I
DEEP INELASTIC
July 1975
(T/E)
ELECTRON AND h/LUONSCfiTTEItING
--
R. E. Taylor
Stanford Linear Accelerator
Center,
Stanford University,
Stanford, California,
USA.
INTRODUCTION
Last summer there was great concern over an apparent contradiction between storage ring data
on hadron production 132) and theoretical predictions based on scaling in deep inelastic scaltering
experiments. 354) Last fall, along with the discovery of the new particles, 526) more accurate data
on the ratio
+-
- hadrons)
e
‘+Tot (e e + P+P-)
Tot@
RA =
became available7)
stant as expected,
(Fig. 1). At low values of ECm, RA now appears
to be compatible with a conand the value of RA in this region is not too far from a model prediction
colored quarks in which RA = 2. The existence of the new particles
in RA between E cm = 3.5 GeV and Ecm =5 GeV so the conflict
scattering
has been removed,
The new particles
and the step in RA may, however, have effects in the deep inelastic.
Figure 2 shows one of these pictures,
indicating
thresholds,
for the,stcp
between these data and deep inelastic
at least for the present,
at Bonn, Bjorken8) drew several pictures interpreting
ways.
provides a rationale
based on
the large values of RA from CEA in diflerent
and Figure 3 is an update of another figure in his talk,
that there may be enhancements of the structure
Obviously,
In 1973,
Figure 3 is just a qualitative
functions above the color or charm
guess, but the discovery
of a new mnss scale
some three times heavier than the proton introduces yet another way in which scaling in the deep inIn addition,
elastic region may bc broken.
In inclusive
produced like p mesons.
important
occur,
scattering
experiments
the low mass vector mesons may be
effects due to the 4 mesons might be seen if O2 > &I2 Even
VJ’
of G’s should
measurements, electroprcduction
at small x, and similar
though + production
the $ mesons are vector mesons and will be diifractivcly
effects may be small in inclusive
although they have not been detected to date.
The Chicago-Harvard-Illinois-Gxford
coilabo-
ration at NAL have searched their p scattering
e’s, but their sensitivity
data tapes for p tridents arising from p pair decay’ of
9,235)
They are improving the sensitivity
and none were found.
is limited,
In an abstract submitted to this conference, lhe
10,23a)
report the observation of muon tridents
Diego group
of the apparatus to such events for future runs.
Cornell.-hfichigan
State-Princeton-San
in their apparatus at NAL.
They will present results to the conference.
The effect of the two li)*s on the elastic form factors is expected to be very small,
Q2 = 30 (GeV/c)2 basically
GeV “disturbance”
because the coupiing of the G’s to hadrons is so weak.
has a larger width and might give a larger contribution,
-3
r: 10
eveli
at
The Ecm = 4, 2
but its properties
are
not yet well established.
A more speculative
possibility
If there existed charged particles
peaks in inelastic
scattering
concerns th e existence of other new particles,
(positive char ‘gz, and baryon number = 1) they could show up as
spectra.
cause a “step” in the spectrum
related to the ii;‘s.
(In addition,
at the appropriate
pair or associated production
lhreshold,
of particies
but since n’s, K’s, Kh, etc.,
should
are noi
detected in this way, this is not a very sensitive way to hunt for new particles. ) In a previous
(Invited paper presented at the Int. Conf. on High Ecergy Physics sponsored by the Eurcpean Physical
Sociely, Palermo, Italy, June 23-28, 1975.)
experiment,
SLAC (Group A)“)
final slale masses of 3 Ge;‘.
“scans” to the limits
had made a high resolution study of inelastic spectra at 4’ UP to
XfkL’ 6L-Z;IrKdJLd~cernentof tile :,e~y pir&iea,
WV ~ornplat.ed t&se
set by SLAC’s beam energy.
NO spikes (or steps) were seen (Fig. 4).
Roughly speaking, anything with an amplitude of about 10’; of the third resonance, and a width less
than a few hundred MeV, would have been visible.
perimental
resolution
(- 5 MeV) such a criterion
For resonances of widths smaller
than the ex-
Corresponds very roughly speaking to an integrated
total photo cross section of 2 8 ,ub-MeV.
SO, for now, the major consequence of the new discoveries
rehabilitation
of the constituent
deep inelastic
scattering
models which grew out of
for
Bjorken's
deep
inelastic
early
predictions
scattering is the
12) and the
data.
We, therefore, return to the problem of measuring the nucleon
structure functions where the principal topic of interest is still the status of scaling of the structure
functions,
This topic was carefully reviewed by Gilman at London in 1974. 4)
ELASTIC SCATTERING
Before covering the progress
since London on that topic, I want to comment on some elastic
electron scattering
surements13)
results.
Figure 5 shows Q4 GG plotted against Q2. There are some new meashown, including a point at Q2 = 33(GcV/~)~, but the main point I want to make is the
convincing evidence for l/Q4 behavior at large Q2. Erodsky and Farrar’4) have pointed out a conP
nection between the power behavior of GM and the number of “fields” in the hadron under their dimensional scaling laws.
For the observed l/Q4 behavior this gives three fields for the proton.
West15) has pointed out (with his tongue at least partly in his cheek) that the lack of diffraction
elastic form factor is some kind of evidence against a large number of constituents.
the obvious difference
(though not conclusive)
in Q2 behavior in elastic and inelastic
scattering
in the
More generally
is in itself significant
evidence for nucleon substructure,
Figure 6 shows some recent results from a coincidence experiment measuring elastic e-d scattering by Arnold et al. 16) The cross section drops precipitously and shows no sign of flattening out,
as might have been expected for scattering
from meson exchange currents.
The data are in rough
-20
depenagreement with some of the standard fits to lower Q2 data and possibly approach the Q
dence which can be obtained from simple quark counting.
INELASTIC
STRUCTURE FUNCTIONS
inclusive electron scattering
In the one photon approximation,
cross sections from unpolarized
nucleons can be expressed as
da
d&lE’
du
= (dx)
!\?v fv ,Q~) + 2 tan20/2 WI(v) Q2)]
Mott l 2
(2)
= Q’ = 4EoE’ sin28/2
,
v = E. - E’ ,
3
if’- = ‘)!~IJ.J+ &I2 - Q2
(3)
I
-3-
Unobserved Hadronic
State with Mass W
Final
’
1
\
w
=2My
Q2
(IJ’
’
=-
W2
+1 =w+2 M2
Q2
K
wl=--$<,
uT
w2
=--
K
Q”
al,+%
M2 Q2+v2
uO
4n20!
