T.OF TEriT.
DEC 2 1G6
INVESTIGATION OF A POSSIBLE TEST OF T
INVARIANCE
by
RICARD EVERETT PALMER
SUBMTITED IN PARTIAL FULFILINENT
OF THE REQUIREMENTS FOR THE
DEGREE OF BACHELOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June, 1966
Signature redacted
Signature of Author
Department of Physics
May 20, 1966
Signature redacted
Certified by
Signature redacted
Thesis Supervisor
Signature redacted
Accepted by
al
Chairman, Departm
Committee rn Thesdt
ABSTRACT
Inelastic electron-proton scattering may provide a test of time
reversal invariance.
The practicality of an experiment using an
unpolarized target was studied for energies of 20 BeV.
The
dominance of background appears to make the experiment unfeasible
at the present time.
Tyger! Tyger! burning bright
In the forest of the night,
Nhat immortal hand or eye
Dare frame thy fearful symmetry?
... William Blake
Table of Contents
I.
II.
Introduction
.................
*............
.*................
Inelastic Electron-Proton Scattering as a Test of T t
Invariance ........
*....*................*......
III.
IV.
5
7
Estimate of the Final Baryon Resonance ...................... 10
Estimates of Counting Rates
13
Chance Coincidence Rates ..............................
21
Measurement of the Final Baryon Polarization
28
VII.
Which Resonance to Pick
........................
32
VIII.
Interference Backgrounds
.................................
34
V.
VI.
IX .
Conclusion ...............................................
Appendices
Tables
Acknowledgements
Notes and References
00 00 0 0 0 0 0 35
5
INTRODUCTION
The validity of symmetry invariances plays a significant
role in modern research.
As the problems before the physicist
become more and more complex, he needs a unifying system of
principles that will bind together and clarify the laws of
Nature.
It is hoped that symmetry invariances will become such a
system of principles.
With the advent of high energy particle
accelerators, symmetry invariances have been invaluable in the
prediction and explanation of nuclear and elementary particle
processes.
Their great value is that they limit the number of
possible interaction terms; those which violate symmetry invariance
can be discarded, if these symmetry laws are found to be valid in
general.
Of course, processes which do violate symmetry invariance
must be resorted to in cases in which symmetry invariant solutions
are unable to explain adequately experimental observations, but at
least, the physicist has had some guiding principle in his work.
Before the discovery of the violation of parity,
of symmetry invariance had remained virtually unknown.
the validity
Their
theoretical attractiveness and the absence of contrary evidence
had resulted in. an almost intuitive acceptance of symmetry
invariances as natural laws.
The observation
of the two-pion
K20 decay has questioned the validity of time reversal as a universal
invariant.
It is now generally accepted that the K4 does indeed
violate time reversal invariance, but the exact nature of the
interaction which violates this symmetry is still in doubt.
relative size of the branching ratio of the
The
42 two-pion decay to
6
0
the branching ratio of the K two-pion decay
is ~ =/7r.
1
decay conserves time reversal invariance.
o
The K1
This suggests that the
violation of time reversal invariance by the
42
decay is attributable
to the electromagnetic interaction.
A number of experiments have been proposed by T.D. Lee3 to
test this conjecture.
A high energy electron accelerator such as
the Stanford Linear Accelerator (SIAC) is ideally suited to
experiments of this type.
The purpose of this paper is to investigate
one of these experiments, inelastic electron-proton scattering with
an unpolarized target, to see if it is feasible to be performed at
SIAC.
The theory in the next section is the work of N. Christ and
Lee.3
Using this theory we estimate the magnitude of the effect to
be measured, namely, the polarization of the final baryon produced
from the decay of N* resonant states.
Approximations to counting
rates and running times have also been made.
Experimental
limitations, such as chance rates and polarization of the background,
are discussed, and a final evaluation of this
:experiment is given.
7
INEIASTIC EIECTRON-PROTON SCATTERING AS A TEST OF T
INVARIANCE
There is good evidence that the strong interaction Ht is
separately invariant under the space inversion Pst, the time
reversal Tst, and the charge conjugation C s.
The subscript st
denotes that these symmetry operators are defined by the strong
interaction alone.
There is also good evidence that the electro-
magnetic interaction H
operator CS T StP St
is invariant under Pst and under the triple
At the same time there is little
evidence that H7 is separately invariant
under C
does violate C
and T
or no
and T t .
If H
invariance, then the relative size m/7r
of the branching ratio of KS two-pion decay to the branching ratio
00
of K1 two pion decay, which conserves T
and Cst, could be
.
satisfactorily explained by the virtual effect of HY2
Since H
and C T P
commutes with P
and with C
ttPt, and since P
are defined to commute with H 2 , then one can make the
identifications:
P
2'
= P
st
CTP = C T P
st st st
Y777
H
can violate C
T7 A
and TSt invariance, if
C
A
cs
and, similarly,
st
The total electromagnetic current
by definition.
If we decompose
and the baryonic current
C
C
j
changes sign under C
ju into the leptonic current
+ 0, where:
JBC .1 = gB
st u st
U
KBC
st u st
then a violation of C
=+KB
u
and T
non-vanishing value of KB.
invariance would correspond to a
Since both P
and C
T
P
are con-
8
served, a violation of Cst invariance requires a simultaneous
invariance.
violation of T
Inelastic electron proton scattering provides an excellent
opportunity to test the conservation of Cst and T t by H7, because while
the particles interact electromagnetically,
there is also a baryonic
current between the ground state proton and the N* resonant states.
In this paper inelastic electron-proton scattering with an unpolarized
target will be considered.
The cross section for the reaction e + p -. e + N*, in the onephoton exchange approximation, is:
2 2
220
de = 4'x: k' ((q )"kw'M)
22
e(w'-kklcose-2m
)W
(~os
1
dk'd(cose) x
+ (ww'+kk'coso4m2 )W2 + (Min(k_))(w
2
,2
W
where the symbols have the following definitions:
C: = fine structure constant
k,w = incident electron momentum, energy
k',w' = scattered electron momentum, energy
2
q = four-momentum transfer squared
M = mass of resonance
m
= mass of proton
m
= mass of electron
p
O = scattering angle of electron
S
=
polarization vector of target nucleon
and where W 1, W 2 , and VT
V2
2
q
and M alone.
3
are real and dimensionless functions of
Since the term S *(k-_ x k') changes sign under
;-in
time reversal, this interaction violates time reversal, unless W
The recoil baryon from the N* decay (N* -+wr + N) will have
perpendicular to the scattering plane a polarization of:
<S,> = + 2(21 + ).<c-
=
0.
9
where I is the orbital angular momentum of the N* decay product
respectively.
1
nd J*
The spin vector of the resonance is given by
<J > =
If p
1
= J
'
(7r + N) and the + and the - signs are for 2
1( kxk t)( 2_w ,2) -2
1*)1+J
~ 1
*3
and p * are the parities of the proton and of the N*,
respectively, then A and '
A
are given by:
2(wwI-kk'cose-2m )w + (wwt+kkcose.
