1.5
2.5 - 3.0
512
66
75
6.2iO.S
3.0 - 3.7
603
34
3 6(b)
2.8 rt 0.7
3.7 - 4.7
631
81
g5(Q
2.9 zk 0.4
18.2 f 2.0
4.7 - 5.8
430
52
57(b)
2.3 f 0.4
13.5 * 1.5
6.8 - 8.2
464
68
731b)
2.0 f 0.3
11.8 i 1.2
(a)
Unique OC events for the bremsstrahluns
data (1.2 -23.7 GeV) and events
surviving the missing mass (-. 18 < MM < . 10 GeV ) and probability
(P(X2) ? .005) cuts for the 1C data (3.7 - 8.2 GeV).
(b)
Including
10 - 13% forward
(c)
Including
w neutral6
scanning
loss correction.
decay modes (10% correction).
where Ey is the photon laboratory
energy in GeV.
It has been assumed that
the energy dependence of the OPE and diffractive
mated by a power law.
o2 should be small
cyI is expected
63
since the diffraction
contributions
can be approxi-
to be in the range 1.5-2.5,
cross-section
and
does not depend
accurate for a good determination
on E . The data arenot sufficiently
Y
of all 4 parameters appearing in Eq. (IV. 11). Hence, an energy dependence
strongly
is assumed for the OPE part ((rI=2.
These values yield CopE=(31.*5.
curve on Fig.
) with constant
) pb and Cl,IFF=(l.
IV. 12 represents
A similar
CeV), and with fixed ol(l.
in Ref.
COPE=(16.4*5.
possible
A2 and f exchanges
(Pomeron)
amplitude,
8) pb,
proportional
65
and their
The full
calculated
fit over a more restricted
range (E =2.0-5.8
would hope to detect terms
term (02=0.).
5*. 3)pb.
the omega cross-sections
Eq. (IV. 11) using these values.
10 yielding
diffractive
with
energy
6) and (r2(0. 08) was attempted
CDIFF=(l.
9*0.9)pb.
Ideally
one
to E -’ and Eyoe5, to account for
Y
interference
with the diffractive
but since the present
data are insufficient,
such terms
are assumed to be small.
The parameterization
(IV. 11) determines
tive (natural)
and OPE (unnatural
cross-sections
at all energies.
the two processes,
elements
the differential
for reaction
The calculated
parity
the diffrac-
exchange) contributions
to the w
Thus, with some plausible
cross-sections
(IV. 9) can be calculated
OPE contribution
above is shown as a function
line in Fig.
IV. 12a.
For comparison,
assumptions
and the density
and compared
to the cross-section
parameters
for w production
independently
about
matrix
with experiment.
determined
by the
of the photon energy by the dashed
the unnatural
at 2.8 and 4.7 GeV as determined
- 121 -
exchange cross-sections
recently
in the polarized
I
I
I
I
I
’
I
I
I
I
I-
. cT This Experiment
A cT Ref. 28
8.0
(a) -
6.0
4.0
g
2.0
.
TOTAL
‘t-A,-
----_ OPE
E
3
. ‘This Experiment
x Ref. 9
0 Ref. IO
A Ref. 28
0 Ref. I I
t
g
8.0
b
6.0
t
if
2.0
0
I
0
I
2.0
I
++\
I
4.0
(b) -
1. *,
+
I
I
6.0
I
8.0
I
IO 16
Ey(GeV)
yp -+wp
total cross sections measured in this experiment
FIG. IV. 12--(a)
and in Ref. 28. a u is the unnatural parity exchange cross sections for 1t 1Il.0
GeV2 at 2.8 and 4.7 GeV. (Ref. 28). The
curves are best fits to Eq. (IV. 11) for crl=2. 0 and cr2=0 (see
text).
(b) Compilation of yp -wp
cross sections (Refs. 9,10,
11,28 and this experiment).
- 122 -
photon experiment
observed
are plotted.
cross sections
The observed
The agreement
and
is good.
differential
above 2.0 GeV is shown in Fig.
cross section dc/dt
IV. 13 (a-f).
ably well with the data, have been calculated
part of the amplitude
between the calculated
in the forward
OPE part is assumed real,
The curves,
which agree reason-
as follows.
Since the diffractive
direction
the amplitudes
for photon energies
is purely
imaginary
do not interfere
and the
and the cross
section may be written:
OPE
da _ da
dtdt
The OPE part of the cross-section
corrections,
Fermi
and
+ d<fFF
was calculated
using a sharp cut off absorption
r(wry)=1.2
MeV.
.
with final state absorption
model
The diffractive
(Iv. 12)
66
with a radius of R=O. 8
part of the cross
section can
be written:
daDIFF
dt
with B=(?. OlO.4)
in the previous
GeV
-2
section.
section
, which is the average value for the so slope obtained
by natural
parity
photon experiment.
(the diffractive
(IV. 13a)
This also agrees with the value of B=7.5*
for omega photoproduction
the SLAC polarized
= A&p ---cw DIFF P)e Bt
part)‘obtained
28
1.5 GeV
exchange at 4.7 GeV obtained
Since the asymptotic
-2
in
omega cross-
above is I. 5&O. 3 pb, the forward
cross
section becomes :
A(yp -w(DIFF)p)
This value together
= QDIFF)*
B=lO. 5*2. I/&/G&
with the corresponding
be used in section IV. 3 to derive
the direct
- 123 -
forward
.
(IV. 13b)
co cross-sections,
VDM couplings
of photons to
will
yP -‘UP
50
IO
I
0.5
IO
5
I
0.5
0
0.2 0.4 0.6
0.2 0.4 0.6
ItI (GeV*)
FIG.
0.2 0.4 0.6
I,a,*5
IV. 13--Differential
cross sections da/dt for the reaction yp ewp
with photon energies above 2 GeV. The curves are the calculated cross sections (see text).
- 124 -
vector
mesons as well as for comparisons
results
from
the omega decay density
H
pl 1 in the helicity
=
Pijtt)
The diffractive
dt
DIFF=
and thus gives poo
matrix
The final results
results
are shown in Fig.
using the relation:
daDIFF
dt
pfFF(t)
has been assumed to be helicity
DlFF
DIFF
= 0 in the helicity
=Repl0
cl-1
IV. 14.
con-
frame.
with the sharp cutoff model mentioned
of the calculations
Dominance
In the preceding
yp -pop
as well as our experimental
Again fair agreement
between theory and
Model Tests and the Photon-Vector
sections
have been obtained,
the constant,
forward
the defining
differential
cross
and a simple
and hence presumably
Assuming
diffractive
sections
Meson Couplings
for the reaction
model has been used to extract
diffractive,
part of the omega cross
the same slopes for rho and omega production,
differential
characteristics
the most valid comparison
direction
H
H and
coo , RePlO
elements
obtains.
Vector
section.
+
da
x
was calculated
above.
IV. 3
pEPEft)
part of the cross-section
The OPE density
matrix
frame were calculated
daoPE
experiment
with
Compton Scattering.
