In virtual Compton scattering an electron is scattered off a nucleon such that the nucleon emits a photon. We show that these events can be selected experimentally, and present the first evidence for virtual Compton scattering from the proton in data obtained at the Stanford Linear Accelerator Center. The angular and energy dependence of the data is well described by a calculation that includes the coherent sum of electron and proton radiation

Arrington, J.

Beise, E. J.

Belz, J. E.

Filippone, B. W.

Gao, H.

McKeown, R. D.

Mueller, B.

O'Neill, T. G.

van den Brand, J. F. J.

English

Caltech Authors - Main

PHYSICAL REVIEW D VOLUME 52, NUMBER 9 1 NOVEMBER 1995 
Evidence for virtual Compton scattering from the proton 
J. F. J. van den Brand,1 R. Ent,2 •a P. L. Anthony,3 R. G. Arnold,4 J. Arrington,5 E. J. Beise,s,b J. E. Belz,s,c P. E. 
Bosted,4 H.-J. Bulten,1 M. S. Chapman,2 K. P. Coulter,6 •d F. S. Dietrich,3 M. Epstein,7 B. W. Filippone,5 H. 
Gao,s,e R. A. Gearhart,8 D. F. Geesaman,6 J.-0. Hansen,2 •f R. J. Holt,6 •e H. E. Jackson,6 C. E. Jones,1 •f C. E. 
Keppel,4 •g E. R. Kinney,9 S. Kuhn,10 •h K. Lee,2 W. Lorenzon,s,i A. Lung,4 •j N.C. R. Makins,2 •f D. J. 
Margaziotis,7 R. D. McKeown,5 R. G. Milner,2 B. Mueller,5 J. Napolitano,11 J. Nelson,2 •k T. G. O'Neill,5 •f V. 
Papavassiliou,6 G. G. Petratos,8 •1 D. H. Potterveld,6 S. E. Rock,4 M. Spengos,4 •j Z. M. Szalata,4 L. H. Tao,4 
K. van Bibber,3 D. A. Wasson,2 •m J. L. White,4 and B. Zeidman6 
1 Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 
2 Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 
3 Lawrence Radiation Laboratory, Livermore, California 94550 
4 Department of Physics, The American University, Washington, D. C. 20016 
5 California Institute of Technology, Pasadena, California 91125 
6 Physics Division, Argonne National Laboratory, Argonne, fllinois 60439 
7 Department of Physics, California State University, Los Angeles, California 90032 
8 Stanford Linear Accelerator Center, Stanford, California 94309 
9 Department of Physics, University of Colorado, Boulder, Colorado 80309 
10 Stanford University, Stanford, California 94305 
11 Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180 
(Received 4 April 1995) 
In virtual Compton scattering an electron is scattered off a nucleon such that the nucleon emits 
a photon. We show that these events can be selected experimentally, and present the first evidence 
for virtual Compton scattering from the proton in data obtained at the Stanford Linear Accelerator 
Center. The angular and energy dependence of the data is well described by a. calculation that 
includes the coherent sum of electron and proton radiation. 
PACS number(s): 13.60.Fz, 14.20.Dh 
A central question in subatomic physics is the descrip-
tion of the nucleon in terms of quarks and gluons. Tradi-
tionally, the electromagnetic structure of the nucleon has 
been investigated with elastic electron scattering, deep-
8 Present address: Continuous Electron Beam Accelerator 
Facility, Newport News, VA 23606. 
bPresent address: Physics Department, University of Mary-
land, College Park, MD 20742. 
cPresent address: Department of Physics, University of Col-
orado, Boulder, CO 80309. 
dPresent address: Department of Physics, University of 
Michigan, Ann Arbor, MI 48109. 
"Present address: DepartJ:~ent of Physics, University of Illi-
nois, Urbana, IL 61801. 
!Present address: Physics Division, Argonne National Lab-
oratory, Argonne, IL 60439. 
8 Present address: Physics Department, Virginia Union Uni-
versity, Richmond, VA 23220. 
hPresent address: Old Dominion University, Norfolk, VA 
23529. 
;Present address: Physics Department, University of Penn-
sylvania, Philadelphia, PA 19106. 
jPresent address: Caltech, Pasadena, CA 91125. 
kPresent address: SLAC, Stanford, CA 94309. 
1Present address: Physics Department, Kent State Univer-
sity, Kent, OH 44242. 
=Present address: Arete, Marina del Rey, CA 90292. 
0556-2821/95/52(9)/4868(4)/$06.00 52 
inelastic scattering, and real Compton scattering. Elas-
tic scattering has yielded the electromagnetic form fac-
tors [1,2] related to charge and current distributions in 
the nucleon. Deep-inelastic scattering has established the 
existence of pointlike partons inside the nucleon [3], and 
provides access to the momentum and spin distributions 
of these partons. Real Compton scattering has provided 
information on the electric and magnetic polarizabilities 
of the nucleon [4,5] which enter as the leading corrections 
to the low-energy theorem (LET) [6]. 
Here, the virtual Compton (VC) scattering process 
'Y* N ---t 'YN is discussed, where a photon with virtuality 