-el
)W2
ppN* exp(i7r(JP-N*))
W4,9like the other W's, depends on the non-leptonic matrix elements.
If the polarization of the final baryon is non-zero, then either
W
3
or W
and C
or both are non-zero, which implies a breakdown in Tst
4t
invariance.
The object of a test of T t and C
invariance
by inelastic electron-proton scattering with an unpolarized target
would be to try to measure such a polarization.
10
ESTIMATE OF THE FINAL BARYON POIARIZATION
W
and W. are related by the inequality W2
2
1*
(q2 /l)W>
For incident electron energies of the order of 20 BeV.,
0.
2
(within a factor of a few), and for the sake of simplicity, we
will set W1 = W2 = 1.
Lee 4 argues that the time reversal non-
invariant terms are of the order of cc/7r smaller, in order to
explain the oberved branching ratio of the
mode.
Thus, we will set W3 = W4 = c/7r.
4
two-pion decay
The polarization
<Sg
does not depend on the absolute sizes of the W's, only upon their
relative sizes.
Using the above approximations we have estimated the final
baryon polarization predicted by Lee's theory.
Figures 1. and 2.
show the predicted polarization for the 1.236 BeV. and the 1.518
BeV. resonance for k = 20 BeV.
U-
Figure 1.
,
...
....
....
- .....
---
Prdite
Polarizati
fte F
l Byon frthe 1.236 B V. Resonance
k = 0BV
0.8
049
0.7
0.6
04
o.4
O~
0.2
0.1
10
20
3o
40
5o
6o
7o
8o go
loo io 120
130 140
150
166"""17o 18o
Figure 2.
Prdited Polar
eon o
the ial
4
4
12
Baryon for the 1.518 BeV, Resonanee
I
049
*4
4'
095
0.7
o4
0.1
E) (deg.)
10 20 30
4o
50
6o
70
8090
100
110)120
1C301
15
620.
13
ESTIMA.TES OF COUNTING RATES
We have assumed the Breit-Wigner shape of the baryon resonance:
F(M) dM =
dM
(M-M )a+f/4
where r is the full-width of the resonance at half-maximum.
The
normalization A can be found from:
0o
f
F(M) dM = 1
m +m
p
p
which integrates to give:
A
T' (r + tan"1(M -M -m
r/ 2
As a first
approximation, we have taken the distribution of the
final baryon to be isotropic in the N* rest frame.
a phase-space density for the final baryon of:
2 N(0M)
= 1
L
F(M) t? (EIM +
2
5
This results in
(see appendix 2.)
2 )-l
where
M = mass of N*
m
p
= mass of proton
m
= mass of pion
P
= momentum of final baryon in N* rest frame
E
= energy of final baryon in N* rest frame
P = momentum of final baryon in lab frame
E = energy of final baryon in lab frame
0 = scattering angle of final baryon in lab frame
The final baryon will be detected in coincidence with the
scattered electron.
The coincidence rate N
c
can be calculated
by integrating the electron cross section times the final baryon
phase-space density over the resolutions of the electron and the
proton spectrometers.
14
The eectroproduction cross section in the single (virtual)
photon approximation is:6
a
,K)
,K)at +
2(Eq
,K)a
m2 )/2m is the lab momentum of the virtual photon.
p
p
the P's are defined by:
where K = (P?
47 q2k
s
-cla
4,21)
rs
cot 2 (0/2)
(Xk'
+
P
1
+(k-k )/q
cot?_(0/2)_
2
For small electron scattering angles q
2kk'(l-cose) is small,
and the virtual photon is similar to a real photon, for which a. = 0.
As a first
approximation, we have neglected the scalar term.
The transverse cross section is equal to:
7
aw = (q / *(0))l GR2(q) a(K,0)
where G' (q) is the proton isoscalar magnetic form factor and a(K,0)
MV
is the photoproduction cross section.
2
(
2
) has been numerically
and is found to be (p. -pn)/2 (1 + q 2/.72)
fitted by Hand,
c
G
2
(in BeV.2
), where pP and pn are the proton and neutron magnetic moments,
respectively.
Measurements at the Cambridge Electron Accelerator
indicate that 1
= 2 gives good agreement with Hand's expression
for the electroproduction cross section.
2M-mp
)
(q /q (0)) 2 = 1 +
When 1 = 2, we have:
The coincidence rate can be calculated from:
2
Nc=(const.) ffaK)
2
2
NE,M)
The limits of integration are determined by the resolutions of
the electron and the proton spectrometers, both of which have
angular and momentum acceptances.
The cross section is constant
15
to within a few percent over the limits of the integral, and in
calculating N
C
we have multiplied the central value of the integrand
times the angular and momentum acceptances of the two spectrometers.
The constant takes into account the incident intensity and the
length and density of the target.
using values of 2 x 1013 sec.*
Our calculations have been made
for the average incident intensity,
20 cm. for the target length, and .07 gm./cm. 3 for the density of
liquid hydrogen.
In the direction of the N*, there will be two final baryon peaks,
one for forward emission of the final baryon in the direction of the
N*, the other for backward emission in the direction of the N* (see
figure 3.).
2
For values of q in which this paper is interested,
the backward emitted final baryon is folded into the forward
direction in the lab frame.
Figures 4.-7. show the predicted true coincidence rates for
forward emission and backward emission of the final baryon for the
1.236 BeV. resonance and for the 1.518 BeV. resonance.
Because both protons and neutrons are produced from the decay
of the N*, the measurable coincidence rates will be reduced by the
fraction of protons produced, which is determined by the ClebschGordan coefficients in the matrix elements of the decay, since only
protons are detected by the spectrometer.
Non-resonant states are
produced as well as N* resonances for a given K, but out of ignorance,
we have assumed that only resonant states are produced by the
inelastic electron-proton scattering.
in the vicinity of the resonance.
over the width of the resonance.
This is a good approximation
aO(K,0) is taken to be constant
Figure 3.
Inelastic Electron-Proton Scattering
e + P - e + IT*
o + p
0
P
w
b
Pfe
Figure 4.
w
17
4
1
I
(sec.
)
True Rates and Chance Rates
1.236 BeV. Resonance
Forward Emitted Final Baryon
(these are average rates)
10 10
10 9
.108
.107
.106
-105
10
103
101
1
10-2
10--
True Rate
10-3
- 104
10-5
-Chance Rate
106
107
108
109
1
2
3 .
5
6
7
8
9
e (deg.)
10
11
22
13
14
15
16
17
Figure 5.
18
(sec.
)
True Rates and Chance Rates
1.236 BeV. Resonance
Backward Emitted Final Baryon
(these are average rates)
1010
109
108
106
10~
105
101
10
3
10
10
10T
10
1
10-2
.10-3
-True Rate
10"05
-
10-6
Chance Rate
-
410
-
%10
-109
1
1168 901 112 13 14 1516
213
e
(deg.)
r(
19
Figure 6.