Finally,
serving
of these cross-sections
cross section
of diffractive
has been deduced.
production
7.5 GeV.
behavior,
in the forward
At this energy
the values obtained are A(yp -+
pop)= 99* 12p b /CeV2(averaging
methods in Table IV. 2) and A(yp
-+wp)=!0.5~2.1~b/GeV2,
- 125 -
Since one of
is its asyptotic
of the rho and omega cross sections
will be that made at our highest energy,
the omega
the three
yieldinga
Ey =3.7-8.2
Ey = 2.0~3.7 GeV
0.6 r
GeV
r
1
-0:
.L
0.4
=i
rr”
0.2
0
-0.2
II-
II
Q
I
-0.4
0
I
0.2
1
I
0.4
I
0
It I (GeV*)
I
0.2
I
I
0.4
1783A6
FIG. IV. 14--The spin density matrix elements poo , ReIO and plWl in the
The curves are
helicity system for the reaction yp --twp.
the matrix elements calculated with the OPE model discussed
in the text.
- 126 -
forward
cross
section ratio of
NY&
It follows
=
gg*12
10.512.1
= 9.4k2.0
.
(Iv. 14)
from VDM that this ratio should be the ratio of the photon-vector
meson coupling
Within
constants.
the framework
photoproduction
can be written
$
where g2
YV
of VDM the diffractive
in terms of vector
(YP --+VOP)
is given in terms
the optical
of the vector
theorem
meson elastic
coupling
2
yv-1
4r
l- I
constant by
(IV. 16)
as the following
between the total cross section and the spin averaged
for elastic
as
(Iv. 15)
.
can be written
meson
scattering
2 da (vop -+v”p,
= grvx
2
o!
gyv=-z
In general,
part of the vector
forward
relation
cross
section
scattering:
(Iv. 17)
where TJ is the ratio of the real and imaginary
amplitude
(i.e.
, n =0 implies
a completely
When combined with Eq. (IV. 15), the optical
6&T
C,(VOP) = 7
where v” is any vector
neutral
gives
meson.
rho and omega meson,
a relation
between y2
1
parts of the forward
imaginary
amplitude
theorem
becomes:
[ 1
‘:’
-I
4n
Assuming
da
dt
(YP -+VOP)
and the forward
- 127 -
at 0 =O”).
t=0
equal total cross sections
as the quark model predicts,
49
scattering
(IV. 18)
for the
Eq. (IV. 18)
cross section ratio IV. 14.
Neglecting
the squares of which are known to be small, 67 the
the real parts,
to g”yw is given by the ratio
ratio of g2
YP
(IV. 14) of forward
cross sections:
2
YzJ
-=
3.L
2
gYW
(Iv. 19)
.
Y2
P
This agrees reasonably
= 7.3&l. 3.
P;p/P;w
9.4+2.0
well with the colliding
beam result
which finds
It is also very close to the most simple
ments I9 which predict
Furthermore,
W(3) treat-
that this ratio should be 9:l.
VDM can also be used to expand the amplitude
Compton scattering
13
in terms
of the amplitudes
for vector
for
meson photoproduc-
tion :
a(-ip -
YP) = 2:
gyp
a&p -V”P)
.
(Iv. 20)
w~=Pc,~,~)
P
Using this expansion,
the optical
the following
between the total photoabsorption
imaginary
relation
(diffractive)
tion of vector
theorem,
part of the forward
with the ratio of yt and yz
of y
;
a value for yz/4a.
and
cross
cross section
21
of cT(yp),
n2)
section and the
for the photoproduc-
IV. 15, with
this relation,
together
given by (IV. 19), as well as assumptions
T$ (nt is estimated67
Our experimental
given in Fig.
a(0) = iJdT,(l+
mesons results
Using the recent measurements
magnitudes
and writing
to be about 0.04),
determines
values for the right hand side of Eq. (lV.21)
y,2/4s adjusted
- 128 -
for best agreement
on the
are
with the total
--
G-
4
4-
-
--a-----X----w--- ”
--@-+F=YF=
s
- 129 -
cross
section
21
measurements
cesses is seen to be similar,
essentially
logical
indicating
both subtract
cross sections
the incoherent
from
that the coupling
while the ratios
and Anderson
et al.
which becomes more prominent
of the omega and phi diffractive
of the couplings
The best agreement
to note that our experiment
section
us confidence
of two different
r,2/47r.
ring experiments).
evaluated
experiment
Eq. (IV. 19)
A similar
that no systematic
experiments
problem
in relation
The recently
sections
certainty
a result
22
direct
allow a further
of the extrapolation
in agreeThis gives
by using the results
experiments
in both hydrogen
a coupling
constant of
(N. 21).
measurements
of Compton scattering
test of the VDM idea, which avoids the un-
to t=O for the p” data and the assumption
real part in Compton scattering.
In the approximation
tudes (IV. 20) all have the same phase (e.g. , all imaginary)
same spin structure
Itis
(IV. 21) to obtain the best value of
with aT (yp) via relation
reported
precisely
in Ref. 21.
is introduced
in the energy range 3-8 CeV require
about 0.3 when compared
com-
the total photoproduction
described
We thus conclude that photoproduction
and deuterium
small
12
et al. , res-
have been obtained from
(see Ref. 1) at 7.5 GeV, obtaining
ment with the more complete
cross
cross
made on 4.3 CeV yd data found the value yi /4~ =O. 28&O. 04.
interesting
at
is obtained for yE/47r =O. 32*0.03
(and not 0.50 as obtained in the storage
cross
are
and phenomeno-
have been taken from section IV. 2 and from Anderson
pectively,
parison
constants
Table IV. 2 has been used since they
background
The magnitudes
lower energies.
The s dependence of both pro-
The average of the &ding
energy independent.
forward
sections
also shown.
at all t values,
one obtains
- 130 -
the following
of a
that the ampliand have the
relation
between
Compton scattering
and photoproduction:
In the general case when the phases can differ
VDM would require
the left
hand side of Eq. (IV. 22) to be less than or equal to the right hand side (the
rho appears to be transverse
from the density
Fig. IV. 16 shows our results
for the right hand side of Eq. (IV.22),
the above value of ~;/4s.
The standard
matrix
815 CeV, where the Siding interference
have been used for the rho term,
explained
cross
above.
sections
standard
22
forward
cross sections
measured
butions.
Excellent
to determine
in Fig.
only diffractive
cross section has already
GeVS2) is in agreement
conclusion
direction
our best
contri-
data and Compton
is available.
the coupling constant,
what different
to the p”
is obtained at all values of s and t
been used in Eq. (IV. 21)
the real meaning of the agreement
IV. 16 is that the slope that we observe
of 7.OkO.4
represent
between the photoproduction
(via the VDM equation (IV.22))
Because the forward
Compton scattering
in the forward
Thus the curves
for the right hand side of (IV. 22) assuming
where data on both reactions
as
cross section plus the omega and phi diffractive
estimate
scattering
estimated
The lines in Fig. IV. 16 correspond
as in (IV. 21).
agreement
using
term is expected to cancel)
slopes from Table IV.2 and are normalized
to the sum of the co standard
IV. 7).
with mass in the interval
with the omega and phi terms
Also shown are the directly
on hydrogen.
of Fig.
values in Table IV. 3 (which are the
raw data obtained from the number of dipion pairs
0.715-o.
elements
in photoproduction
with Compton scattering.
observed
(an average
This is a some-
than that reached in Ref. 22, since the slope they
- 131 -
YP-YP
I
I
1.0
i
I
l
Predicted From This Experiment
(Effective r;/47r
=0.3 2)
o
Anderson
et al. (5.5,8.5
x
Boyarski
et al. (8 GeV)
n
Optical Points (Caldwell et al.)
GeV)
n
7
1.0
-
0.5
;G‘
0.2
-
0.2
2
?