= = 127 pb ,
M2
(4)
Q
(5)
ao
“S
R =-,
“T
K = W2-M2
2M
Ideally,
one wishes to obtain WI and W2 from measurements
12)
test the resulting structure functions for scaling.
Q
Definition
21im vW2(v ,Q”)
-CC
of a kinematic
= F2(o)
,
Q
(6)
of differential
cross sections and
2 lim 2MWI(v ,Q2) = F~(w)
-CO
region in which scaling is expected to hold is not a trivial
task.
Fig. 7
shows some of the problems which occur:
1)
Two-photon Exchange,
The usual analysis neglects two-photon exchange effects,
such effects are present,
will be incorrect.
If
the measured values of vW2 and WI obtained from experiment
Such terms should show up first at high Q2 and low W where the
cross sections are smallest.
2) Q2 Turn On. W2 = 0 at Q2 = 0, so vW2 will not scale for low Q2. This region is
further complicated by diffractive processes (e. g. , vector meson production).
3) Resonance Region. The structure functions will not scale in a region where resonances
occur at fixed values of W and therefore different values of v/Q2. Strong assumptions
about local duality have been used to connect average values of VW 2 from these regions
2 1’7)
to values at higher Q .
4) Non Leading Terms. In the region of finite Q2 the structure functions may contain
terms with powers of I/Q” which can produce measurable effects. Such terms may be
more important
5)
at low w where the cross sections are small,
Choice of Scaling Variable.
The scaling variable,
any variable which approaches w in the limit
cause elastic scattering
w, can in principle
be replaced by
Q2 - M. w is an appealing variable bc-
from light, free constituents
would give a peak at w = M/;\Ic,
where Mc is the mass of the constituent.
6) Sc:de 3ronl;inf$
been proposed.
“arious
ways in which the scaling conjecture
Popular examples of scale breaking arc:
might be modified have
-4color or charm “thaw”; 13)
parton form factors, 19) anomalous moments ;20)
theories with anomalous dimensions; 21) and
asymptotically free theories. 22)
The experimentalists’
aim is to establish scaling in some region (and to some accuracy),
and
then look for various scale breaking phenomena such as those listed under No. 6. It is difficult
reach definite conclusions when the observation
or more of the other effects listed above.
As the range and precision
understanding
behavior may be due to one
There are both old and new examples of this problem.
of the data increase,
and precision
of apparent non-scaling
to
we need a corresponding
increase in theoretical
to deal with effects at finite Q2.
ELECTRON SCATTERING
The past two years have seen considerable
the first results
Fermilab
growth in the amount of experimental data, including
scattering using both neutrinos 4) and p mesons 23) from the
on really deep inelastic
accelerator.
Figure 8 shows the kinematic range available in the Q2, W2 plane for SLAC
energies and for 56 and 150 GeV n mesons, the latter two energies being those of the “scale invariant”
~1experiment
at NAL.
That Bjorken’s
predictions
by almost an order of magnitude is truly impressive,
trino experiments
experiments
earlier
with the simple quark ideas.
have continued,
experiments
electrons
increasing
have withstood the strain of increasing
as is the spectacular
hleanwhile,
both the precision
agreement of the neu-
back at the Farm, electron scattering
and kinematic
range compared with
Data taking has recently begun on an experiment
target, but no results are available yet. 24)
at SLAC.
and a polarized
u
using polarized
The structure functions WI and W2 can be determined from measurements of the differential
.cross section. Figure 9 shows the region in which measurements can be made for energies employed at SLAC and in the Cornell-Michigan
of the structure
between W1 and W2 to obtain the value of either structure
the structure
at various angles for a given
exist at only one angle, some assumption must be made about the re-
usually described in terms of the longitudinal/transverse
kinematics,
apparatus at NAL. 25) Values for each
functions can only be obtained by doing measurements
Q2 and W. If measurements
lationship
State-Princeton
function,
ratio R = aS/oT (see Eq. (6)).
functions are not very sensitive to R.
is
For some
For example, we can write
(1+&Q2)
2
-1
tan20,2
VW2
The relationship
(l+R)
If 0 is small enough, then the second term may be quite unimportant.
1
The region where uW2 varies
less than 10% as R varies from 0 - m is shown in Fig. 2 (for 20 GeV incident energy this region is
smaller than the region in which measurements of Ii have been made). If 6 <R < 1, the maximum
error
in the indicated region would drop to 5%. %‘Ure 10 shvs
in more detail the, regions in which
WI and W2 have been separated to date.
(SFG
Group). 26)
The most recent published results on \\‘i 2nd \\‘?., :lre whose of the ikIlT-SLAC
Using
these results, from measuremCntS at :1nglCS bChVfX11
15’and 34’, combined with some older
data at 6’ and IO’,~~) they find that Ii is - O-5 Or less 9 everywhere in the region of measurement, 28)
At 10~ values of w, VR is
nppI?OXilllatCly
lightcone algebra, whereas at large
COllSt:lnt
W,
[It iI f$Vell
VdX
of
W,
I~R :lppears to bC increasing with
as expected
Q2
from
the
rather quickly,
quark
as
I
-53k1-;2 IL1Fig. 11. In oLJcl LULeach
“turn on”.
large w, Q2 is raLher small,
and the effects could be due to
Work is continuing on this data set, and more results are expected soon.
SLAC (Group
A) now has an independent set of data at angles from 4’ to 6Oo and will generate similar
From the time of the first
in the kinematic
values of W.
29) it has been clear that yW2 is not a function of w
R determinations,
region covered,
These deviations
information
but that systematic
deviations from scaling in w occurred at small
could be removed by assuming that scaling holds in
W’
= w
+
M2/Q2
= W2/Q2 + 1 so that
2
VW 2 (Q > 1) = F (w’) to N 1096
2
Since Qpnjw w’ = w, this has no consequences for the theory.
There was even a bonus in that F2(mt)
17)
‘appealed to average nicely over v W2 in the resonance region,
including the elastic peak. Scaling
in w can never “average” the elastic peak since F2(w) = 0 when iv = Mp:
If one takes this averaging seriously,
one can evaluate integrals
over the data of the form
vW;(w’,Q2)
(9)
as Bloom did in 1973. 30) The condition fcr true Bjorken scaling is that all Bn should approach a
finite nonzero limit as Q2 increases without limit.