True Rates and Chance Rates
(sec. -)
1-518 BeV. Resonance
Forward Emitted Final Baryon
(these are average rates)
108
10
107
106
103
10~
10
103
10
10-2
10-
-
True Rate
10
10-1
10
-
Chance Rate
10
510
1011
10-10
10"ll
1
2
3
4
5
6
7
8
9
e (dei.)
10
11
12
13
14
15 16
17
20
Figure 7.
Is
6
True Rates and Chance Rates
)
(sec.~
1.518 BeV. Resonance
Backward Emitted Final Baryon
(these are average rates)
10
a
101
10
10-2
10-3
40
- True Rate
-10-5
'10
-1
.107
10
R10
-
Chance Rate
41
20
a
-9
4
1 2
3
4
5
6
7
8
a
9
(deg.)
10
11
12
13
1
5
16
17
21
CHANCE COINCIDENCE PATES
A chance coincidence occurs when two uncorrelated particles
enter the spectrometers within, the resolving time of the
coincidence circuit.
0
They may come from two different N* -+ p + r
decays, or from a different process, such as elastic radiative
tails br the production of protons from non-resonant states or of
neutrons from resonant states.
These chance coincidence produce
a background from which it is necessary to extract useful
information about the true coincidences.
In this particular
experiment an asymmetry would be measured, and if
the uncertainties
in the background are as large or larger than the asymmetry,
valid measurement cannot be made.
Ideally, it
a
is hoped that the
chance coincidence rates will be much smaller than the true
coincidence rates.
The electron singles counting rate is calculated by integrating
the electron cross section over the limits of the electron
spectrometer:
2
N
e
JJ
2
a(e,,K) (const.)dk'do
e
nek'
2
S (const .)a 2
,
2 ,(3'i
K)
bodk'
heA
As before, the constant takes into account the incident intensity,
the length of the target, and the density of liquid hydrogen.
We will assume that only electrons from one resonance will be
detected; electrons from the production of other resonances with
the proper momentum and direction to be detected will be neglected.
This is probably a good approximation, if the acceptances of the
spectrometer are small, since the electron is constrained in k'
22
and
e,
because it
sees a two-body scattering.
Using this approximation that only one resonance contributes
to the counting rates, the average proton singles rate is: (see appendix 3.)
2
(nt.)AArj
N
pp
p
,K)
eBC
ea
N(,M) M d(cose)dM
1+k (-cose)
m
1,
To be consistent with calculations elsewhere in the paper, we have
assumed that only protons are produced from the decay of the N*.
The final baryon has more freedom than the electron, however,
since the N* decays into two particles.
Protons from other resonances
will thus be able to enter the proton spectrometer.
To account for
this we have arbitrarily multiplied the proton counting rate above by
a factor of 10 in our calculations.
Figures 9. and 10. show N
p
for the first two resonances.
The chance coincidence rate is given by:
N
~NeN (2T)D
where 2T is the total resolving time of the coincidence circuit and
D is the duty cycle (defined to be greater than one) of the machine.
Using the above approximations for N
was calculated, N
and Np the chance rate N
being numerically integrated on an IBM 7044 computer.
p
The resolutions used were as follows:
M
=
=
.13 mst.
.65 mst.
AP = + 2% (P)
&'
=+.8% (k' ) for the 1.236 BeV. peak
Ak' =+1% (k') for the 1.518 BeV. peak
2T = 5 nsec.
D = 106 /720
The values for Ak' will be explained later in this section.
chance rates are compared to the true rates in figures 4.-7.
The
It
23
e decreases, the chance coincidences become as
can be seen that as
large as and rapidly dominate the true coincidences.
Another contribution to N
the elastic scattering peak.
e
and N
p
is the radiative tail of
A computer program is currently being
developed at M.I.T. to calculate the radiative corrections for the
electron singles rate.
Corrections for the proton singles rate have
been calculated for momenta very close to the elastic peak,9
but the
inelastic peaks are far below the elastic peak in momentum at the
same proton scattering angle VN* (or $
radiative corrections to N
more general solution.
p
) (see tables. 4--5.), and
from the elastic peak will require a
Furthermore, corrections to N
p
and to N
e
for the 1.518 BeV. resonance and higher resonances will also
require radiative corrections from inelastic peaks of the lower
resonances.
Figure 11. shows the locus of the elastic peak positions and
of the inelastic peak positions of the first two resonances .in the
focal plane of the electron spectrometer.
For a given inelastic
peak the full momentum resolution of the spectrometer of + 2%
does not exi-ude the other peaks.
Hence, we have used in our
calculations improved resolutions of + .8% for the 1.236 BeV. peak
and + 1% for the 1.518 BeV. peak.
of the central pea
These acceptances include most
0
and exclude the other peaks.
It may prove
necessary to improve the angular acceptances as well in order to
isolate the peaks in the electron spectrometer, so that hopefully
only small corrections due to radiative tails will have to be made
for contributions from the other peaks.
Corrections to Np from the elastic radiative tail may be
quite serious, because the inelastic peaks for the same 0N* have
24
momenta much less than the position of the elastic peak, and for
momenta far below the elastic peak, radiative corrections to the
elastic cross section grow enormously with decreasing momentum.
Another contributing factor to Ne,
and hence to the chance
rate, is the Dalitz decay of the 7r 0 into 7 + e-+ e+.
of the e
0
in the r
rest frame is calculated in appendix 5. for
constant matrix elements.
This spectrum, transformed into the lab
frame, can be integrated over the T
cross section to find the
contribution to Ne from Dalitz electrons.
of the 7T
The spectrum
Insufficient knowledge
cross section for energies ~ 20 BeV. prevents such a
calculation, until more is known of the 7P cross section.
T 's wdull enter the spectrometer as well as protons, and a
means of distinguishing between pions and protons must be developed
to remove this ambiguity.
Otherwise, the contribution to N
p
from
pions wouE have to be accounted for in calculating chance rates.
This would probably be a significant correction.
25
vigure Q
-
103
. 14 I
11-1
i
.
.
.
.
.
11
- 4 ..
I
1.24 S BeV. Reso ance
Proton.Sin les Counting Rates (sec.')
(hse are average rates)
~
Fia ay
101
----
{
--
---
A-
rwr Jmitte
+++
+
+++++++++4............ ++++
+++
+++
..
.
...
.....
~~
. ...
n~
6 (de4.)
2
3
4
5
lo 9
1
11
12
13
14.
15
26
Figure 10.
_
.
...
.......
.........
.....
.... ......
...
....
..........
..
..
.~F
_..........-
.
...... ......
....- .
d
k.....
..........
7
_
I
8 $eV. Resoi ance
4
Jimoutiii
Rte
rates).
sizeare ave
Led
(se.
......
I..
ackw4 Emil ted
Fina1 3ryon
101A
Rmi -F.
. - IW
- I - Pnrwn.rA
- - .. I-
1nnaX Baryo
E) (deg.)
10
1
2
7 8
9
10
11
12
13
14
15
27
Figure 11.
ak.