**
I .o
=
0.1
0.5
-
0.05
-
5
0.02
0.1
0.05
I
0.2
0.4
0.6
Itl (GeV2)
FIG. IV. 16--da/dt for Compton scattering calculated from the present
photoproduction
data of Table IV. 3 using Eq. (JY. 22) and
-$ /47~=0.32.
The straight lines represent our standard
fits (see text).
The VDM predicted cross sections are
compared with recent Compton scattering measurements
of Ref. 22 at 5.5, 8 and 8.5 GeV.
- 132 -
assumed for photoproduction
be noted that our forward
counter
experiment
“inelastic”
was about 8.5 CeV
rho cross sections
values. l2
rho production
a larger
mass interval
function.
Furthermore,
observed
if there were any anomalous
that the two processes
within
and over a restricted
stant,
it is possible
to satisfy
pairs
range of comparison
value of 72/4s
disagreement
smaller
meson mass shell).
with the production
obtains rough agreement
of ~:/47
that is required
they seem to require
or the electron-positron
ring value (which has
in the comparison
of vector
in magnitude
mesons by pions ,
with the VDM predic-
71
on complex
This coupling
nuclei
12
values of ~:/411 (0.6-I.
storage
ring experiments.
7: /4~,
0) than this experiment
This implies
that simply
a change of coupling with meson mass cannot account for the deviation
- 133 -
has
and
such studies did not yield a unique value for
larger
of
around 0.30, ‘70 but in this case there may be
in the t dependence of the two processes.
72 Although
con-
by our VDM
Furthermore
also been evaluated from rho photoproduction
deuterium.
the same s
determined
than, the storage
constants
and
the VDM tests.
is close to, but significantly
tions for coupling
and
the y-p coupling
The magnitude
one also usually
would be completely
of photoproduction
tests in hydrogen is not at all clear.
single pion photoproduction
of the differ-
have the same t dependence,
only one parameter,
The meaning of the effective
photons on the vector
by using
t values ( 1t I< 0.04 GeV2), this experi-
of electromagnetic
so that by varying
69
extrapolation
behavior
We conclude from our comparison
large errors
than some
may be accounted for by the
in this and other experiments,
Compton scattering
dependence,
In this context it should
to define the o” or by using a different
ment with its large background
to it.
.
and slopes are lower
This discrepancy
ential cross section for very small
insensitive
-2
from
the storage
ring value and therefore
of y-p coupling
in the nuclear
further
at the photon mass shell.
effects
the discrepancy
seems to lead away from a unique value
involved,
However,
because of uncertainties
and the other differences
between our results
and the complex
in the experiments,
nuclei
results
needs
form.
It is
investigation.
Thus VDM appears to be violated
conceivable
that more vector
in its most simple
mesons (or multi-pion
structures
same quantum numbers as the photon) are required
to saturate
(IV. 21) with the photon on its mass shell,
even though no direct
V-nucleon
Similar
scattering
conclusions
deuterium.
amplitude
relation
evidence for
is that the
73
changes when the V is off mass shell.
such objects can be found in this experiment.
Another
having the
possibility
have been reached in studies of photoproduction
68
- 134 -
on
CHAPTER
RESONANCE
PHOTOPRODUCTION
As discussed
in Chapter III,
are much more complex
multi-neutral
eliminate
to isolate
mechanism
beams.
for determining
energy is calculated
was the complete
superior
the missing
production
obscuration
Fig. III. 9.
mass),
making the analysis
Equally
production
O-C
could be
troublesome
in the single
of the photon energy for the
dominance
model.
and
the
with the rho because
As can be seen in Fig.
IV. 11,
from the rest of the channel at the
Consequently,
most of the work in this chapter
the omega reflection
of the remaining
in Section III.4
found in these final states,
has been done with a cut on the 3-pion mass spectrum
This cut removes
final states
experiments
only upper limits
in Chapter IV together
the omega events are quite well separated
meson.
that
beams had no
and presented
resonance
has been discussed
they are related by the vector
are visible.
background.
as a function
The most prominent
peak energies.
to earlier
which was observed.
channels have been derived
omega meson,
annihilation
results
of some resonance
The total cross sections
and
mass of an event (because their
a missing
final states by multi-neutral
single neutral
to the class of four-body
Since the bremsstrahlung
assuming
given for the resonance
from bremsstrahlung
particle
This has been one of the main areas where
photons.
beam has provided
using bremsstrahlung
STATES
mass squared were determined
most of the events not belonging
the annihilation
FINAL
than those channels where all particles
cuts on the missing
produced by annihilation
neutral
IN FOUR-BODY
the channels with a single neutral
and difficult
background
In Section III.4
V
to remove
in other particle
the omega
combinations,
events much more straightforward.
- 135 -
This chapter presents
- ++
and yp ,A&,
A
YP-P
rho production
by yp -P
nucleon isobars.
results
on the quasi
as well as presenting
paN and a complete
The fits to resonance
using the multidimensional
maximum
production
without
into account the reflections
likelihood
ground to other channels.
channels where many resonances
The fractions
multidimensional
Ai +=‘n-,
likelihood
A”&ro
A%-,
, p+pn-,
omega events had been removed.
and unassociated
in computing
each in fairly
fit to the states : A++p-, A+p”,
p”p7ro , p-p=+ and phase space,
The cross sections
program
Furthermore,
monochromaticity
using the SLAC backscattered
sections
The final states
laser beam.
31
events were similar,
considering
the different
types of
involved.
improved
by “shaping”
phase space with
factors
(l+a* m 2(ps+))/[(l+b.m2
These factors
multineutral
could not be identical
The fits were substantially
the empirical
after the
used were the same as those for the recent
the methods for excluding
although they clearly
A”p+,
obtained for the various
considered
experiments
for
were obtained by a
in Table V. 1 for all three energies.
photoproduction
the back-
small amounts.
final states are presented
and the fitting
takes
is very advantageous
of events in the channel p?r’r,-*’
maximum
74
MURTLEBERT.
It also automatically
fitting
are present,
of fits to possible
program
resonances
This simultaneous
on inelastic
have all been performed
associated
double counting.
of the various
observations
summary
production
This method allows us to fit simultaneously
resonance
two-body reactions
did not alter
for unassociated
(T+t - )) (l+c* m2(r+no))
the delta-rho
rho production
(l+d. m2(nor-))]
fractions,
significantly,
- 136 -
.
(V. 1)
but they changed the cross
while simultaneously
TABLE
Cross sections
resonance
obtained for the reactions
production
the single resonance
therein.
v. 1
yp,pi~+a-no
Associated
resonance
values and no correction
and yp *nx
production
++ ‘TI T , and for
is excluded from
(except w) was made for decays into
other channels.
T
Final
State
a)
1
Ey(GeV)
3.7 - 4.7
4.7 - 5.8
6.8 - 8.2
pATIT
18.2~2.0
up(*)
2.9io.4
2.3 ~0.4
2.0~0.3
o-A”
1.8 i 0.4
0.920.35
1.120.2
p”A’
O.lrtO.2
0.5 + 0.2
0.3 t 0.2
;A0
O.likO.2
0.4 k 0.3
0.2~0.2
p-p7T+
0.8t0.5
1.7io.5
0.7LO.4
POPTO
0.5t0.5
(**)
p+PT-
1.8~0.5
7.950.5
3.110.4
A+++lTOll-
0.5L
0.62
0.O;tO.l
A+ ?: A-
0.320.3
O.OkO.3
0.5 to.2
A07TiT0
o.ot0.3
0.0 + 0.3
O.OkO.5
7.5Ll.5
4.6 it 1.4
4.0+
0.5 i 0.3
0.220.2
0.6~0.3
0.3 + 0.3
b)
0.4
A-77+1:
1.4*
+
“A2
0.8~0.3
pOnr+
1.2k
(*)
(**)
pb
0.4
13.5 L 1.5 pb
0.7
(**I
Including 10% neutrals.