Low moments (e. g. , B. in Fig. 12a) appear
quite flat for Q2 > 1.5 (GeV/c)2. Higher moments (e. g. , B3 in Fig. 1.2b) are not quite flat, but the
contribution of the elastic peak and the resonance region is larger, and conclusions depend heaviiy
on the “averaging”
MIT-SLAC
assumption implicit
in the procedure.
(Bloom’s analysis included most of the
(SFG) e.xperiment at No, 26’, 34’ and a preliminary
data and so is still fairly
version of the SLAC (Group A) 4o
up-to-date).
There is really no evidence for scale breaking in vW2 in the MIT-SLAC
(SFG), SLAC-MIT,
or
SLAC (Group A) results,
when R is taken to be . 1G-. 18 everywhere in the Q2,W plane, and wf is
VW behaves as expected in scaling theories for small values of w but
used as the scaling variable.
is not a function of w for large w, rising with increasing
In an,interesting
paper last
of assuming that the non-scaling
(and, therefore,
year,
33) the MT-SLAC
in (:, was not due to
could not be “repaired”
Q2 at constant w.
(SFC) group investigated
k3rlnS
the consequences
of order M2/Q2 in the scaling variable
by Ch;ill$l:g 10 u”) but rather was due to scale breaking.
They obtained coefficients
for several proposed kil:cis of brc:l!iing, giving estimates for the para,n-.
sugFor e~:~inPle, ill fitting to a form F(Q2) = a(l-2Q2/A2),
I!))
.I IUrl)s
Wt
LO be around 8 C;e\‘.
This is another
gested
by the postulated parton form factors,
.sc;llin::
in
;i
;u~ri
(,,J’
.
way of describing the difference between I’\\‘,,
can trade changes in variable for changes
in the paralneters
Of SCX~C? bI*C':ll;ill!:
Il!C'cll.iC'!<.
‘f’k reader is referred to the orig26)
for
the
details
of
fits
to
other
hC:llC
lil’l,:ti:in:
hypotheses.
inal paper
eters of different
kinds of breaking.
One
During the past year, SLAC (Group A) lxl> j!Ui~ll~;ll(‘~l rCSUitS from measurements at * 0 , 11)
Among
other things, the data give new infoL’llJ:i tl
2’ The data are shown in
‘iI::!:71Gt
tiic:ur~~-o~~
ofvw
Fig.
13 and
can
from
WI depelldence
be
approximnted
by Cl Sil>;:lc
and can be approsilllatcil
f~l:('li\'li
)‘J
$11 0".
'I'hiS
(2'
dCpeildcnce
can
be fa,ctored
out
I
where
GE(Q
7Ghl(Q
2
W;‘(Q2) =
Any respectable
2
2
I+
1+7
theorist will tell you that a “closure”
2
1
(11)
T:: Q2/4M2
relation like this cannot be applied to a rela-
tivistic system, so this is just a convenient way to remember how tjW2 behaves as Q2 - 0.
In any Case, the form is a reasonable fit to the data, so we have used the expression to estimate
vW2 for large values of w(, even though the data do not reach values of Q2 where scaling “holds.”
The results of this are shown in Fig. 14. Extrapolation from data wholly outside the scaling region
(Q2 < 1) begins at
- 25, SO above this value the specific form of Eq. (10) is important.
Data at
large values of w’ have always tended to decrease for values of wl > 6. There has been suspicion
that #is decrease was an artifact of “turn on, ‘1 The new data suggest that this is not the case, and
W’
. that there is a maximum in vW2 at ~1 - 6.
The most recent single arm experiment
at SLAC13) completed data taking about a year ago.
Data were taken at 50’ and 60’ using the 1.6 GeV spectrometer, reaching values of Q2 near
30. (GeV/c)2 but limited to values of w < 2 (Fig. 15). At large angles, WI can be extracted from the
data without detailed knowledge of R if R is small. For these kinematics
= WI(R= 0) (1 - 2E’R,‘Eo)
WICR=R)
(12)
If R < 0.5, then W1 is determined within about 5% at 60’ and 20 GeV incident.
and extract WI from the measured cross sections.
spin i and spin 0 (glue) constituents,
have any validity,
with a prediction
In a model where the scattering
W1 is determined by the properties
while W2 includes additional contributions
We assume R = .18
takes place on
of the spin i particles
If the simple pictures
from spin 0 particles.
the proton
of
we expect W1 to scale at least as well as vW2. We can compare our values of W1
based on vW2 measured at smaller angles and our assumed value of R since from
Eq. (5) and the definition
of R
Q2 + v
(Wl)predicted
= vw2
The values of W1 and the “prediction”
2
(13)
vQ2(1+R)
are shown in Fig. 16. The agreement is reasonable over
nearly three decades in the value of W1, but WI tends to fall somewhat lower than the prediction at
large values of Q2. Of course, WI will not Scale esactly if vW2 scales and R is constant, The differences are small, as shown in the figure by “prediction” for different energies.
A clear-r picture of WI behavior
~33 be Ob’iZklC:l
fro111 Fig.
17. Here values of WI measured
for each incident energy are plotted against
Q2.
The measurements
are binned in ~1 and particular
values of ~1 are connected by straight lines. If WI scales, the connecting lines should be horizontal.
about
R in the hope that some other
Obviously W1 is not scaling. We can re-esaminc thC 2SSUlli)tion
behavior of R will restore scaling. Incrcnsilg R )o\v~‘r~ the extracted value of WI.
R to zero at high Q2 we can raise the values ()I’ \\‘I d)OUt 8’; iI this region and by rai&g
Q2,
values
of WI
be approximately
can
be
lowered.
2 in the low
Q2
region9
Yihich
(The correct way to show this is to include ’ t.h(’
program is not yet complete. ) The COIlClllSi(~ll
SO
that
WI
A more
is
just
in order
Ullfort~~l~:itCIY,
C()nfliCtS
MY!
to I-IX&~
\!‘it.h
v:lri;ltions
&atc?. Scale,
l?lEaSure]nentS
~~~C~~SIlI’ClIlCIlfS
iS th:It
this
in the
evaluation
change
decreasing
R ai: Innr
R would
of R in
in R cannot
By
this
to
region.
of R,
tile
have
but
values
that
of WI
a function (3’.
qUantibtiVe
lllEWIre
each value of wI in Pig. 17. The
of this
no!l-se:lliIlg
reSLlltS
t0
Cl!1 be
Obt;lined
a lit. of thC form a(1 +
by
bQ2)
fitting
the
Q2
slope
Of W,
at
are shown in Fig. 16. Each
- 7-
mtiasured slope should b:: LC:L’Uior scaling to hold.
using different
Figares i;,,
iiL,
;:;d 182 s&v
the efticts
ol‘
scaling variables.