Le Pe
of I
Pek in 20 BeV.
=202 Be*V.
2k
19
Elatic Peak
17
1.236 Bev. Peak
1.-518 BeV.- Peak
17
15
13
11
1 (deg.)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
28
MRASUREMENT OF THE FINAL BARYON POIARIZATION
The polarization of the final baryon can be detected by
elastically scattering a second time from a carbon analyzer.
Scattering to the left and to the right are associated with
opposite orientations of angular momentum with respect to
k x k', and spin-orbit coupling in the elastic scattering from
the carbon will produce an asymmetry- in the scattering cross
section, if the polarization of the final baryon in the direction
of k x k' is non-zero.
The asymmetry parameter c is defined by:
C = (R-L)/(R+L)
where R and L represent scattering to the right and to the left
with respect to the plane formed by k' and k x k' from the carbon
analyzer.
If the direction cosines of the scattered proton are not
the right or into the left hemisphere, e is given by:
where a is the analyzing power of the carbon target.
(see appendix
The standard
deviation in the measurement of a can be shown to equal:l
A
1
1
(1-a )2 (N) 2
0
where N is the number of observed events and e 0 is the mean
measured value.
will neglect it.
Since in most cases a
0
is much less than 1, we
If 6 is the percentage error A/e, then the
number of required events is:
N2
N =(7r/2ca'<>
and the total running time for the experiment is:
S= N/Nc = (7r/2<y6<_ >) 2 /N
.
measured, but only whether the proton scattered from the carbon into
29
A literature search was done to study the behavior of the
analyzing power a as a function of the kinetic energy of the final
baryon.
References
2.-II.
summarize the results in the kinetic
energy range from 180 MeV. to 1 BeV. for both carbon and hydrogen
as analyzers.
Little is known for kinetic energies greater than
1 BeV., and for these energies we have extrapolated the data for
energies less than 1 BeV.
In the case of carbon, a peaks sharply at a kinetic energy
of about 200 MeV. and decreases at higher energies because of
the increasing effect of inelastic proton-carbon scattering, for
which there is no spin-orbit coupling term.
The analyzing paer of carbon was averaged over the elastic
differential cross section for a given kinetic energy, and the
points were crudely fitted by:
a(x)
(.42) e(x-.2)2/.03
~ 4
x
.- x/ 4
+ .0001
where x is the kinetic energy of the final baryon from the initial
inelastic scattering.
Figure 8. shows cy as a function of kinetic
energy of the final baryon.
Using this approximation for a, the total running times have
been estimated for forward emission and for backward emission of
the final baryon for the first two resonances.
The results are
summarized in table 6.
It has been tacitly assumed that all of the protons from the
inelastic scattering will be detected.
If narrow gap spark chambers,
in which are sandwiched many radiation lengths of carbon sheets, are
used, then this is a fairly good assumption.
Thus, we have taken the
efficiency of the spark chambers to be 100% in our calculations.
30
By referring to table 6., one can see that the estimated
running times are well above the limits of practicality.
be reduced, however.
They can
Theycan be decreased by a factor of 2 by
using a 40 cm. long target, instead of a 20 cm. long target, for
which the calculations in this paper have been made.
Also, the
protons can be detected by the 1.6 BeV. spectrometer available at
SIAC, instead of the 8 BeV. spectrometer.
The larger angular
acceptance bf the smaller spectrometer will increase the counting
rates by a factor of --9.
Finally, the energy resolution of the
incident beam can be increased from .1% to 1%, to reduce the running
times by another factor of ~10.
The net improvement in the running
time will thus be a reduction of the order of 180.
Unfortunately,
at these increased counting rates chance rates will become far more
significant than beftre, and this alone will most likely make the
experiment unfeasible.
One possible solution to this apparent impasse is to decrease
the accuracy to which e is measured.
A 30% measurement will take
l/9 as long as a 10% measurement, without having to increase the
counting rates.
This seems to be the only way to minimize the
effects of chance rates and at the same time perform the experiment
in a reasonable length of time.
Figure 8.
owe ofCaronin
p- Scattering
rsim
14
.
...
..
I..
..
.
09J
05
0
K
Kietic Energy of Proeton (BeY.)
32
WHICH RESONANCE TO PICK
The 1.236 BeV. resonance is preferable to the 1.518 BeV.
resonance in this experiment in two respects.
First, the lower
counting rates and the smaller final baryon polarization in the
higher resonance make the running times for the 1.518 BeV. peak
of the order of ten times longer than the corresponding running"
times for the 1.236 BeV. peak.
Second, radiative corrections must
be made for contributions to the 1.518 BeV. peak from both the
1.236 BeV. peak and from the elastic peak, whereas radiative
corrections for contributions to the 1.236 BeV. peak must be made
only for the elastic peak.
However, there is also a strong argument in favor of choosing
the 1.518 BeV. resonance in order to test T
invariance.
A
transition to the 1.518 BeV. resonance conserves isotopic spin,
while a transition to the 1.236 BeV. resonance requires a AI = 1.
If the time reversal non-invariant term K
conserves isotopic spin,
then no effect at all will be observed for the 1.236 BeV. resonance,
even if
KB
u
/
0.
Lee's claims that one can determine whether or not
K1u conserves isotopic spin by looking for an asymmetry in the
6
+
have attempted to measure
w 4 r + 7T + 7 decay. Flatte et al.
such an asymmetry, predicted to be of the order of o/w by Lee, but
poor statistics gave the inconclusive result of e = .11 + .09
(66% confidence).
No valid conclusions could be made from this
measurement, so that it
is not yet determined whether K
conserves
isotopic spin.
At the present time the experiment seems more feasible for the
1.236 BeV. resonance.
If a null result were observed for this
33
resonance, then one could await better results from measurements of
the three-pion w 0 decay asymmetry, before deciding to repeat the
experiment for the 1.518 BeV. resonance.
34
ERENCE BACKGROUNDS
INT
An important background to the final baryon polarization
arises from interference terms between continuum (i.e. non-resonant)
final states with the N*, as well as interference terms between the
various continuum states themselves.
produce a correlation between S
reversal invariance.
These interference terms can
and k x kt without violating time
By averaging over the N* resonance peak,
interference terms due to states of different 1 can be subtracted
out, but interference terms due to states of different isotopic
spin must still
be accounted for, before a test of T t invariance
can be made from this experiment.
Such a correction may prove
impossible at the present time.
A similar experiment (also proposed by Lee) to be performed
2.7
at Harvard University
has the advantage that these interference
terms do not have to be subtracted out.
In this experiment a
polarized solid target will be used, and an asymmetry in the
initial
inelastic scattering will be measured.
It
is estimated
that e = .7% + .06% for an incident electron energy of
twenty hours running time.
6 BeV. in
The major disadvantages of this
experiment are radiative damage to the solid target, and only a
2.5% polarizing efficiency for the target.
However, improved
technology will diminish these limitations, and it
may prove more
:8
desirous to repeat this experiment at SIAC energies,
perform the experiment discussed in this paper.
than to
35
CONCLUSION
The test of T
by inelastic electron-proton scattering from
an unpolarized target appears to be unfeasible at this time.