Unacceptable fits: see text.
- 137 -
11.8 & 1.2 pb
0.9 + 0.4
0.3
1.2
2.0~0.6
improving
the chi-square
of the fit in the various
It has been assumed that this empirical
determination
mass projections.
mass shaping allows
of the amounts of specific
when all the deviations
two-pion
resonance
of the backgrounds
a more accurate
production
in the channel
from pure phase space are not
fully understood.
There are numerous
possible
expected phase space shape.
duality,
that all background
crossed
channel,
inappropriate
tion of the resonances
priate
to modify
is merely
75
present
reflections
a manifestation
Another
possibility
(observed
this would change the resulting
to return
but with each curve consistently
In the mass projections
low mass enhancements
to something
A; and A;.
of multi-neutral
76
events
The net result
of these
like hand drawn backgrounds,
can be noted at all energies,
the presence
cussed in the next section,
phase space.
of the 3-pion final state (See Fig. IV. 11) signi-
The shape of the data deviates
Considering
in the 3.0-3.7
may change the
into all mass combinations.
by phase space together with the reflections
channels.
in a
i. e. , it may be appro-
phase space.
projected
of
phase space is an
the usual phase space to a so called peripheral
present,
higher ones.
invariant
and unobserved)
if there were indeed a large contamination
ficant
of resonances
in other mass combinations,
is essentially
from the
is that the angular distribu-
Finally,
modifications
for this deviation
It may be, as suggested by some forms
in which case the usual Lorentz
assumption.
shape of their
explanations
strongly
the
from the shape implied
of all the resonances
of Ai in the afn’r-n
and the suggestive
especially
in other
final state,
as dis-
bumps at the A2 mass visible
CeV and 7.5 CeV data, fits were made to final states including
These fits allowed
CeV of A mesons.
0*2% at 4.3,
This corresponds
SW% at 5.25 and 13*2% at 7.5
to an upper limit
- 138 -
of 1~ b on AI production
at 7.5 GeV with 90% C. L.
the deviation
rather
These percentages
of the shape of this mass spectrum
than actual presence
of. A;
in Table V. 1)obtained
using the shaping factors
Moreover
effect on the fractions
,fitting
This topic will
above.
with the
of the final states
in the data when the backgrounds
discussed
of
from pure phase space,
mesons.
Ax
or
A mesons included had no significant
(listed
may be just a manifestation
were obtained
be examined
more
fully in the Section V. 2.
v. 1
Associated
Rho and Delta Production
Associated
rho and delta production
-
YP-+P
has been observed
in several
previous
Since the p- cannot be produced
tion is that reaction
rho radiative
difficult
given
decay width,
ii-
W.2)
bubble chamber
for reaction
are proportional
of I’(war))
of &H
This experiment
(V. 2) up to 8.2 GeV.
as a test of the OPE assumption.
In fact,
dominated
by an OPE process.
of
which were based on this assumption.
r(pay)
Only the monochromatic
This questions
events,
the
by SU(3)lg and
y) have therefore
been
extends the cross section
Thus the energy dependence
serving
the dependence of this cross section
on the photon energy is found to be quite different
63
assump-
to I’(pny),
- ++
can be studied for a wide range of photon energies,
A
ofw-p
9,lO
through one pion exchange (OPE).
(l/9
Estimates
experiments.
the next most simple
mainly
which is small
using an OPE model.
measurements
A
- f-t
A
cross sections
to measure directly.
9,lO
in the reaction
diffractively,
(V. 2) proceeds
in this case the yp -+p
in the Final State p7r+n-?r”
than that found for reactions
the validity
of the estimates
which give constrained
were used in the study of the energy dependence of the delta-rho
- 139 -
kinematic
cross
fits,
To avoid systematic
sections.
been previously
criteria,
published,
cuts,
resonance
2,3 were reanalysed
shapes and fitting
with low confidence
or with competing
by demanding
the 4.3 and 5.25 GeV data, which had
and the same selection
procedures
were used for all
The cuts excluded events with missing
energy ranges.
pi-zero,
biases,
3 or 4-constraint
m(n+s-?P)>O.
A scatter
levels,
masses not near the
with very fast forward
fits.
neutral
Omega events have been removed
81 GeV.
plot of m(pn+) versus
m(x’a-)
for the channel p?r’n-x’
7.5 GeV is shown in Fig. V. la
together
jections
The shaded areas correspond
(Fig.
V. lb and V. lc).
- ttproduction
p A
thus there are no difficulties
smallness.
Similar
a somewhat
larger
p- A ”
in determining
background.
cuts are introduced
to At+ events
It can be seen that at this energy
is well separated
signals
from
the background
are obtained at 4.3 and 5.25 GeV with
on the four-momentum
become more pronounced
transfer,
1t ( y, p-)I<O.
The fitted amounts of p, A and pA as found by MURTLEBERT
for p- production
distribution
in reaction
(V. 2) are given,
In addition,
energies
are plotted together
at 2.8 and 4.7 GeV.
31
6( G~V/C)~.
in all charge
a momentum
matrix
have been evaluated
cross sections
and are also
a, b,
in Table V. 2.
for our three monochromatic
with two recent cross section
The events in both these experiments
- 140 -
transfer
elements,
the values of the shaping parameters
c, d of Eq. (V. 1) obtained in the fits are listed
V. 2 the p-A+’
assuming
The diagonal density
in the Jackson sys tern, for the p- and At’
In Fig.
when
In Table V. 2 the slopes B of the t distribution
of the form Aexp(-Bt).
given in Table V. 2.
and
the cross section in spite of its
The signals
states are given in Table V. 1.
at
with the non- and pT+rnass pro-
in Fig. V. lb and to p- events in Fig. V. lc.
the associated
systems,
determinations
have much less
5
2.6
6
$ 2.2
a
=
1.8
I .4
1.0
0
0.4
0.8
1.2
MT-+
1
0
is
>
0.8
1.6
2.0
2.4
(GeV)
MT-+
(b)
!
1.6
2.4
20
IO
0
1.0
1.8
2.6
3.4
FIG. V. 1-- (a) Scatter plot of M(pa’) versus M(~‘T-) for yp pats-?P
at 7.5 GeV. (b) and (c) are the M(?PA-) and M(pn’) mass disThe shaded areas are: M(r”a-)
tributions respectively.
distributions
for Ait events (l.l2<M(pa+)<l.
32 CkV) in (b),
and the M(ps+) distribution
for p- events (0.66~ M(?r’n-)<O. 86
81 GeV were removed
GeV) in (c). Events with m(r’a-#)<O.
from the plot to exclude o events.
- 141 -
TABLE
V.2
Momentum transfer slopes B and density matrix elements obtained in
this experiment for the reaction yp -p-A++.
B is the slope of the t distribution, p{O and & the diagonal elements for p and A, all for this reaction.
Errors in the latter include an uncertainty from the unknown background decay
distribution.
Also listed are the fitted values obtained for the mass shaping
parameters
of Eq. (V. 1).