Fig. 18a shows that scale breaking will be even worse in w =
Bjorken variable.
Fig. 18c shows that WI can be made to scale in a new ad
2Mv/Q2, the original
hoc variable ws, which is similar
in form to W’ = ~3+ M2/Q2 = o + 0. s~(G~V/C)~/Q~.
= w + 1.42(~ev/c)~
W
6
This is not very satisfactory,
particularly
Q2
since vW2 does not appear to scale in ws.
more unpleasant is the behavior of WI at low values of ws.
W1 = g
Perhaps even
In a fit of the form
an(l-xs)n
the coefficient
a3 is small and compatibIe with zero, while a4 is Iarge and positive.
This is in31,32)
compatible with the Drell-Yan-West
relationship,
The same dependence holds for W’ fits ex2
cept that the x is larger and a5 and a6 are more important.
The choice seems to lie between a somewhat artificial
search for more complicated
in which WI and vW2 scale and accepting some scale breaking
I’m sure that both alternatives
press the non-scaling
as parameters
will be explored.
in terms of the experimental
for a particular
(perhaps due to nonleading terms).
l?or the present, it seems less confusing to exnumbers and (tit scaling with R = .18, rather than
theory expressed in a particular
40% low at Q2 - 25-,3O(GeV/c)’ compared with our expectations
All the recent measurements
variables
have included measurements
variable.
Our data for WI fall 30based on vW2.
on deuterium
so that structure
func-
tions for the neutron can be extracted.
Fig. 19 is a composite of available results on the ratio
11,13,32)
The 50’ and 60’ data are preliminary
and assume R = Rd = .18. The data are
n/p.
P
crowding the current algebra limit of i, but there is no evidence that the limit is violated.
The comprehensive
studies of data being undertaken independently by MIT-SLAC
SLAC (Group A) should provide new checks of Rd and Rp and new comparisons
(SFG) and
of deuterium
and
neutron scaling.
It is obvious’ly of great interest to know how D2 behaves in the region where W1
exhibits non-scaling behavior.
’
MUON SCATTERING
Knowledge of vW2 for deuterium
the NAL data taken with Fe targets.
periment,
I want to consider
is necessary for a clean comparison
Before describing
of data from SLAC and
some of the recent results from this ex-
three topics which are relevant to the comparison
with the electron data: ~1-e universality,
2-photon exchange processes,
of their muon data
and A-dependence.
p-e universality
The past two years have seen the publication
ments at BNL involving experimenters
results add considerably
of several results from a series of muon experi-
from Rochester, Columbia, Rarvard, and NAL. These new
33)
and taken together present a picture of p-nucleon
to previous results
scattering very similar to that obtained with electrons.
Radiative corrections tend to be considerably smaller for p-meson scattering, so the general agreement is weicome confirmation that there
are no gross errors
in the radiative
of possible p-e differences
corrections
to electron e.xperiments.
can be obtained in both elastic and inelastic
Quantitative
scattering
expressions
experiments.
I
-av.1
’ tne ~1results are shown i;l Fig. 20 and show a small systemaLic trend
away from careful fits to e-p data (the “dipole” curve in the figure is actually slightly modified to
For elastic scabterm;:
represent
the e-p data more closely).
The data are fit to a form
(16)
where N is a normalization
parameter
and A is a possible difference
presented in Fig. 21, and a value of l/A2
to n’p-,
inelastic
The results are
= 0.051 f 0.024(CeV/~)-~
authors conclude that possible deviations are not proven,
annihilation
parameter.
results from the fits. The
+and that other experiments (g-2, e e -
(see below), etc. ) provide little if any corroborative
support for this
large a deviation from universality.
Some preliminary data presented at London last year by the
Santa Cruz-SLAC collaboration showed good agreement between e’s and p’s, 35) Nevertheless, as
for some years past, the elastic results continue to nag us for a definitive experiment.
In another paper 36) results are given for:d20/dQ2dv,
as shown in Fig, 22. The agreement with
electron scattering is quite good, as demonstrated in Fig. 23, where the parameters of an overall
fit similar to the elastic case are given for the BNL experiment and a combination of this experiment and the older experiment from SLAC. 33)
Two-photon effect
A comparison of CL+and ~1~scattering from beryllium has been made in a search for two-photon
exchange amplitudes. 37) The experiments measure only the real part of a two-photon amplitude.
The results are shown in Fig. 24b, and there is no evidence for any asymmetry
Similar
experiments
have been done recently with electrons
and positrons
from the UC-Santa Barbara campus quote a result of38) e’/efrom deep inelastic
yields out to Q2 = 15 (&V/C)~,
ratio of yields,
amplitude,
Recently,
from
of their search for wide-angle
SLAC (Group A) has results
on’ e+/e-
as shown in Fig. 24a. I must emphasize that the figure shows the
not cross sections.
other processes
collisions.
on H2 and D2. A group
= 1.000 -+ .003 for scattering
hydrogen in the Q2 range from 1 to 3 (C~V/C)~, as a by-product
bremsstrahlung
between pf and ~1~.
At high values of Q2 there are contributions
of up to half the total yield.
to the yield from
To extract a limit for the ratio 2-photon to l-photon
one must (a) assume that the backgrounds have no asymmetry,
and (b) increase the error
proportionately.
The Cornell-MSU-Princeton
the Fermilab
experiment
In another contribution
tron and positron-proton
collaboration
have compared the scattering
of 150 CeV 1-1’and w- in
and detect no asymmetry with an accuracy of better than 5%. 39)
to the conference, 40) no asymmetries
scattering,
both elastic and inelastic,
were observed in comparing elecat DESY.