The
predicted asymmetry in a second, elastic scattering from a carbon
analyzer would be too small to be extracted from a probable
asymmetry in the background arising from interference terms between the resonant and non-resonant states, which would produce
a polarization without violating T
invariance.
Also, chance
rates from reactions other than e + p -+ e + N*(-+ p + 7?0) would
dominate true coincidences between the electron and final proton
from N* decay for any reasonable counting rate.
will most probably make it
for a valid test of T
These limitations
necessary to look to other experiments
invariance.
36
APPEDICES
37
Appendix 1.
Here we shall derive the kinematical equations for inelastic
electron-proton scattering to produce an N* of mass M.
of the electron has been neglected.
The mass
Definitions of symbols can
be found in the text.
i)
Given k end 0, what are k,P *'
conservation of energy:
conservation of momentum:
?
k + m
kt + (1?-+.
)2
k = k'cose + P
cos4
0 = ktsine - P
sinN*
N*
N*
(1)
(2)
(3)
Moving k'co9E in (2) to the left side, squaring (2) and (3), and
then adding (2) + (3), we get:
+k,2 -2kk'cosE
(4)
Moving k' to the left side of (1), squaring (1), and then
substituting (4) into (1), we get:
p-
(M - m ))/(mP + k(l-cose))
(5)
From (3) we get:
=sn(k'sinG
$~~N* =sn
( PN*(6)
Equations (5), (4), and (6) determine k', P *, and
of k and
ii)
in terms
e.
Given PN* and k, what are Pf, k', and 0?
By using the method to obtain (4), we can similarly show:
k-2 =2
+
- N*
2kPN*cos N*
(7)
Moving k' to the left side of (1) and squaring (1), we get:
k
+m
p
+kt- 2kk' - 2k'm
p
+ 2km
p
=
N*
(8)
+
Substituting (7) into (8), we get:
2
2p
p
N
38
Make the following definitions:
ai=
-2
p
+a
a2=k + m
a3 = kCosN*
(10)
SquarjI~ng (10), again substituting (7), and solving the quadratic
equation for PN*, we get
2
2
l3
2aa
(aa a3 - aa3) + ((a 2a3 - ala 3) - (ak2 - al)(a2- a3))2
2
2
2- a3
-
PN* ~~
22
2
2
(11)
Also, from (3), we have:
N*s inIN*
-L
e=sin
(2
(*)
Equations (11), (7), and (32) determine k', P *, and
e
in terms
of k and $N*
Note that PN* has two physically possible solutions for the
same value of "N**
To adapt these equations to elastic kinematics, we can simply
replace M by m p
k'l i
elP
In this case equation (5) reduces to:
I(m + k(1
-
cosE))
(13)
and equation (11) reduces to:
2km cos
(N*m, k)
P
el
p
=l
2
k(1c
N
2
p +2km p+m
(14)
21
39
Appendix 2.
In this section we will derive the phase-space density of the
is isotropically distributed in the
final baryon, assuming that it
N* rest frame.
A +
/
F(M) dM
The total kinetic energy of the decay products p + 7T is:
T = M-m-
dT = 1
The total energy of the proton in the N* rest frame is:
-m/
M+
S=mp + m +m+T
w p
The momentum of the proton in the N* rest frame is:
2 1
!21El
2)2 'dx
Y
= P,
P11 =(E
Therefore, we find that:
dM = (dM/dT)(dT/dE,) (d /dP
) dP1
1
and:
2F(M)
B
(E M
-1)1
The transformation to the lab frame is performed by :
d AdP
=
dJbdP
1
The final result is:
.b ONC)
M+
- )2=1 WF(M),
dA-dP
-,
2(9M)2
drt, dP
\EMim.-m
ipr&ix 3.
The singles counti:S rate for detecting protons can be
calculated by integrating the electroproduction cross section
times the phase-space density of the final baryon over all electron
momenta and angles that can produce a final baryon with the proper
momentum and direction to be accepted into the proton spectrometer
and over the acceptances of the proton spectrometer itself:
2
D=
(constv-.)Jj
2
2
0 le k'
braP
d,dk
Cd
The transformation of the integral over k' to an integral over M
is performed by:
dk
N
dM.
K and k' are related by:
2
k- k'=
+
K
2m
p
K + - (l-coso).
m
p
Therefore,
1 + L-(l-coso)
p
1
=
e
1.+
1-cose)
p
From the expression for K
.dK
n -(-m
), we get:
M
T14
The azimuthal angle is constrained by 0,M, and by the momentum and
direction specified by the proton spectrometer.
over y is weighted by 6( y
be done directly.
y(e,-,,))
Thus, the distribution
and the integral over p can
We have assumed a flat distribution over the
acceptances haf and AP of the proton spectrometer in our calculations.
The final result for the singles counting rate for the proton is:
41
2
(17( C.),
P
2
2
.l
11(70,M)
Md(coSO)dM
2. + k1-cos)
p
The limits of the inte-ral are constrained by the requireent that
the Maxmnr
value and the mininm
value of the momentum of the final
baryon that can be produced for a given 0 and M contain P.
The extra
degree of freedom in cp allows the direction to conform to 0, when
the
oimentum of the final baryon for a given 0 and M is P.
Apper.dix 4.
For a given protcon poariz"tion < 2> and a given carbon
analyzing power a the differential cross section for elastic
proton-carbon scattering is:
a (0) (1 + <S,>z(O)cosT)
If cp is the azimuthal projection of the elastically scattered
0 arbitrarily set
proton on a plane perpendicular to k', with c
to lie along k x k', then I is defined to be p
on this plane.
-
It is the projection of the nornal to the elastic scattering plane
along the direction cp = 0.
91/
I'
sine de do
R af27 T
0-a
0 (0) (9 + <S.(e)cos)
Let
(k' into page)
R
L
sine de
N <1 M>
R
7 a (e) (w +a2<S.>) sine de
7 + 2a<S ?)
F(e), where F(e)
Similarly,
L) 0
sine de d 9
=fa(G)
S(7r -
(c
+ 2c<S
4<Sg) F(e).
)
sine de
fJ
a ()sine
de.
4)3
The asymmetry parc-to,
c is defined to be (R-L)/(R+L).
Using
the above expressions for R and L, we find that:
2
This is the asymmetry parameter when the direction cosines of the
elastically scattered proton are not measured, but only whether
it
scattered into the left or into the right hemisphere, which
are separated by the plane formed by k' and k x k'.
414
Appendix 5.
The decay of the 7Tr into a 7-ray and an e+ e + pair will
yield electrons that will cont'ibute to the singles rate in the
electron spectrometer.
The addition to the chance coincidence rate
from the Dalitz electron will be negligible for small values of K,
but its effects become rapidly more important as K gets large.
momentum spectrum of the e
The
determined by kinematical relationships
can be found by assuming that the matrix elements of the decay are
constant.