E
3.74.7
Y
(@VI
4.7-5.8
6.8-8.2
(GeV)
(@V)
B(GeV-2)
7.7 *1.1
6.4 a3.1
7.6 *2.5
40
0.2WO. 13
0.64iO.27
0.60*0.22
A
p11
0.26*0.10
0.41*0.1s
0.21&O. 13
2.25&O. 85
9.04i2.67
10.0 *3.87
--
0.96iO.48
0.13*0.10
a
mW+)
b
m(7r07r-)
C
m(s+n-)
0.41&O. 24
1.95io.72
5.95*1.57
d
m(7r09+)
1.58&O. 55
--
2.56*0.78
- 142 -
background
because of their quasi-monochromatic
case for the bremsstrahlung
same resonance
events used in earlier
parameters,
resonance
been used for both the present
systematic
errors.
photon beams than was the
experiments.
shapes and fitting
experiment
programs
the
have
and that of Ref. 31, minimizing
A least square fit of the five cross
a(YP -p-A++)
Also,
sections
to the form
= CEy-a
(V. 3)
gave C=3.5* 1.2 and a=O. 6* 0.2 where cis expressed
in microbarns
and Ey
in CeV.
There is no unique prescription
Eq. (V. 3) to the production
mechanism.
used to study this relationship:
exponents for reactions
for relating
energy dependence of cfrom
Therefore
(a) comparing
believed
three approaches
with similarly
to be dominated
da/dt,
the energy exponent a in
by OPE;
are
obtained
(b) extracting
the
which in a Regge model should be pro-
portional
to E -’ with n=2, I, 0 for pion, vector meson or Pomeron exchange
Y
respectively
(at least for small t); (c) attempting to fit the data with a
specific
OPE model.
III approach (a) it has been noted
believed
to be OPE-dominated
the reaction
NN-+
63
that for our energy range,
have a in the range 1.6-2.5.
AA, an especially
likely
reactions
In particular,
OPE candidate which has been
studied up to 30 GeV, 77 has been shown to have an energy dependence with
a3.5i0.3.
In addition
the reaction
examined
in this experiment,
(See Fig.
IV. 9).
this range,
Clearly
No firm
yp --+
- ++
?TA
, another
has an energy dependence yielding
the dependence of reaction
conclusion
OPE candidate
may be reached,
- 143 -
a=l. 74+ 0.16
(V. 2) falls outside
however,
since the effects
of the kinematic
boundaries
tance of the minimum
Approach
momentum
transfer
due to the increased
with energy.
of the Chew-Low
of the finite physical
This occurs because
plot for reaction
impor-
at lower photon energies.
(b) takes intp account these effects
range of t varying
small
may be substantial,
(V. I),cuts
tmin
(the minimum
off a substantial
fraction
t)
of the
t region and reduces the total cross section at low energies.
The form
-a’ Bt
du/dt =AEY e
is assumed in the formula
t
dEy)
=
dmngBWm,,$
/
where BW(m) is a relativistic
representative
Breit Wigner
J
factor
of the values given in Table V. 2.
over the mass range within
question,
/
t
The integral
exponent,aeff.
sharp cut-off.
66
a fair description
two body reaction.
and R , the cut-off
t-dependence
1 fermi.
66
of our results
of the reaction
Using the relation
r(pry),
is usually
introduced
78
to
value.
by a
another quasi-
the rho radiative
determined
width,
by a fit to the
studied and in hadron induced reactions
R2=4B,
an
our experimental
for omega photoproduction,
The latter
in
been shown in Section IV.2 to give
It has two parameters,
radius.
yields
that a’ =2 corresponds
(c) uses an OPE model with absorption
This model has already
, taken as
u(Ey) over our energy
aeff =l. 4 and only for a’ =l. 2 does one find a eff = 0.6,
Approach
-2
side of the resonance
The resulting
The fit determines
9
was performed
range was then fitted to the form of Eq. (V. 3) and for each a’
effective
da
min
and B =7 GeV
two full widths on either
and tmax put equal to infinity.
l-IlZlX
dtdt
dmppWpa)
is about
the slopes in Table V. 2 would also
- 144 -
imply
a radius
observed
of about 1 fermi,
for hadron-induced
which is the same order
reactions.
The broken lines in Fig. V.2 show the cross
this model for R=O. 5, 0.7 and 1.0 fermi,
r(pny)
the SU(3) value. lg
of magnitude
= (l/9)
As R increases,
sections
79
all assuming
T(wsy)
obtained with
= 0.134
the t-dependence
(V.4)
becomes steeper,
and
the low energy cross sections
are depressed
of the kinematic
Hence the energy dependence found can indeed
boundaries.
be reproduced
by OPE, but only if
same conclusion
Apparently
OPE process
with an OPE mechanism
et al.,
--
the ratio
a(yn -+
a2
using an
possible
discrepancy
(V. 2) was recently
reported
by
of yp and yd reactions
that
--+ p-A ++) at 4.3 C&V is in disagreement
wA’)/u(rp
and found the cross
section for the reaction
A similar
who found in a comparison
OPE + SU(3) predictions.
By combining
for reaction
y).
Such
level.
GeV cannot be reproduced
of r(pn
The
of a search for the process
the energy dependence of the cross
and the SU(3) value
is applied.
6 MeV at the 97% confidence
in the energy range 2.5-8
Eisenberg
5 MeV (with RZO. 8 fm).
with the result
p ----t a y which found 81 r(pry)<O.
- ++
r(pny)>O.
is reached when the OPE model of Wolf8’
a large value is in contradiction
YP-+PA
more than the high by the effects
This experiment
looked for the reaction
with
yn ---&A’
section to be less than 0.5pb in the mode where A0 -Pa
SU(3) and the OPE model,
should in fact be 2, indicating
however,
it follows
again that the combined
that this ratio
prediction
of OPE
and SU(3) is violated.
One possible
dominate
explanation
these reactions.
for this discrepancy
It is possible
that vector
- 145 -
is that OPE does not
meson exchanges are
-.
3.0
0
THIS
H
REF
35
OPE
Calculations
----
2.0
b,
EXPERIMENT
r (prr
1
y)=O.l34
Me\
/
I .6
0.8
2 0.6
.z-
\
’ R,=Q.7f
0.2
-1
‘\ R,= l.Qf
2.0
4.0
6.0
8.0
10.0
15.0
EJGeV)
-
++
cross sections determined in this experiment
FIG. V.2--yp~p
A
and from Ref. 31, versus the photon energy Ey. The full
line is best fit of the data to Eq. (V. 3) which yields a=@. 6
The dashed curves are the OPE calculated cross
i-0.2.
section for various absorption radii and fixed coupling
(r (pw) =O. 135 MeV).
- 146 -
important
o+o-o’
in these reactions,
couplings
since within
could be quite strong.
83
the vector
dominance
model
Moreover
in a Regge pole model
-1
for vector meson exchange.
Y
energy dependence observed for
the energy dependence of (T should be given by E
This could account for the unexpected
- A ++, but more accurate
YP-P
data on the production
final state p-A++ are needed to determine
Table V. 1 lists
quasi two-body
other than p-A++
states do not, for example,
The cross sections
small,
of this reaction.
the reactions
but no significant
The delta-rho
ratios
yp +
of 3:2:1 which
VA.
Even allowing
observed
do not support
for nucleon isobars
as can be seen in Fig.
energy (See Fig. V.4).
nucleon resonance
Although
production
othar than A
V. 3 for the 7.5 GeV data.
that there are substantial
ciated with any resolved
in detail
v.2
rho signals
baryon resonance
++
OPE
are all
A- producrapidly
with
much about
it is easily possible
to
in all charge states not asso-
production.