Q2 is absorbed on a nucleon which subsequently radiates 
a real photon with energy (momentum) w' (qi). This 
process is intrinsically a rich probe of nucleon dynamics, 
since one can independently map out the dependence of 
the VC process on Q2 , the virtual photon's polarization, 
and the invariant mass of the hadronic intermediate state 
W, given by 
(1) 
Here p{, Ep, and M are respectively the momentum com-
ponent along the qi direction, the energy, and the mass 
of the outgoing proton. In addition, one can experimen-
tally select the polarization of incident beam, target, or 
recoiling proton. In the limit Q2 ---t 0 the VC reduces to 
the real Compton process, while in the limit W 2 ---t M 2 it 
becomes equivalent to elastic electron-proton scattering. 
The VC process provides a particularly interesting 
4868 @) 1995 The American Physical Society 
52 EVIDENCE FOR VIRTUAL COMPTON SCATTERING FROM THE ... 4869 
probe of nucleon structure, since it represents a fully elec-
tromagnetic exclusive reaction, where significant initial-
and final-state interactions are absent [7]. Already more 
than 40 years ago Drell recognized the sensitivity of 
this reaction to negative energy states [8]. After this, 
several authors have discussed the virtue of this reac-
tion to study various aspects of nucleon structure. In 
the nonperturbative QCD (NPQCD) regime, below the 
1r0-production threshold, the VC process allows the de-
termination of electromagnetic polarizabilities through 
the measurement of q' -dependent contributions to the 
LET [6,9]. These observables are determined by the 
virtual excitation spectrum of the nucleon. In the re-
gion above the 1r0-production threshold VC scattering al-
lows the study of s-channel effects of baryon resonances 
[10]. Here W 2 can be chosen to optimize the sensitiv-
ity to the electromagnetic decay of a particular reso-
nance (e.g., W 2 ~ Mj.). In the hard-scattering region, 
Q2 > 1 (GeV /c)2, VC scattering can be employed to in-
vestigate the perturbative QCD (PQCD) description of 
the nucleon wave function [11]. However, up to now no 
data have been obtained for VC scattering. Recently, a 
discussion of this process to test nucleon models in the 
NPQCD [12] and PQCD region [13,14] has started, in 
large part motivated by the advent of high-intensity con-
tinuous beam electron accelerators [e.g., the Continuous 
Electron Beam Accelerator Facility (CEBAF)]. 
The reaction eN -t eN -y is dominated by contributions 
from the photons radiated by the incoming and outgo-
ing electrons. The corresponding lowest-order Feynman 
diagrams can be calculated exactly using QED and are 
termed Bethe-Heitler contributions. The VC contribu-
tions are due to photon radiation by the nucleons and 
can only be unambiguously calculated in the soft-photon 
limit, where the cross section is independent of nucleon-
structure ambiguities. In general they involve a sum over 
all possible intermediate hadronic states. The calculation 
0.12 -0.0~) 
-0.1 
of the VC contribution requires either solving QCD or a 
realistic nucleon model to describe its dynamical behav-
ior and must also take into account the propagation of 
intermediate nucleon resonances and other intermediate 
states. Note that the reaction eN -t eN-y will also pro-
vide phase information on the nucleon matrix elements, 
due to the interference of the (calculable) Bethe-Heitler 
and VC contributions. This phase information can be 
used to determine the real part of the Compton ampli-
tude (15]. 
Experimentally, the reaction eN -t eN -y can be kine-
matically determined by detecting a scattered electron 
in coincidence with a proton using high-resolution mag-
netic spectrometers. The NE-18 experiment at the Stan-
ford Linear Accelerator Center (SLAC) measured the 
A(e, e'p) reaction for several target nuclei, using the 1.6 
GeV fc and 8 GeV fc spectrometers (16] in coincidence. 
Data for the 1 H(e, e'p) reaction were taken in order to 
calibrate the coincidence detection setup, for an incident 
(scattered) electron energy of 2.015 (1.400) GeV, scatter-
ing angle Oe = 37.29° and Q2 = 1.15 (GeV/c)2. A 2~-tA 
electron beam was incident on a 4 em LH2 target and a 
total of 5 x 104 counts were measured. The electron beam 
had a duty factor of 2 x 10-4 , and an energy resolution 
of ± 0.1 %. A coincidence time resolution of 0.8 ns [full 
width at half maxium (FWHM)] was achieved. Uncer-
tainties (FWHM) are 0.1% for the beam energy, and 0.5 
mrad for the scattering and outgoing proton angle. Fur-
ther details on the detector setup and the data analysis 
can be found in Refs. [17-19]. The measurement of the 