The spectrum will be isotropic in the 77P rest frame,
for which the following calculations have been made.
The density of states for a decay producing three particles is:
d Z
where e
and
2 2
6
(2rahc)6
2 3'-012
d%0Ud0
dnA. dpl0
2dp
2 (E-ey -
*
-
36N
3N
are the energy and momentum of the particles and
E and P are the total energy and momentum of the system.
7J*
In the
rest frame E is the mass of the pion and P is zero.
Let particles 1, 2, and 3 be the electron, the 7-ray, and the
positron, respectively.
Therefore, m
= m3 = me and r
0.
The
phase-space density of the electron can be found by integrating over
2
2
d (-) -= cep d 4
~
E 2dlT ~
2
2e
3p
(cose 2
P (m7rdpd(,
r(-61 )+e 22p2 plcos
2
Cos2
The three decay particles must be coplanar in order to conserve
momentum:
e
e+
e2
e3
30
45
From conservation o-
cr L -y ad -=antum we have the relationships:
consetvatiah o-' enery:
C3
conservation off ricrZnturi:
mi -''
2
p1 +P2 cose 2 =p
p2 sinG 2
3 cos0 3
p 3 sine 3
.
Using the methods in appendix 1. we get:
2
2
2
2
P1 hP12cosG2 + P2 = p3 = C3 - m3
Using the conservation of energy relationship above, we get:
P
2
2
2
2
p+
2pp2 cose2 + p2
2
+ c2 - 2y, - 2y2
+ 2Cic2 -7r
2
+ 2e
Using m = i
3
23
Because
e
1+2ml,
- 2m e
62
get:
2
2 2
and
=
2plp2 cose 2 + 2, 62
1 2
2
.5rr - Zprel
pcosO2 + m
2 = 0,9 p2 = e2 and two powers of p2 can be cancelled:
owe r s2s
o,, =dd p2(au
m
- e
+ plcose 2
2
7
2
=(5%r - r, 21)
2
2
J
cP2 PjfjO0
-r1-
.5r--mrei
pIcoseP+rr-el
(p cose 2 + m
e)w3(Cose2)
We will drop the leading terms in front of the integral and restore
them at the end.
We will make the following definitions:
u
p cose 2
e n - 6
2
12
2
M=.5(e + e1).
Then, the integral reduces to:
57pp1
m2 + eu
2 + e)
(u
(1p +l) 3 (
-3{ (2
2
2
2
2
)
d2 &111
ddE)
Restoring the leading terms to the expression and absorbing all
the constants into a nw constant, we get:
d (
) = c p (.5:
-e ) (e+pli) 3 (e-pl)- 3
adan
The constant was evaluated by integraying over 47r and then
numerically integrating over the limits of p1 on an I4 7044
ccmputer.
The lower limit of p is 0; te upper limit is determined
by e 1<.55r
to keep egO.
branching ratio for 7r
The result was set equal to /80,
-+ 7
the
+ e-+ e , which yielded a value of 2.66
(c /BeV.5),for c'.
Thus, the final result for the phase-space density for the
Dalitz electron is
d-N
4
5
d2($) = 2. 6 6(c /BeV. )(.5mwr~
1)
2
-3
-3 2
(e+p)-3(e-p_)-3da
x{p'j(2e2 +e')+3e2 (e 2 +el)j
Figure 12. shows the momentum spectrum- for the Dalitz electron.
The mass of the electron, although small, prevents the peak from
diverging at p1 s 67.3 MeV.
Mcm
n
I
Spetr + of Dat Elcto fo
-
est. Fme
-r
K.
..
....
J
+L
aki S. fi dte
Ca
4-3
-t
I
I
Momentu of e10
10
20
30
40
50
20
30
40
50
6o
60
(Mev./c)
70
80
80
9C
100
90
100
TABLES
4.9
Tables 1.-3. list the kinematics for the 1.236 BeV. resonance,
the 1,518 BeV. resonance, and for elastic scattering. The symbols
are defined as follows:
k = incident electron momentum (BeV./c)
e = angle through which electron is scattered (deg.)
k' = momentum of scattered electron (BeV./c)
2 /c 2
)
2 = four-momentum transfer squared (BeV.
PN = momentum of resonance (BeV./c)
P
= momentum of final baryon emitted in forward direction (BeV./c)
be = momentum of final baryon emitted in backward direction (BeV./c)
PN* = scattering angle of resonance (deg.)
Pp= momentum of elastically scattered proton (BeV./c)
scattering angle of elastically scattered proton (deg.)
$=
p
50
Table 1.
Kinematics for the 1.236 BeV. Resonance
k
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.o
20.0
e
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.o
6.5
7.o
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
12.5
13.0
13.5
14.o
14.5
15.0
19.59
19.51
19.40
19.26
19.08
18.90
18.68
18.44
18.18
17.90
17.60
17.29
16.96
16.62
16.28
16.21
15.57
15.21
14.85
14.48
14.12
13.76
13.41
13.06
12.71
12.37
12.03
11.71
11.39
2'
qN*
P
Pfe
P
be
0.12
0.27
0.47
0.73
1.05
1.41
1.8
2.27
2.77
3.30
3.86
4.44
5.06
5.69
6.34
7.00
7.67
8.34
9.42
9.70
10.38
11.05
11.72
12.38
13.07
13.67
14.30
14.91
15-52
0.535
0.673
0.&85
1.002
1.199
1.4i4
1.648
1.899
2.166
2.448
2.745
3.055
3.376
3.707
4.047
4.393
4.744
5.099
5.456
5.814
6.171
6.527
6.879
7.229
7.574
7.913
8.247
8.575
8.896
9.210
0.165
0.287
0.423
0.568
0.720
0.881
1.049
1.225
1.408
1.599
1.796
1.999
2.208
2.120
2.636
2.854
3.075
3.296
3.517
3.738
3.957
4.175
4.390
4.60e
4.811
5.016
5.218
5.415
5.6o8
0.711
0.911
1.129
1.356
1.617
1.884
2.168
2.466
2.777
3.101
3.437
3.781
4.134
4.493
4.858
5.225
5.595
5.965
6.334
6.7c2
7.067
7.428
7.784
8.134
8.479
8.818
9.149
9.473
0
N*
39.71
45.94
48.04
48.09
47.09
45.55
43.76
41.88
39.99
38.15
36.38
34.71
33.14
31.66
30.28
28.99
27.78
26.66
25.61
24.63
23.71
22.85
22.05
21.29
20.58
19.91
19.28
18.69
18.12
51
Table 2.