A-dependence
The interaction
of the photon with nuclear matter should show shadowing whenever the interaction with vector mesons is appreciable, as was clearly discussed by Gottfried at the Corneli conference. 41) Several experiments
have demonstrated this shadowing in total photoproduction cross
43)
measuring small angle photon scattering from comsections. 42) A pretty esperiment from DESY
plex nuclei shows evidence for diffraction
agreement with VhID is not impressive,
dips in heavy nuclei and shadowing. The quantitative
but the qualitative features of the theory are verified.
-9-
The situation for viitd,l pJ;lvkvilu id sarilmarized ti Fig. 22, wioch iaclrldes data froill 6’ eiec44) 0
4 electron scatterin,g, 11) and the scattering of 7.2 GeV @mesons. 45) The electron scattering,
tron results have quoted systematic
errors
The g experiment
ing in these data.
of -+ . 02 so that there is no positive evidence for shadow-
shows a definite decrease at <x3
that their result is in fair agreement with a generalized
The disagreement
vector dominance model by Schildknecht. 46)
will arise for this x
of D2 and Fe cross sections (as was stressed by Hand at London). 47)
region in the comparison
for x Fr x’) < 0.1, then significant
of p data from Fermilab
shadowing occurs.
curring.
and the authors state
between electron and muon data is mild because of possible systematics.
If shadowing is important
Comparisons
= .I,
corrections
and SLAC electron data are currently
made assuming that no
The values of vW2 obtained from iron should be increased if shadowing is oc-
Comparisons
of high and low energies from a given target are not affected if the A-
dependence is a function of w only (w and w1 are almost equal for large w),
Recent results
Let me now turn to recent results from the Cornell-Michigan
which was especially
that,at two different
apparatus.
experiment,
designed to test scaling directly.
incident energies,
The apparatus (Fig. 26) is itself scaled so
of a given w pass through the same location in the
particles
At the same time the multiple
points where the tracks are sampled.
cally significant
State-Princeton
scattering
is held tonearly
identical
values at those
In a publication25)
effects in the direct comparisons
last year by the collaboration,
statistiThe
between 150 and 56 (;eV are barely visible.
values of r(150 GcV/56 GeV) are somewhat less than 1 except at low Q2. The ratio of data to
“Monte Carlo” predictions
badly in a statistical
based on MIT-SLAC
sense.
The implication
data for vW2 fits the simple scaling hypothesis
is that their data are high for low Q2 and high w (where
any A-dependence effects would make the disagreement
worse) and low for high Q2 and low w. The
data have now been more fully analyzed, and results on the direct scaling have been submitted to the
conference. 48) The specific problem of difference
in beam shape at 150 and 56 GeV was solved by
selecting 56 GeV p’s to produce a beam distribution
similar
to the distribution
for 150 GeV p’s.
If
the values of r obtained are fit to a constant, the result is consistent with unity, r(direct) = 1.02 *. 02
2
with x of 11’7 for 108 degrees of freedom. Nevertheless, a look at plots of the data (Figs. 27 and
28) shows some systematic
trends,
haps decreases with increasing
very slightly
and it again appears that r increases with increasing
Q2. The “nicest”
w, and per-
fit is one in which r is not a constant but depends
on w
(17)
n = . 096 -I- 0.028
, w 0 = 6.1 “i’i
.
errors, the iargest of which is an uncertainty in relative enin an error of +. 056 in II. The same data can be used in conjunction
with fits to the MIT and SLAC data, Similar effects are observed, and the resulting statistical precision is better. These data are to be discussed by the authors at the conference. 48)
There are some additional systematic
ergy calibration
which results
Conclusions
In conclusion,
on scale breaki.
consider Table I, which summarizes
the evidence concerning scale breaking.
Looking at the data from both electrons and muons, it seems s:.:e to conclude that we are not oljserving perfect scaling in the simplest variable, w. Scaling in w’ is better, but the eviderlce for 0’
-
10
-
c..
2
w
Q
3
_
-3
2
w
C
t-l
2
- 11 -
scale breaking is titruiig:ar uuw tnan a year ago.
is smooth enough, and the errors
all data scale.
Un
other hand, the r>reaking in eldler variable
th2.
are large enough, so that we can probably find a variable in which
From there , it is not hard to see that your i’avorite scale breaking theory ai!d a
scaling variable
of greater or less complexity
can be made to fit the data.
I believe that it will take
a lot of insight to pick out and pursue a sensible path from here on. Clearly more accurate data
from electron and muon experiments
v scattering,
ese- annihilation,
etc.
will be necessary,
as well as data from related processes like
We aIso need to move the theoretical
W2 plane and begin the study of scale breaking in earnest.
observed scale breakings are small effects,
It is important
studies back into the Q2,
to keep in mind that the
with equivalent masses about an order of magnitude
greater than the proton mass (when expressed as propagators).
OTHER TOPICS
Iiadronic
final state
Many of us expected that the final hadronic states for very virtual photons would be spectacu.
larly different
from photoproduction.
This was probably a result of the different
The success of VMD in photoproduction,
proaches to the two regions.
theoretical
ap-
and of the quark algebra for
the deep inelastic,
the earliest
_-.-
seem to demand a transition region in which qualitative changes occur. From
49)
the most striking thing about the hadronic states in deep inelastic has
experiments,
been the similarity
Very little new data has surfaced since the London conferof data on mean charged multiplicity. 5 O-54) The multiplic-
to photoproduction.
cnce. 4, Figure 29 shows a compilation
ity appears to be somewhat lower than photoproduction,
dence in the electroproduclion
data.
but there is no evidence of any Q2 depen-
There appear to be several processes in which changes occur
A-dependence, pro exclusive final
over a small range in Q2 - 0. 2(Gev/c)2, including multiplicity,
state, etc. It will be interesting to see if these are somehow connected with a transition region. If
I suspect that we will eventually find
so, the transition
region is Small, and the changes are subtle.
that very similar
mechanisms are producing lhe final states in the large Q2 region and at Q2 = 0.
n
The one process which shows strong and steady Q‘ dependence is forward pion production 50,55-57) Figure 30 shows the present data, excluding data from UCSC-SLAC (Streamer
.
sleasurements on deuterium
Chambe’r Group), who are bringing new results to the Conference.
should provide a nice test of the quark-parton
Total photoproduction
While not strictly
predictions.
ci’oss-I section
a part of deep inelastic scattering,
the Chicago-Harvard-Illinois-Oxford
col-
laboration
have obtained a result (Fig. 31) for the total photo cross section at 100 GeV by estrapolating 1-1scattering data at low Q2. The result agrees with extrapolations from lower energy data.