VC contribution is complicated due to the fact that an 
abundance of photons will be radiated by the incoming 
and scattered electrons. This will lead to radiation tails 
in the missing-energy and momentum plane, defined by 
Em= w- Ep' + M and p;. =if- i), with w (qj the en-
ergy (momentum) transfer and Ep' (:ii) the final proton 
FIG. 1. Event distribution versus E.,.. and p.,. (in GeV) without radiative corrections for the reaction 1 H(e,e'p). The two 
radiative tails due to photon emission of the electron before and after the interaction can be observed. The sign of p;. is + (-) 
in case the angle of p;., with respect to the incident electron, is < (>) Be/2. 
4870 J. F. J. van den BRAND et al. 52 
energy (momentum). For the reaction eN -+ eN"/ one 
has w' = Em and q-; = p-;.,. Figure 1 demonstrates this 
effect with the data recently obtained at SLAC. The tails 
due to radiation of the incident and scattered electrons 
are readily observed. It is seen that the radiated events 
are distributed along lines with E"' = IP-:..1 as required 
for real photons. 
The angular distribution of the emitted photons can 
be reconstructed from the measured p-;.,. We will only 
consider events with a missing energy (~ w') larger than 
20 MeV since in the region w' -+ 0 MeV the experimental 
resolutions, 8 MeV {10 MeV /c) in missing energy (mo-
mentum), do not permit an accurate reconstruction of 
the photon angle. Furthermore, applying a lower cutoff 
in w' is needed to minimize effects due to multiphoton 
emission. Figure 2 shows the angular distribution of the 
count rate for events with E"' > 30 MeV. The invari-
ant mass of the photons has been reconstructed from the 
kinematics and the photon events are well separated from 
the 1r0-production channel. It is seen that electron radi-
ation is predominantly in the direction of the initial and 
final electrons, in accordance with the peaking approxi-
mation [20]. Note that a broad distribution of events is 
seen in the direction of the outgoing proton. 
Next, the angular distributions were calculated in the 
soft-photon limit. Here, the proton contribution corre-
sponds to radiation from a Dirac particle with the usual 
form factors F 1 (Q2 ) and F 2 (Q2 ). The standard formal-
ism by Mo and Tsai [21] was extended to coincidence 
(e, e'p) reactions [22], enabling a calculation of the soft-
photon differential cross section of the 1 H ( e, e' p )"! reac-
tion. This differential cross section was reduced to the 
Cf.l 
E-< 
600 1-
~ 400 
0 
u 
200 
0 
-
-
!~ ~~ -
0~~ lfJ t 
-50 0 50 
®7 (DEG) 
FIG. 2. Calculated angular distribution of radiated events 
in comparison with NE-18 data for w' > 30 MeV. The 
solid (dotted; see inset) curve shows the prediction in the 
soft-photon limit for Bethe-Heitler and VC contributions 
(Bethe-Heitler only). The central angle 9-r for the incident 
(scattered) electron and outgoing proton are 0° (37.29°) and 
-43.29°, respectively. Note that the inset shows the region 
-60° < 6-r < -20° with a different vertical scale. 
cross section for (multi)photon emission with total en-
ergy w' and angle (J'"t in the scattering plane. For this 
we used polar coordinates, integrating over the range of 
tan( ¢'"1) accepted by the phase space. Effects arising from 
imperfect knowledge of the phase space were suppressed 
through an energy cut, w' < 80 MeV, applied for radiated 
photons along the incident electron beam. The absolute 
photon rate was calculated by folding the cross section 
over the spectrometer acceptances and including experi-
mental resolutions. No normalization factors were used. 
The data has a systematic uncertainty of 6.6%, which is 
mainly due to uncertainty in the detection phase space. 
As Fig. 2 shows, the agreement between data and simu-
lation is excellent. 
Having verified that we satisfactorily understand the 
angular distribution of radiated events (note that only 
about 3 x 103 out of a total of 5 x 104 events have ra-
diated more than 30 MeV), a region sensitive to the VC 
scattering process is selected. That such a region exists 
is illustrated in Fig. 3, which shows the calculated angu-
lar distribution of radiated photons in the single-photon 
limit. For this, the total radiative effects can be divided 
into three parts, one solely due to electron radiation (Oee), 
one due to the contribution from electron-proton inter-
ference (oep), and one due to the contribution from direct 
proton radiation (ow) only. It is seen that radiation from 
the proton is dominant for photon angles less than -80°, 
while in the photon angle range between -60° and -20° 
one expects about a similar amount of photons originat-