Kinematics for the 1.518 BeV. Resonance
N*
fe
be
N*
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
19.18
19.10
18.99
18.86
18.69
18.51
18.29
18.05
17.80
O.J2
0.26
o.46
0.72
1.02
1.38
1.78
2.23
2.71
0.890
1.034
1.124
1.422
1.652
1.902
2.168
2.452
2.750
1.139
1.262
1.417
1.601
1.808
2.036
2.284
2.550
2.832
0.083
0.159
0.251
0.353
o.462
0.576
o.696
0.819
o.947
22.10
28.92
33.09
35.35
36.32
36.45
36.04
35.29
34.34
20.0
5.5
17.52
3.23
3.061
3.128
1.078
33.27
20.0
20.0
20.0
6.0
6.5
7.0
17.23
16.92
16.60
3.78
4.35
4.95
3.384
3.718
4.061
3.438
3.76o
4.091
1.212
1.349
1.489
32.15
31.01
29.89
20.0
7.5
16.27
5.57
4.411
4.430
1.631
28.79
20.0
20.0
20.0
8.o
8.5
9.0
15.94
15.59
15.24
6.20
6.85
7.50
4.767
5.128
5.491
4.776
5.128
5.48
1.774
1.918
2.063
27.72
26.71
25.73
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
9.5
14.89
8.17
5.856
5.839
2.208
24.81
20.0
20.0
20.0
20.0
20.0
10.0
10.5
11.o
11.5
12.0
14.53
14.18
13.83
13.47
13.13
8.83
9.50
i0.16
10.82
11.47
6.222
6.586
6.948
7.308
7.663
6.196
6.553
6.908
7.260
7.609
2.353
2.497
2.640
2.781
2.921
23.94
23.10
22.31
21,57
20.86
20.0
32.5
12.78
12.12
8.014
7.953
3.058
20.20
20.0
13.0
12.44
12.76
8.359
8.292
3.194
19.56
20.0
20.0
20.0
20.0
13.5
14.0
14.5
15.0
32.11
11.78
13.38
14.oo
14.60
15.19
8.698
9.030
9.356
9.674
8.625
8.952
9.272
9.585
3.326
3.457
3.584
3.708
18.96
18.40
18.86
17.35
11.46
11.15
52
Table 3.
Kinematics for Elastic Scattering
k
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20,0
20.0
20.0
20.0
k'
1.0
1.5
2.0
2.5
3.0
3.5.'.
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
22.0
22.5
13.0
13.5
14.0
14.5
15.0
19.94
19.85
19.74
19.60
19.43
19.24
19.01
18.77
18.50
18.21
17.91
17.59
17.26
16.92
16.56
16.21
15.84
15.48
15.11
14.74
14.37
14.01
13.64
13.28
22.93
32.59
22.25
11.91
11.58
pp
0.12
0.27
0.48
0.75
1.07
1.44
1.85
2.31
2.82
3.35
3.92
4.52
5.15
5.79
6.45
7.12
7.80
8.49
9.18
9.87
10.56
11.25
11.93
22.60
13.26
13.91
14.55
15.18
15.79
0.354
0.541
0.739
0.591
1.178
1.1121
1.681
1.958
2.251
2.559
2.881
3.214
3.559
3.932
4.273
4.639
5.009
5.381
5.755
6.128
6.500
6.868
7.234
7.594
7.949
8.299
8.642
8.978
9.306
p
78.97
73.71
68.72
64.04
59.70
55.71
52.07
48.75
45.74
43.01
40.53
38.28
36.23
34.36
32.65
31.09
29.65
28.34
27.12
26.oo
24.95
23.99
23.09
22.25
21.47
20.74
20.05
19.40
18.80
53
Tables 4.-5. list the kinematics for elastically scattered protons
scattered into the angle ,* * The momenta of forward emitted and
om inelastic scattering are also listed
backward emitted protons
for comparison. We have let k = 20 BeV., as elsewhere in the
are defined in Tables 1.-3. The other
, and P
, P
paper.
de~ned as 0llows:
symbols ae
P
= momentum of elastically scattered proton (BeV./c)
k
= momentum of elastically scattered electron (BeV./c)
four-momentum trxnsfer squared for elastic
scattering (BeV.'/c 2
=
angle through which electron is elastically scattered (deg.)
)
=
G
54
Table 4.
Elastic Scattering Kinematics for Protons Scattered into
8 BeV.
Hodoscope
(compared to 1.236 BeV. Peaks)
N*
39-71
45.94
48.04
48.09
47.09
45-55
43.76
41.88
39.99
38.15
36.38
34.71
33.14
31.66
30.28
28.99
27.78
26.66
25.61
24.63
23.71
22.85
22.05
21.29
20.58
19.91
19.28
18.68
18.12
fe
o.673
0.&5
1.002
1.199
1.414
1.648
1.899
2.166
2.448
2.745
3.055
3.376
3.707
4.047
4.393
4.744
5.099
5.456
5.814
6.171
6.526
6.879
7.229
7.573
7.913
8.247
8.574
8.896
9.210
be
0.165
0.287
0.423
0.568
0.720
0.881
1.049
1.225
1.408
1.599
1.796
1.999
2.207
2.420
2.636
2.854
3.074
3.296
3.517
3.737
3-957
4.174
4.390
4.602
4.811
5.016
5.218
5.415
5.608
el
el
el
el
2.997
2.231
2.024
2.019
2.115
2.271
2.470
2.700
2.957
3.235
3.531
3.842
4.166
4.501
4.844
5.194
5.548
5.905
6.263
6.622
6.070
7.334
7.686
8.033
8.376
8.713
9.043
9.367
9.684
17.80
18.52
18.71
18.71
18.62
18.48
18.30
18.08
17.84
17.57
17.28
16.98
16.67
16.34
16.oo
15.66
15.31
14.96
14.61
14.25
13.90
13.54
13.20
12.85
12.51
12.18
11.85
11-52
11.21
4.13
2.78
2.43
2.42
2.58
2.85
3.20
3.60
4.06
4.56
5.10
5.66
6.25
6.87
7.50
8.14
8.80
9.46
10.12
10.79
11.45
12.11
12.77
13.42
14.05
14.68
15.30
15.90
16.50
6.18
4.97
4.61
4.61
4.77
5.03
5.36
5.72
6.12
6.53
6.96
7.4o
7.85
8.31
8.78
9.25
9.72
10.20
10.68
11.17
11.65
12.14
12.63
13.12
13.61
14.10
14.60
15.09
15.59
55
Table 5.