This will be studied
in Section V. 3.
A2 Meson Production
The first
reported
these data do not reveal
in these final states,
the
the simple
tion in the =+x+x-n channel is large at 4.3 GeV, but decreases
conclude
charge
decay of A’ and A0 into proton and neutron channels,
amounts of A+ and A0 production
rather
is found.
seem to appear in simple
would be expected if OPE dominated
hypothesis.
the mechanism
the other charge states of delta-rho,
production
for the relative
and decay of the
observation
in a previous
the following
grounds.
Since it has spin-parity
of the photoproduction
publication
84
on this experiment.
of the A2 meson was
4
It was expected on
The A2 is known to decay predominately
2+, it should couple only to transverse
- 147 -
into PT.
rhos.
518 NON-OMEGA EVENTS
c
7.5 GeV
M
0
1.0
1.4
I.8
2.2
M (pr)
2.6
GeV
3.0
3.4
,.PIA,?
FIG. V. 3-- M@n) in all charge states for 1-C fits in the 7.5 GeV data with
-0.18<mm2<0.10
GeV2, P(X2)>0. 005 and omega events removed. The fit curves incorporate the resonances listed in
Table V. 1.
- 148 -
-149
-
Invoking
the vector dominance
and show a substantial
not been directly
this coupling
model,
it should thus also couple to photons
decay into the yx
observed,
mode.
Although
this process
if there is indeed an appreciable
should allow the photoproduction
has
decay width,
of A2 mesons via OPE in the
reaction
yp -A$.
The reaction
rapidly
is observed
to reaction
It is the only quasi two-body
V. 5 shows the invariant
(5).
than 5%.
neutron cut,
that the production
combines
the small
(0.6,
1.2) GeVf
likelihood
events at all energies
production
r(A2)
V. 5d
(i. e. , the
=O. 070* 0.044 GeV.
fits to all the data in the channel
summarized
n+r+a-n at our
in Table V. I.
Note
in Table V. 1 at 4.3 and 5.25 GeV are somewhat
lower
are corrected
Also note that the presence
the structure
Figure
data. 65
than those of Ref. 4 because of more accurate
The results
levels
< 0.5 (GeV/c )2,
transfer
energies yield the results
that the cross sections
mass squared
V. 5a-c) and has been used to fit the A2 mass and
These agree with hadronic
three annihilation
It (p,n)l
is highly peripheral.
M(A2) = 1.30+ 0.01 GeV and
Maximum
for fits
and with confidence
mechanism
momentum
shaded events of Figs.
tion.
observed
mass distributions
The shaded events are those with
indicating
yielding
three-pion
All of the data shown are 1-C fits with missing
inside our standard
width,
reaction
7rfrfr-n.
Figure
better
in our data with a cross section which decreases
with photon energy.
in the channel
w. 5)
fitting
for all experimental
of a small Al
of the data at the small
and a revised
and analysis
normalizalosses.
signal at 7.5 CeV is supported
momentum
- 150 -
transfers.
by
The fits in fact
(b)
n
I61 everh
)i-
2( 1,
3bO events
I( 3
FIG. V. 5--M(a’lr+ir-)
distribution
in the reaction
yp ---tT’?r*?T-n at (a) 4.3
GeV, (b) 5.25 GeV and (c) 7.5 GeV. The shaded areas reprecomsent events with )t@,n)l < 0.5 GeV2. (d) Mass distribution
The
curves
are
best
bining the three energies for above t cut.
fits to A$ resonance (M(A2)=1. 30 GeV, r(A2)=0.1
GeV) and
phase space (see Table V. 3).
- 151 -
reject
the three-pion
decay mode, yielding
the branching
+
o+
ip
77
A2
+
A2 -all(a+r+n-)
which also agrees with hadronic
a rho in one of the two n**-
combined
+o
= 1.0
production
data.
events for which at least one neutral
exclusive
This figure
subsets:
with
shows the
those 3-pion
is in the rho region
is in the rho region.
A2f signal is only found in those events associated
because the kinematics
of Ai
is also shown graphically
dipion combination
and those for which no such combination
into three pions constrains
This association
4.3 and 5.25 GeV data.
data, divided into two mutually
convincing
(V. 6)
-0.2
charge combinations
in Fig. V. 6 for the combined
ratio
with a rho,
Although
the
this is less
of the decay of an object of mass 1.3 GeV
the two pion combinations
to be preferentially
in
or near the rho region.
The energy dependence of the A2 cross
expected for an OPE production
derive
entirely
the Ai
mechanism.
width by assuming
section
is consistent
with that
As in Ref. 4 it is possible
that A2 production
to
in this channel is due
to OPE. 66 This yields
r(A;
-
Yx+)
g2A RY
4r2
= +j-
This value is obtained for an absorption
calculation.
radius
q5
4
mAO
Z 0.5 MeV.
of about 1 fermi
This same radius has been found to give reasonable
our omega data (See Section IV. 2).
- 152 -
(V. 7)
in the OPE
results
with
50
•I ALL
q
p”
EVENTS
yp -
n TT+TT+TT-
I
EXCLUDED
n
40
30
20
2
2
IO
z
\
r
cl
z
0
YP 30
np”lr+
(b) /
20
IO
0
0.6
1.0
FIG. V. 6-- (a) M(a’ir+n-) distribution
for yp n+?r+a-n, combined data
from 4.3 and 5.25 GeV. The shaded area represents the 3 pion
effective mass for events with no ~T+H- combination in the p band
(0.60-o. 85 GeV). The curve is a one dimensional fit to an At _
resonance plus Lorentz invariant phase space. (b) The M(s+n T )
distribution
for events having at least one T+T- combination in the
p band..
- 153 -
The clear
signal of the A2 in the neutron channel leads us to reexamine
our 3-pion mass spectra
in the proton 4-body final states.
mass plots for eight different
Fig.
IV. 11.
photon energy intervals
tion of multi-neutral
be drawn from
events,
GeV data there is a
Since the O-C data may contain a large proporno conlcusions
about the 4-body final state should
it except in the case of extremely
sharp and well separated
In the 7.5 GeV data, on the other hand, there is a excess of
resonances.
about 16 events/80
MeV over an average background
in the mass interval
1.28-l.
opposite
tions are such that the Ai should not be produced
mechanism
invoked to explain
channel must be more complicated.
said to exist
deviation
to the y, and so clearly
In addition,
could not be diffractive.
fore any production
MeV
of significance.
The A2 has charge conjugation
Ai production
level of 24 events/80
This is about a 3 standard
36 GeV.
effect ,and thus it is on the threshold
pr+n-?P
have been shown in
In both the 7.5 GeV data and the 3.0-3.7
bump in the A2 mass region.
These invariant
m the A2 region in either
the isospin
coupling
by pion exchange.
the presence
Moreover,
any
rela-
There-
of A2 in the
no structure
can be
the 4.3 GeV or the 5.25 GeV data,
although the entire low mass region is enhanced over what phase space predicts for these data, so a mechanism
tion at higher
must be considered
energy if the 7.5 GeV effect is to be accorded
The structure
has been subjected
A2 (1300) accounts
for 6.8*2.3%
standard
signal corresponding
deviation
about 0.7*0.25
momentum
which favors
pb.
transfers
very large portion
to multidimensional
of the channel.
of the background
any significance.
fits where
This is again a three
to 35*12 events or at this energy
This signal is found to be largely
to the final proton,
produc-
associated
1t(P,p)I < 0.5 (GeV/c)‘,
goes away (see Fig. V. 7).