ing from VC processes as from Bethe-Heitler procesSes 
(see also the inset of Fig. 2). We would like to point 
out the differences between Figs. 2 and 3. In Fig. 3 
the prominent dip along the proton angle reflects the 
character of dipole radiation boosted along the particle's 
momentum, emphasized in the single-photon limit. The 
electron radiation peaks (t5ee) also have sharp minima at 
their maxima, but because the boost of the dipole pat-
tern is so large, the minima are so narrow that they are 
not shown in the figure. In Fig. 2 a complete angular 
distribution of radiated photons is calculated, where all 
multiphoton contributions are taken into account. 
In Fig. 4 we show the number of radiated events versus 
-100 0 100 
0 7 (DEG) 
FIG. 3. Angular distribution of radiated photons in the 
single-photon limit. No acceptance effects are taken into 
account. The various curves denote the dee (dotted), dep 
(dot-dashed), and dpp (dashed) contributions. The solid curve 
shows the coherent sum of the various contributions. 
52 EVIDENCE FOR VIRTUAL COMPTON SCATTERING FROM THE ... 4871 
80 
60 
40 
20 
2500 
1500 
Ul 
E-< 500 z 
:::> 
0 2500 
u 
1500 
500 
80 
60 
40 
20 
0 
a 
b 
c 
d 
10 20 30 40 50 60 
E7 CUTOFF (MeV) 
FIG. 4. Number of radiated events versus the cutoff en-
ergy w', in the intervals -60° <()"I < -20° [radiation along 
the proton direction (a}), -20° < ()"! < 20° [radiation along 
the incident electron direction (b)), 20° < ()"! < 50° [radia-
tion along the scattered electron direction (c)), and the re-
gion 50° <()"I < 90° (d). The solid {dotted) curve shows the 
prediction in the soft-photon limit for Bethe-Heitler and VC 
contributions (Bethe-Heitler only). 
the cutoff energy w', in various intervals f::.(}"Y. The dotted 
curve shows the prediction when only Bethe-Heitler con-
tributions are taken into account. This calculation gives 
a good description of the energy dependence of the data 
measured in the intervals -20° < (}"Y < 20° [Fig. 4(b)], 
and 20° < (}"Y < 50° [Fig. 4(c)J, corresponding to radi-
ation along the incident and scattered electron. A good 
description is also obtained for the radiated photons in 
the angular range 50° < (}"Y < 90° (Fig. 4(d)J, which is 
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especially sensitive to the effects of experimental resolu-
tions. However, the calculation with Bethe-Heitler con-
tributions only shows a deficiency in the description for 
radiation in the angular range -60° < (}"Y < -20° [Fig. 
4(a)], which corresponds to radiation along the proton di-
rection. The solid curves represent the prediction in the 
soft-photon limit for both Bethe-Heitler and VC contri-
butions. The good agreement between data and predic-
tion of the number of counts when proton radiation is 
included clearly demonstrates the experimental viability 
of the technique even with the 2 x 10-4 duty factor avail-
able at the SLAC end station. The number of counts in 
this regime is too low to allow for a meaningful study of 
the nucleon structure. However, with the advent of the 
high-luminosity beam at CEBAF and the projected high-
resolution spectrometers, high statistics virtual Compton 
scattering experiments should be possible [12,14]. 
In summary, we have presented the first data on the 
virtual Compton scattering process from the proton. We 
have shown that these experiments are possible, and that 
one can select a region where the virtual Compton contri-
butions dominate. The results give important impetus to 
future measurements of the virtual Compton scattering 
cross section in the reaction eN-+ eN-y which will allow 
for a clean test of our understanding of the nucleon. 
This work was supported in part by the Depart-
ment of Energy under Contracts No. W-31-109-ENG-
38 (Argonne), No. DE-FG02-86ER40269 (Colorado), 
No. W-2705-Eng-48 (LLNL), No. DE-AC02-76ER03069 
(MIT), No. DE-AC03-76SF00515 (SLAC), No. DE-
FG03-88ER40439 (Stanford) at.d by the National Science 
Foundation under Grants No. PHY-9014406 and No. 
PHY-9114958 (American), No. PHY-9115574 (Caltech), 
No. PHY-9101404 (CSLA), No. PHY-9208119 (RPI), 
No. PHY-9316221 (Wisconsin). R.G.M. acknowledges 
the support from the NSF Presidential Young Investiga-
tor program. B.W.F. acknowledges the support of the 
Sloan Foundation. 
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[22) D.A. Wasson et al. (unpublished). 


Evidence for virtual Compton scattering from the proton

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Evidence for virtual Compton scattering from the proton

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