Elastic Scattering Kinematics for Protons Scattered into
8 BeV.
Hodoscope
(compared to 1.518 BeV. Peaks)
N*
4)
fe
PP
be
kt'
el
2e
el
el
22.10
28.92
33.09
35.35
36.32
36.45
36.04
35.29
34.34
33.27
32.15
31.01
29.89
28.79
27.72
26.71
25.73
24.81
23.93
23.10
22.31
21.57
1.139
1.262
1.417
1.601
1.808
2.036
2.284
2.550
2.831
3.128
3.438
3.760
4.091
4.430
4.776
5.128
5.482
5.839
6.196
6-553
6.908
7.260
0.083
0.159
0.251
0.353
0.462
0.576
o.696
0.819
0.947
1.078
1.212
1.349
1.489
1.631
1.774
1.918
2.063
2.208
2.353
2.497
2.640
2.781
7.660
5.212
4.176
3.719
3.541
3.518
3.592
3.730
3.916
4.137
4.386
4.658
4.947
5.251
5.566
5.889
6.219
6.554
6.891
7.229
7.567
7.903
13.22
15.64
16.66
17.10
17.27
17.30
17.23
17.09
16.91
16.70
16.45
16.19
15-90
15.60
15-29
14.97
14.65
14.31
13.98
13.65
13.31
12.98
12.72
8.18
6.27
5.44
5.11
5.07
5.21
5.46
5.80
6.20
6.66
7.16
7.69
8.25
8.83
9.43
10.04
10.66
11.29
11.92
12.55
13.17
20.86
7.609
2.921
8.237
12.65
13.79
13.41
20.20
19.56
18.98
18.40
17.86
17-35
7.953
8.292
8.625
8.952
9.272
9-585
3.058
3.194
3.326
3.457
3-583
3.708
8.567
8.893
9.213
9.528
9.837
10.140
12.32
12.00
11.68
11.36
11.06
10.76
14.41
15.02
15.62
16.20
16.78
17.35
13.89
14-37
14.86
15.35
15.83
16.33
12.59
9.27
7.87
7.23
6.98
6.94
7.05
7.24
7.51
7.81
8.16
8.53
8.92
9.33
9.75
10.18
10.62
11.07
11.53
11.99
12.46
12.93
56
Table 6. lists the predicted running times based on a 10% measurement of E for forward emission and for backward emission for the
first two resonances. Corrections have not been made for chance
rates nor for radiative tails. Entries have been omitted in the
cases where the final baryon has a kinetic energy greater than
1.6 BeV., for which the validity of the approximation to the
analyzing power of carbon is doubtful. These running times can
most likely be reduced by a factor of 1/180 (see text).
57
Table 6.
Predicted Running Times
(hours)
1.236 BeV. Resonance
1.518 BeV. Resonance
0
fortard
backward
1.0
3.7x10 3
9.6x10
1.5
2.5
3.9x103
8.xO3
1 .3x10 4
3.0
3.5
2.0
4.0
4-5
5.0--
backward
1.4x10 1
3 .0xj106
5.5x10
8.6x1014
1-7x10 5
1.5x10 5
2.6x1io4
3 -x105
2.1x10
1.6x10)4
7.3x10 5
3.9x10
8.8x10 4
2 .4x10
1.9x10
1.5x106
5 -lxl 4
5.7x106
1.2x106
2-4x,05
7.8x101
1.6x10 6
1.2X1-05
3 -lx10 6
7
'
forward
2.6x109
2 .1x08
2.9x107
58
ACKNOWEDGEME1I2S
The author wishes to thank Professors Jerome I. Friedman and
Henry W. Kendall for their immeasurable assistance and kind
patience in acting as my thesis supervisors.
I would also like
to express my deep appreciation for the willingness and
attentiveness of G. Hartmann, M. Sogard, and J. Elias, who
gave much of their time in helping me.
M. Breidenbach and
D. Freeman are to be thanked for their perceptive criticism.
Notes and References
1. Wh, C.S., Ambler, E., Hayward, R.W., Hoppes, D.D., Hudson, R.P.,
Phys. Rev., 2Q5, :113,(1957).
2.
Christenson, J.H., Cronin, J.W., Fitch, V.L., Turlay, R., Phys.
Rev. Letters, 13, 243, (196.
3.
Christ, N., Lee, T.D., Phys. Rev., 1U.1 1310, (1966).
4.
Lee, T.D., Wolfenstein, L., Phys. Rev., 28, 1490, (1965).
5. Actuaily, this may not be a very good approximation.
BeV. resonance, for example, is in a 1 = 1 state..
The 1,236
.29, 1834, (1963).
6.
Hand, L.N., Phys. Rev.,
T.
Proposals for Initial Electron Scattering Experiments wing the
SIAC Spectrmeter Facilities, Proposal Number 4b, January, 1966.
8. Proposals for Initial Electron Scattering Experiments using the
SIAC Spectrmeter Facilities, Proposal Number ha, January, 1966.
9.
Meister, N., Yennie, D.R., Phys. Rev., J30, 1210, (1963).
10.
The peaks are about this wide in momentum at a given electron
scattering angle. See reference 7.
11.
Orear, J., Notes on Statistics for Physicists, Lawrence Radiation
Iab, August, 1958.
12. Batty, C.J., Goldsack, S.J., Proc. Phys. Soc., ,1, 1'; (1957):
970 MeV. for carbon.
13.
Mescheriakov, M.G., Nureshev, S.B., Stoletov, G.D., Soviet Physics,
JETP, 6, 28 (1958):
summary for bydrogen.
3,
580, (1961): mari
kinetic energies
14.
Batty, C.J., Nuc. Phys.,
for carbon.
15.
Brown, G.E., Proc. Phys. Soc., AL0,,361, (1957):
16.
Bareyre, P., Detoeuf, J.F., Smith, L.W., Tripp, R.D., Il Nuovo
Cimento, 2.Q, 1049, (1961): maximum polarization vs. energy for
carbon and for hydrogen.
17.
Wolfenstein, L., Ann. Rev. Nuc. Sci., .6, 43, (1956): good
theoretical article, also gives polarization for marr energies
for hydrogen.
.BeV. for hydrogen.
18. Venter, R.H., Frahn, W.E., Ann. Phys., .27j 385, (1964): 183 NeV.
for carbon.
19.
Heiberg, E., Phys. Rev., .1_6, 1271, (1957): 424 and 220 MeV. for
carbon.
60
20.
Chamberlain, 0., Pettengill, G., Segre, E., Wiegand, C., Phys.
Rev.,
, 1348, (1954): 300 MeV. for hydrogen.
21.
Chamberlain, 0., Garrison, J.D., Phys. Rev., .,
170 and 260 MeV. for hydrogen.
1349, (1954):
22. IcManigal, P.G. Eand, D., Kaplan, S.., Moyer, B.J., Phys. Rev.,
-3,. 620, (196t): 723 MeV. for carbon and hydrogen.
23.
A measurement for Beryllium at 1.16 BeV. suggests that the curve
falls more rapidly at large kinetic energies. See reference 16.
24.
The increase in the uncertainty in the asymmetry measurement that
would result from this increase in the uncertainty in k would
have to be studied.
25.
lee, T -D., PIvs. Rev., Q32, B1415, (1965).
26.
Flatte, S.M., Huwe, D.O., Murray, J.J., Button-Shafer, J., Solmits,
F.T., Stevenson, M.L., Wohl, C., Phys. Rev. Letters, 1., 1095, (1965).
27. Wilson, R., CFA Project Proposals, January, 1966.
28.
The asymmetry parameter goes roughly as.7k 2 , because of the presence
of Is x It in the time reversal non-invariant term.
i
Kinematics, W.A. Benjamin, Inc., New
29.
Hagedorn, R.,
York, 194, p.43.
30.
Williams, W.S.C., A Introduction to Elemertary Particles, Academic
Press, New York, 1961, p. 373.