Parih; noncocservation
in sczttcL*I!:$ esoeriments
currents 1s well established in neutrino interactions.
Measure“0‘ *cement with gauge theories of weak interments of v + N - v + X and y + N - ; + X are in fair +,l
actions and the parton model. The same mtdel Predicts neutral current effects in deep inelastic
delepton scattering. 58) lhe
-’ observed asyillmCtl:ics should be iu the range of (10-4 _ lo-“)Q”,
pending
on variolls
kinematic
factors and the h~Cillber!Z
angle.
59)
results :Irc reported for an experiment in which polarized
h a contribution to this conference
The existence of weak
beams
of
neulr:tl
20 GeV p meso~1s from 7; decay x’(’ clnl)loJ’ed.
No usymmctry
was observed ot Ievels of
- 12 -
-4
Lt!W.X10 . This measuremenL excit&s
other neutrai axial-vector
currents
(on which previous
limits were quite poor) but the result is not in conflict with our present ideas about the weak neutral
currents.
CONCLUSIONS
The puzzle of deep inelastic
the new particles.
scattering
Paradoxically,
vs. annihilation
has been replaced with the challenge of
the evidence for the simplest
quark-algebra
models of deep in-
elastic processes is weaker than a year ago. Definite evidence of scale breaking has been found,
but the specific form of the scale breaking is difficult to extract from the data, a situation which is
The size of the scale breaking observed implies reasonable parameters
unlikely to improve rapidly.
in theories of anomalous dimensions,
in which the experiments
progress
in unraveling
work continues.
free theories,
are analyzed doesn’t appear to be in trouble.
the mysteries
For the future,
gether with theoretical
in experiments
or in asymptotically
of final state hadrons,
so the general framework
We have not made much
although a ‘great deal of experimental
progress will depend on precise experiments
investigations
of the deep inelastic
at high energies to-
region where Q2, v , and the investment
do.not approach infinity.
ACKNOWLEDGEMENTS
I wish to express my thanks to my colleagues at SLAC for their generous help in the preparation
of this talk.
My particular
H. DcStaebler,
thanks go to Drs. Atwood, Prescott,
without whose constructive
thanks also to the Publications
understanding
criticism
and help this manuscript
and Technical Illustrations
help in the preparation
and Rochester,
of the manuscript.
and to Professor
would not exist. My
Groups at SLAC for their patience and
I also gratefully
acknowledge the help of
Ms. M. L. Arnold for her assistance and enthusiasm.
Finally,
I owe thanks to the U. S. Energy Research and Development Administration
and the
National Science Foundation for their support.
*
+
*
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7
6
Q?
5
4
2
0
3
2
Fig.
1
4
5
Lm. (GeV)
6
7
The ratio,
I(,, of the total
annihilation
cross section
of e+e- into%adror:s
to that into 2 pairs,
versus
center-of-mass
energy, E . (Reported to this conference by G. Feldman.)
cm
8
11111.0
8
R=
c (e+e- a- (e+e- -
hadrons)
p+p-1
6
R
4
2
I
i
0
0
IO
15
Q* (GeV*)
Fig.
.2 R
circa 1973, as interpreted
B8& conference.
25
20
,402*3
by Bjorken
at the
150
100
CHARMED (COLORED)
‘-HADRON-S ? ’
50
0
0
50
-
100
150
200
W* GeV/c)*
Fig.
3 Possible
plane.
color
and/or
charm thresholds
in the Q2- W*
E,= I3 GeV
8=4”
-
1.2
1.0
0.8
0.6
0.4
0.2
0
I.0
Fig.
2.0
4
3.0
4.0
W !GeV)
5.0
6.0
273,111
Inelastic
cross sections
versus missing
mass for incident
electrons
of 13 and
20 GeV scattered
at 4'.
A slight
normalization
discrepancy
exists
across the
vertical
bar which separates
previous
data from the extended data.
The dlsturbance at W = 3.9 GeV in the second
spectrum occurs where two scans were
joined and is thought to be an instrumental effect.
I
0.6
0.5
y
a,
0.4
‘8
0
Q
0
!?
0.2
x
4” SLAC Data
0
Previous SLAC Data
i
<
@ This Experiment
-
0. I
0
0
I
I
I
I
I
5
IO
I5
20
25
I
30
35
Q2 (GeV*
Fig.
5
Q4 G'/u versus Q2. Form factor scaling for
G h!!s geen assumed. The straight
line is2
t Fie weighted average of the data above a Q
of 5 GeV2.
I
lO-3
lO-4
lO-5
IO+
2
)
-lo-7
lo-8
\
-..
..
..
..
..
..
..
.\
lo-g
Io-l0 I
I
I
0
I
2
3
I
I\
4’
5
.
l
.
6
7
q2 [(GeV/c)2]
Fig.
6
The dcuteron form factor A(q') versus q2
compared to various models.
The models shofm
are of Chemtob, Moniz and Rho (CMR);
Blankenbecler and Gunion, ~410were calculating an upper limit on A(q2)(BG); BetheReid soft core @R-SC); and Feshbach and Lomon
with 7.5% D state.
(FL-15).
8
Z-Photon
Exchange
?
Scale Breaking ?
Scale
Breaking ?
Diffraction
?
Turn On ?
2723C33
Fig.
7
The Q2-W2 plane
showing regions
where the data might
not scale.
50
0
100
150
200
W2 (GeV2)
Fig.
8
Kinematic
limits
for inelastic
scattering
at incident energies of 20, 56 and 150 GeV. Practical
considerations
further
limit
the kinematic
range.
40
20
0
1,
L
20 GeV, 60°
N
I.00
80
60
40
20
0
50
100
W2 (GeV2)
Fig.
9
Currently
explored kinematic ranges for incident
energies of 20, 56 and 150 GeV. The angles shown
are the maximum measured at the three energies.
In the regions to the left of the dashed line,
changing R from 0 to m changes vW2 by less than
10%. At 20 GeV, R is already known in the corres-2
The small cross section at high Q
ponding region.
severely limits
the amount of data in the dot-dashed
region.
IO
0
IO
0
20
w2 (GeV2)
,Fig.
10
Detail
of Figure 9, showing the region in
separations
have been made. At least two
required
to make a separation
but, in the
three or more angles have been
indicated,
the region to theright
of the dotted line,
fromwto
w' changes the calculated
value
by less than 5%.