- 154 -
with small
whereas
a
The signal
5
0
N
co
-
I
N
-
I
co
Aa9 bO’O/SlN3A3
*
i. .,.l.,.r,.,.,.,.,.
$$:y::::::::
..ty...>i.:.:.:.:.:
::::::
,::::
:::.:.
.:.:.:.:.:.:.:.:.:.:.:.:.:.:::::::::::::::
““““‘.:::::g
:.:.:.:
::::::~.::::::::::::::::
.i....i A....
::::::::‘.>
:::::::::::::::
.>~.:+:.:.:.:::::::::::::::::
. . . ..~~........:.:.:.:.:.::::::::
.w,.:.:.:.: .,.,....
;gi
sy:;
.,.:.iin.,...
............A,.
... :.:.:.:.
...
- 155 -
remains
quite strong when the final state pions are required
one charged
rho combination.
If the signal were due to an Ai meson,
decay mode p”no would be forbidden
of a p” signal does not reflect
to be in at least
by isospin
on the presence
conservation,
of A;.
the
so the presence
This is why charge rho
cuts have been applied.
In the structure
of the 3-pion spectrum
shown in Fig.
V. 7, enhance-
ments can also be noted in the A; region and also in the mass region
1700 MeV.
The overall
mass spectrum
observed
in the m(a+x-?r’)
gtL23
They see a three-humped
to that observed here.
spectrum
is very reminiscent
at 8 GeV/c in rfd
They identify
their
by isovector
exchange.
by Bugg
structure
three enchancements
and @(1670), and at least for the Ai they speculate
explained
of the structure
interactions
low mass enhancement
similar
at A:,
A;,
that their data may be
This also might be the production
for Ai in our data, if indeed this enhancement
1600-
persists
mechanism
in high statistics
experiments.
v.3
Inelastic
Rho Production
The preliminary
substantial
production
reports
on this experiment
of rhos in the inelastic
YP-+
~3 have already
reaction
pxN.
(V. 8)
As can be seen from the fits of Table
V. 1 , there is a substantial
amount of unassociated
in all charge states.
our missing
tions.
function
rho production
mass cut eliminates
The relative
most events produced
abundance of neutral
of their production
noted
mechanism.
Furthermore,
in multi-neutral
and charged rhos in yp +
Charged rho production
- 156 -
reacp7rN is a
cannot be
diffractive,
while neutral
produced
various
via isovector
rho production
exchange.
will
be suppressed
if the rhos are
Therefore
the production
mechanisms
charge states may be reflected
shows the invariant
p,“r-~~’
in their cross
masses of the various
production
dipion combinations
are present
the 7.5 GeV data is more clearly
at all energies
as is shown in Fig.
darkened
events are those with small momentum
system.
Photoproduction
Significant
The cross
dimensional
as explained
fitting
single resonance
program,
production
production.
separated,
rho
sections
are clearly
transfers
above,
exclusive
deviation
when possible
The
to the dipion
visible,
but not all of
in Table V. 1 are from a multiso the cross sections
for
of those for associated
None of the rho cross sections
more than one standard
these signals
V. 9 and Table V. 1.
of p+, p- and p” is clearly
these events are peripheral.
fits.
in the channel
is seen in every charge state.
Although
resonance
Figure V. 8
sections.
for the 7.5 GeV data with omega events removed.
for
has
been changed by
A: and Ai were allowed
in the
For the 5.25 GeV data good fits could not be obtained to the =+A- mass
spectrum
in either
was anomalously
the proton or the neutron channels,
broad with a background
because the rho signal
unlike phase space.
We are unable
to account for this effect (see Section II. 5), which does not occur at other
energies,
but which does occur to a lesser
states at 5 GeV.
observed
energies,
This effect probably
at 5.25 GeV.
we prefer
at this energy.
degree in the other rho charge
diminished
the p-A++
cross section
Since the signal is clear at the other annihilation
not to give a cross section
for unassociated
We conclude that there is an appreciable
duction in the channel p,‘r-7r”
which does not decrease
energy.
- 157 -
p” production
inelastic
rapidly
rho pro-
with photon
518 NON-OMEGA
EVENTS
7.5 GeV
50
Mb--W’)
40
30
20
IO
>
s
O
40
fz
Q 30
2
5
iTi
20
IO
0
30
r
20
IO
0
0.2
0.6
1.0
1.4
1.8
M(-rr-rr) GeV
FIG. V. 8-- Dipion
the 7.5
GeV2,
curves
2.2
2.6
,,,,,,.
masses in all charge combinations
for 1-C fits in
GeV data to yp pn+lr-?P with -0. 18<mm2< 0.10
The fit
P( x 2)>0. 005 and omega events removed.
incorporate the resonances listed in Table V. 1.
- 158 -
YP
-pi+
rr- T”, oil energies (1573 ev. 1
FIG. V.9--M(aa)
distributions
for the reaction yp --PPT +T - TO at4.3,
5.25 and 7.5 GeV combined.
Shaded areas represent events
with It(-y ,aa)l < 0.5 GeV2. All w (M(?T+T-?~~)<~. 81 GeV) and
60-O. 85 GeV and M@a+)=l. 15-1.30
P-A ++ events (M(fln-)=O.
GeV) are removed.
- 159 -
Figure
at 7.5 CeV.
possibility
V. IO shows the invariant
The fits in the neutron channel at all energies
of an Ai decaying
channel varies
Wigner
into p”.
to a skewed shape by varying
not so impressive
The exact percentage
at other energies,
laser beam experiment
In order
but is present
rises with energy.
has also observed
to gain information
mesons produced
at all energies
very prominent
about the possible
rho signals
production
the p’
transfer
associated
and that it is peripheral
discussed
V. 11.
Excluded
production.
p” may be at least in part diffractively
To examine the possibility
that if the p” signal were produced
charge state nxf as to proI
Table V. lb,
as much
inviting
p”
after all these cuts
rho production
This has led Wolf to suggest that these
produced.
of a diffractive
24
production
by pure Pomeron
nucleon system produced at the nucleon vertex
l/2
remaining
The signal for charged
inelastic
an isospin
Thus reflections
above are eliminated
with both pa0 and mr’,
It I values is much weaker.
Moreover,
from the
Fig. V. 11 that there is quite a significant
at small
state.
mechanism
and p” invariant
- ++
graphs are all events having w, p A
or Ai production.
production,
in all
( 1t I< 0.5 GeV2) between
the photon and the vector meson are plotted in Fig.
It is evident from
with a
The SLAC backscattered
in these channels,
two-body reactions
The signal is
31
masses for events with small momentum
from the quasi
Breit-
the exponent n in Eq. (IV. 5), but in all
charge states in these 4 body channels.
as possible.
the
of p” in this
40-50Y0 of the neutron channel at 7.5 GeV.
section that apparently
of the vector
included
as the shape of the rho is changed from the standard
cases it constitutes
cross
dipion mass in the channel n+ir+n-n
mechanism,
exchange,
would remain
note
then the pion-
in an isospin
l/2
state is expected to decay twice as often to the
a comparison
of these two channels.
the ratio at 7.5 GeV is indeed consistent
- 160 -
with two, 2.1iO.4.