30
1173A55
which R
angles are
region
used.
In
changing
of VW2
I
Fig,
II
WR versus Q2 for
va Yues of w from
1.5 to 10. -The
solid lines are
fits to vRp= a t
bv, and the dashed
lines are R = Q2/v2.
P
I
0.10
- 0.08
N
-a
0
0
B,(Q’)
m 0.06
,
0.04
vs Q2
I
I
x to-*
(b)
0
0.1
s--(r
m”
0
B,(Q’)
% X
vs Q2
X
o =TotaI
x= Elastic
0.05
R
X
X
Q
L
I
0
xI
5
0
x
IO
"
?(
I5
Q2
Fig.
12
A scaling
Bo(Q2) and B3(Q2) for R = 0.168.
fit in w' is used where no data exists.
The crosses give the contribution
from
The errors shown
elastic
scattering.
include estimates of systematii: uncertainties.
I
0.35
0.30
0.25
Hydrogen
W >2 GeV
R=0,18
0.05
0
0
0.2
0.4
0.6
0.8
1.0
1.2
q2 (GeV/c I2
Fig.
13
2
versus Q for w' > 6 from data taken at
. It can be seen that the turn-on to
scaling
can be approximated
by a single
function
of Q2. The errors are statistical
OTllY.
At a Q2 of O.G, o' varies between
about 6 and 45.
;I2
0.35
0.30
0.25
VW2 0.20
0. i 5
0. I 0
0.05
r”I
0
I
,
I
2
5
IO
I
I
20
50
100
ti’
Fig.
14
R is assumed to be 0.18 (at
vW2 vs. w'.
WI = 30, changing R from 0.18 to 0.36
increases
VW2 by only 5%). The data
above w' = 8 are extrapolated
from a fit
to the Q2 turn-on at each value of w'.
The solid line is a polynomial
fit
to the
data.
Above w' = 25, the value of VW2
depends sensitively
on the parameterization
of the turn-on.
The systematic
error may
be as large as 20% in the highest
U' bin,
as indicated.
1111.11
al
0
0
CJ
0
G
s
Q2 ‘(GeV2)
G:
w
0
G
?a.
-.
0
cn
J
::
m
Q
7I3
(0”
-.
10-l -
lo-2
=
lo-3
=
0.3
I
I
I
I
I
I
0.4
0.5
0.6
0.7
0.8
0.9
x’
Fig.
16
1.0
,bP,B,O
2Mwl VS. x ' from measurements at 50' and 60'.
The dashed and solid lines are "predictions"
based on a scaling
fit
to vW2 and R = 0.18.
.10-’
“o:g
0:60
0.65
5
5
0.70
0.75
IO-*
0.80
0.85
1o-3 1
1
5
IO
15
20
25
30
1695.43
Q* (GeV*)
Fig.
17
Data at tly same
2MIJ- vs. Q* binned in x'
I
are fit
to a straight
line in QL. WI
clearly
does not scale in x' since all data
in
w' should be constant
ints at a given
P!i!
Q > and the connecting lines should be
horizontal.
X’
0.0
I
o-7 0
I
I
I
I
I
I
I
I
Cl* Slopes for x
x2= 2.2 /D.F.
-----------__
---_------___-------
-0.01
<s,>
=-.0168-
-0.02
+.t
I
I
t
I
0.0 I
I
+t
I
+
+
-
I
t,
I
I
-------__--------I tl,ittt’
Q* Slopes for x’
X2 = l.S/D.F.
0
‘X
0-l
,------es----.
. <Sx’>
-0.0 I
=-.0083
I
I
-0.02
-
t
I
I
I
I
I
I
Q* Slopes for xs
x2 = 1.2/D.F.
0.0 I
In
cl?
0
<sxs>
=0.000
-- - -t--+--t--t--fq
-- -- ___-----I
I
t
I
0.2
0.3
0.4
-0.0 I
-0.02
0.1
Fig.
18
I
0.5
SCALING
I
0.6
VARIABLE
I
0.7
0.8
I
0.9
Plots similar
to Figure 17 were made for?ths
variables
x and x . ( w = l/x,=
~&IV+ N",/Q >.
Plotted
here are the sloses of the lines fit
of the form 2MW= a(l+S Q*) in the variables
R2 was chosen to make the average
x3 x ' and xs.
S
slope zero.
1.0
269SR.5
1.6
I
I
I
I
I
I
A
0
x
0
.
1.2
I
I
I
6”-IO” Data
18”-34”
Data
4” Data
15”-34” Data
SO”, 60” Data
0.8
\k?
I
0
0.2
0
I
I
I
0.6
0.4
X’
Fig.
19
1
I
I
0.8
1.0
2*9,.0
The ratio
of the neutron cross section
(as extracted
from II2 data) to the proton cross section.
The
effects
of Fermi motion in deuterium increase the
systematic
errors
(not included)
as ~'31.
.
I o-3’
N
<
>
-1
g lo-3”
w’E
v
I o-331
I o-34
1.0
2.0
q’(GeVic)‘-
Fig.
20
3.0
2713644
The djfferential
cross section
da/dq for p-p elastic
scattering.
The solid curve represents the
e-p data, and the dashed line is
the best fit to the e.-p function-2
times a function r(q2)a(1+q2/A2>
.
.
1.20
cc
969
0.80
I I
-0.02
Fig.
21
0.02
5.8 GeV RECOIL PROTONS -
l/A2 COMBINED FIT
I
0
-
0.06
It
0.10
I
I
I
0.14
I
I
II
I
0.18
One standard deviation
contours for a fit to the results
of 5 sets of u-p scattering
data, with independent
but constrained
normalizations,
N., and a common cutoff parameter 1/A2.
The best fit'gives
l/A2 = 0.051
-+ 0.024.
NU’ 2g-2.8
I.3
NV= 2.8 - 3.2 GEV
I
‘20’ ’ 3.0.?
E.
7.3 Q*V
t
!WGN
t
-
IQ
5
2
1
.
.6
10
. IN”=%%;‘”
3.
NU=4.4 - 48
2 713A45
Fig.
22
Inelastic
for fixed
represent
scattering
cross section d2a/dQ2dv versus
v intervals.
The solid and dashed curves
e-p data at E = 7.3 GeV and 5.8 GeV.
2
Q
I
0.90
-,
COMBINED’ SAMPLE
95 % CONFIDENCE
I
I
I
- 0.02
Fig.
A fit
P
l/A
(
4
2,v)
I
I/A2 -
to the ratio
p( 2 ,v)
I
0.00
23
I
I I I
0.02
(GeV/c
I
= N(1
+
q2,Ag)-2.
= 0.006 2 0.016,
=
I11
I
0.04
ID2
I
0.06
vW"/vWR of the form
The z est'fit
gives
compatible
with zero.
1.10
I.05
I
0.95
l
LH2
A LD2
0.90
0
5
15
Q*(Gev/c)*
1.3
(b)
1.2
I
0.8
0.7
0
0.5
I .o
I.5
2.0
Q* (GeMI*
21138.2
Fig.
24a)
Ratio of yields Y'/Y-,
of positron
electron
in lastic
scatterin
5
values of Q up to 15(GeV/c) 2 . for
to
Fig.
24b)
Ratio of VW for p+ to that for p- .
for Q2 up tg 2.1(GeV/c)2.
In both
cases, the data are consistent
with
a ratio
of unity.
I
I
1
I
1
I
Shadowing Parameter E vs x’
0.04
Aeff -AE
A
0.03
.-
-0.01
-0.02
-0.03
E
-0.04
-0.05
Electrons
l3,20 GeV (4”) )
7-19 GeV (6”) [ SLAC
0
0
-0.06
Muons
-0.07
-0.08
x
1 Columbia, Rochester,
7GeV
1 Harvard, Fermi Lab
A
Photons
4-16 GeV UCSB
5 GeV DESY
'I
-0.09
-0.10
-0. I I
I
0.1
I
0
Fig.
25
-
l
I
0.3
0.2
x" 02/(a2+w2)
I
0.4
0.5
1723C36
The measured total
cross section
for a heavy
nucleus divided
by the cross section calculafed
for 2 protons and A-Z neutrons
is called Aeff/A
Statistical
errors
which is then fit
to A".
are shown.
ii= 1.6 (150 GeV)
TARGET
X= 0.6 (56 GeV)
I----
4.03m-
HORIZONTAL =VERTICAL
Fig.
26
SCALE
I
BEAM DIRECTION----c
254lAl5
Apparatus of the Cornell-Michigan-LBL
experiment at FNAL. Shown are the
configurations
for 150 GeV and 56 GeV incident
muons. The apparatus "scales"
in the sense that particles
of the samewgo through the same part of the
detector
at both energies.
Also, the number of iron magnets is adjusted so
that the multiple
scattering
is the same in both cases.
q2(GeV/c)2 for E=l50(E=56)
5( I .875)
I
Z(O.75)
I
IO (3.75)
I
50 (18.75)
I
20 (7.5)
I
z 1.4
In
$j 1.2
f
. . . . . . .*. . . . .
. . . ..
-- P -Y
--*****-***
Q
r=
(V/V,)”
;;r--‘----i
“Z- 0.083 f 0.032
v,= 0.041 z!I0.01 I
x2= 10.5/7 df
1.0
-Y
1
NJ 0.8
W
T
‘2
-W
II
c 0.6&
T
T
- -
x2= 28.3/22
I
0.005
Fig.
27
1
0.0 I
T
-
* . .-Z
. . . . . . .y
i All data
0 <w>=3.7
@ < w>=5.4
o <w>=9.8
df
I
I
0.02
0.05
v = q2/2ME
I
0.1
I
0.2
2723A51
The ratio,
r, of the cross section at 150 GeV to that
at 56 GeV vs. V. The solid lines are a power law fit
The dashed line corresponds
to increasto the data.
ing E' at 150 GeV ‘by l%, and the dotted line to assuming scaling
fn ui rather than w' in the Monte Carlc.
1.0
I
0.5
I
0.2
I
r=(w/w*)”
n =0.096 2 0.028
I
2
0.6 ’
I
Fig.
28
X
0.1
0.05
0.0 2
I
0.01
I
50
J
100
+QQ
I
5
I
I
IO
w
20
2723A52
The ratio,
r, versus w.
The meaning of the lines
is the same as in the previous
figure.
I-m
z-m
0.5 < Q2 < 1.0
0
X
-
0
0
51
(0)
SLAC -Berkeley-Tufts
Photoproduction
SLAC
40”
40” HBC
DESY Streamer Chamber
UCSCISLAC
Streamer Chamber
I
I
I
,
I
1
I
I
I I I
I
I
I
I
Iillllll~l
~llll~lll~~
I<$<3
-
(b)
0
x
SLAC -Berkeley
-Tufts
SLAC
40” HBC
Photoproduction
0
0
DESY. Streamer Chamber
UCSC/SLAC
Streamer Chamber
A
Cornell
I
-
J.-J---
’
5
l
I
I
s (GeV*)
Fig.
29
l1ttt1M1
IO
15
20
1721C>‘
The mean multiplicity
for charged
hadron production
in inelastic
c p and
p p scattering
is plotted
versus s
for two ranges of 42, .5 to 1.0 and
Photoproduction
1 to 3 GeV2.
data are also shown. The solid line
.
is a fit of the form a + b in s to
the photoproduction
data.
3
---T---I
2
I
x > 0.3
A
CI
X
Q)
SLAC- Berkeley-Tufts P hotoproduction
SLAC 40” HBC
SLAC Dakin, et al.
DESY- Dammann, et al.
0
0
I
2
Q* (GeV*)
Fig.
30
3
4
2 723A58
The ratio
of positively
charged hadrons to negatively
charged hadrons in the forward direction
is plotted
versus 42 for x (=p*,, jp*max) >.3, for inelastic
e p and
The
value
for
photoproduction
of
scatterings.
?JP
hadrons is shown for comparison.
The DESY values
report
the ratios
E+/v-, while the other experiments
include
K's and p's as well.
Totol
QrN
I
I
I
1
I
I
in pb
140
120
IOC
Numerical fit from
measurements eat
lower energies (up to 27 GeV)
8C
60
a;,
Tota I = 96.5+63.1
%K
40
2c
0
20
40
60
Photon
Fig.
31
80
100
Energy in GeV
120
140
?,?,A34
The total photoabsorption
cross section,
o
(yN) derived
by extrapolation
of inelastic
muon scatter!::
to Q2= 0.
The equivalent
energy is given by Ey=K=(FJ2-M 4 )/2M