From
This is
50
I
yP-T
I
I
+r+
7-n
40
7.5 GeV
2 x 233 Combinations
30
20
IO
0
a
0.2
0.6
1.0
1.4
1.8
2.2
M ,,-+T- (GeV)
FIG. V. lo--
M(T+T-) for a 1 C fits to yp +R+T+H-n
with 0. 6<mn2<
GeV2 and P(X I- )>O. OU5 in the 7.5 GeV data.
- 161 -
2.4
1895A18
1.2
..
t-
t
L.
- 162 -
I
I L
P
consistent
with the assumption
the SBT collaboration
errors)
parity
of diffractive
for inelastic
production.
p” production
Also the results
are consistent
(within
of
large
with twice as much p” in the neutron channel and also with a natural
exchange production
ascertain
exactly what fraction
should be considered
test is impaired.
associated
produced,
Also the large errors
uncertainty
compelling;
indeed,
positive&charged
co seen in each channel
of this ratio
on all of these determinations
the majority
transfer
it is not clear how to
so the usefulness
in the correct
with small momentum
than the final-state
However,
of the unassociated
peripherally
well as the systematic
far from
31
mechanism.
as
p” shape make this evidence
of this inelastic
co production
is
to the final state nucleon rather
pion-nucleon
system.
This latter
fact
tends to suggest that some three pion object is being produced diffractively
which decays into a rho.
Although
this production
in the .rr+lr-x’ final state,
there can be no diffractively
in the neutron channel by charge conservation.
there is no obvious candidate
for a diffractive
mechanism
produced
is conceivable
3-pion system
Even in the proton channel,
three-pi
system which could
then decay into a pox”.
If this peripherally
dissociation”
process,
tive photoproduction
This is similar
reactions.
87
associated
to inelastic
Unfortunately
p” were associated
one could conclude
to the ratios
to study this process
However,
87
produced
diffractive
with a “diffraction
that the ratio of elastic
production
obtained in pion-nucleon
is abut
diffrac-
30(15nb/O. 5pb).
and nucleon-nucleon
our small signal does not yield enough statistics
in detail or even to prove that it is really
it is worth noting that when the invariant
with the p” are plotted
in Fig.
masses of the NT system
V. 12, no clear
- 163 -
diffractive.
evidence is seen for
-
I
0
N
I
I
0
AW
I
t
i70’0
I
0
N
/wJ~V
- 164 -
I
I
0
-
I
the production
of any of the known N*(I=1/2)
such an N* associated
energies.
production
resonances.
that
would be seen at much higher photon
24
Finally
,we wish to comment
in this experiment,
and the reactions
that the inelastic
yp --+V ’ T- A ‘+(V’=pow)
mechanism.
may be due to OPE (w-production),
Much more extensive
these inelastic
experiments
in
coupling
would be required
processes.
- 165 -
previously
Some may be diffractive
‘yn reactions),82
and p* production
meson exchange since the pfp-po
observed
in yn reactions
which were reported
(like the no in Fig. V. 11 above and the one observed
charged vector
p production
the final states pox-p and UT-~ observed
need not all have the same production
others
It is possible
may be due to
could be large.
for the detailed
83
study of
CHAPTER
VI
CONCLUSIONS
Results
on the photoproduction
photoproduction
The principal
of their appearance
Diffractive
section
results
are summarized
o” Photoproduction
results
(see Chapter
of previous
section is slowly decreasing
production
mechanism.
This result
model,
We extend previous
observations
possibly
density
matrix
cleanly
separable
recurrences,
up to -0.8
elements
into pp” and n-A
stringent
in the channel
exchange (OPE) contributions
reaction
++
a largely
the rho cross
the &ding
interference
using the double differential
lo,16
that s-channel
by our determination
production,
(see Chapter
helicity
of the rho
and no o’ or higher mass
IV. 2):
are obtained
model, 15 are ob-
Cross sections
the “diffractive”
to omega production.
is shown to reproduce
yp -+wp.
- 166 -
for omega
in eight energy inter-
A fit of these data to a constant
to E;” enables us to separate
and OPE contributions
namely that
The data at 7.5 GeV are seen to be very
yp--tpx’=-x’
between 1.2 and 6.2 C&V.
proportional
in our
upper limits.
Omega Meson Production
vals
16
such as might be expected from the Venziano
served within
production
(G~V/C)~,
at 7.5 CeV.
9-12
holds whether
calculation
is conserved,
here in the order
above 2 GeV, which implies
is obtained from a phenomenological
section.
in the pre-
IV. 1): We confirm
experiments,
model, lo’ l7 or a model-independent
cross
mesons and on the
in the main body of the text.
data the well established
diffractive
vector
of other 4-body final states have been presented
ceding two chapters.
the co cross
of neutral
plus a term
and the one pion
This mix of diffractive
the observed
t dependence of the
Vector
Dominance
(see Section IV. 3): The omega forward
section can be compared
the predictions
the forward
of the vector
19
model l4 plus SU(3). l8
dominance
in agreement
21
our forward
cross
r2,/41r of 0.32&O. 03, which disagrees
and heavy nuclei results,
Associated
Rho-Delta
with the behavior
6
plus SU(3) calculation.
yp ---to-
This raises
mechanisms
the question
with the usually
of the radiative
directly
energy,
in this experiment
the applica-
decay width of the
about
coupling,
however,
in the channel
and is consistent
to reach any firm
conclusions
Although
- 167 -
has
a decay mode not
are not only much smaller
but also they decrease
from this amount of data.
The photoproduc-
An OPE model calculation
of the A2ny
The cross sections,
making it difficult
mechanism
observed
the strength
than those for p - A ++ production,
OPE
for this reaction.
accepted mass and width.
observed.
1s shown to
new speculations
In our combined data the signal is clear
been used to estimate
++.
as to whether
of the A2 Meson (see Section V. 2):
meson was first
yp -~~+x+x-n.
A
expected on the basis of a simple
rho into a pion and a photon is valid and introduces
Photoproduction
in both the
(see Chapter V. 1): The energy
tion’ ’ lo of these models in the derivation
production
ring results
22
data on Compton scattering.
Production
ring
section data imply a
with the storage
dependence of the cross section for the reaction
tion of the Ai
SLJ(3)
total photo-
l2 but which does give a good agreement
s and t dependence with existing
possible
We obtain
with simple
theorem 20 and existing
Using the optical
cross section data,
be inconsistent
to examine
a ratio of 9 and the value from the ORSAY storage
results ,13 7.5H.5.
value for
rho photoproduction
cross section ratio of 9.4i2.1
which predicts
production
to our diffractive
cross
Ai
more rapidly
with
on the production
production
in the channel
13
yp -+
pr+x-?p
servation,
..
could be neither
diffractive
there is a peripheral
CeV data for which an upper limit
ments in the neutral
23
actions.
This similarity
Inelastic
the remaining
observed
pi-rho
enhancement
at exactly
is given.
Very similar
system have been observed
extends to several
Rho Production
(see Chapter
to be associated
which is consistent
may indicate
with the production
low mass enhancein 8 GeV/c x’d inter-
other features
of this distribution.
V. 3): A very large amount of
with our data, but the presence
vector
not
or decay of other resonances.
that some of the o” signal may be produced
a significant
con-
this mass in the 7.5
events in the 4 body final states is due to rho production
It has been suggested2*
signals
nor OPE by spin and isospin
diffractively,
of strong charged rho
meson exchange in these final states.
- 168 -
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