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0>91+9)+;3:> ;*31+):1659 0>91+9
Scaling Tests of the Cross Section for Deeply
Virtual Compton Sca!ering
C. Muñpz Camacho
A. Camsonne
M. Mazouz
C. Ferdi
G. Gavalian
Old Dominion University
See next page for additional authors
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Scaling Tests of the Cross Section for Deeply Virtual Compton Scattering
C. Mun
˜
oz Camacho,
1
A. Camsonne,
2
M. Mazouz,
3
C. Ferdi,
2
G. Gavalian,
4
E. Kuchina,
5
M. Amarian,
4
K. A. Aniol,
6
M. Beaumel,
1
H. Benaoum,
7
P. Bertin,
2,8
M. Brossard,
2
J.-P. Chen,
8
E. Chudakov,
8
B. Craver,
9
F. Cusanno,
10
C. W. de Jager,
8
A. Deur,
8
R. Feuerbach,
8
J.-M. Fieschi,
2
S. Frullani,
10
M. Garc¸on,
1
F. Garibaldi,
10
O. Gayou,
11
R. Gilman,
5
J. Gomez,
8
P. Gueye,
12
P. A. M. Guichon,
1
B. Guillon,
3
O. Hansen,
8
D. Hayes,
4
D. Higinbotham,
8
T. Holmstrom,
13
C. E. Hyde-Wright,
4
H. Ibrahim,
4
R. Igarashi,
14
X. Jiang,
5
H. S. Jo,
15
L. J. Kaufman,
16
A. Kelleher,
13
A. Kolarkar,
17
G. Kumbartzki,
5
G. Laveissie
`
re,
2
J. J. LeRose,
8
R. Lindgren,
9
N. Liyanage,
9
H.-J. Lu,
18
D. J. Margaziotis,
6
Z.-E. Meziani,
19
K. McCormick,
5
R. Michaels,
8
B. Michel,
2
B. Moffit,
13
P. Monaghan,
11
S. Nanda,
8
V. Nelyubin,
9
M. Potokar,
20
Y. Qiang,
11
R. D. Ransome,
5
J.-S. Re
´
al,
3
B. Reitz,
8
Y. Roblin,
8
J. Roche,
8
F. Sabatie
´
,
1
A. Saha,
8
S. Sirca,
20
K. Slifer,
9
P. Solvignon,
19
R. Subedi,
21
V. Sulkosky,
13
P. E. Ulmer,
4
E. Voutier,
3
K. Wang,
9
L. B. Weinstein,
4
B. Wojtsekhowski,
8
X. Zheng,
22
and L. Zhu
23
(Jefferson Lab Hall A Collaboration)
1
CEA Saclay, DAPNIA/SPhN, F-91191 Gif-sur-Yvette, France
2
Universite
´
Blaise Pascal/CNRS-IN2P3, F-63177 Aubie
`
re, France
3
Laboratoire de Physique Subatomique et de Cosmologie, 38026 Grenoble, France
4
Old Dominion University, Norfolk, Virginia 23508, USA
5
Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA
6
California State University, Los Angeles, Los Angeles, California 90032, USA
7
Syracuse University, Syracuse, New York 13244, USA
8
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
9
University of Virginia, Charlottesville, Virginia 22904, USA
10
INFN/Sezione Sanita
`
, 00161 Roma, Italy
11
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
12
Hampton University, Hampton, Virginia 23668, USA
13
College of William and Mary, Williamsburg, Virginia 23187, USA
14
University of Saskatchewan, Saskatchewan, Saskatchewan, Canada, S7N 5C6
15
Institut de Physique Nucle
´
aire CNRS-IN2P3, Orsay, France
16
University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA
17
University of Kentucky, Lexington, Kentucky 40506, USA
18
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
19
Temple University, Philadelphia, Pennsylvania 19122, USA
20
Institut Jozef Stefan, University of Ljubljana, Ljubljana, Slovenia
21
Kent State University, Kent, Ohio 44242, USA
22
Argonne National Laboratory, Argonne, Illinois, 60439, USA
23
University of Illinois, Urbana, Illinois 61801, USA
(Received 26 July 2006; published 29 December 2006)
We present the first measurements of the
~
ep ! ep cross section in the deeply virtual Compton
scattering (DVCS) regime and the valence quark region. The Q
2
dependence (from 1.5 to 2:3 GeV
2
) of the
helicity-dependent cross section indicates the twist-2 dominance of DVCS, proving that generalized
parton distributions (GPDs) are accessible to experiment at moderate Q
2
. The helicity-independent cross
section is also measured at Q
2
2:3 GeV
2
. We present the first model-independent measurement of
linear combinations of GPDs and GPD integrals up to the twist-3 approximation.
DOI: 10.1103/PhysRevLett.97.262002 PACS numbers: 13.60.Fz, 13.40.Gp, 13.60.Hb, 14.20.Dh
Measurements of electroweak form factors determine
nucleon spatial structure, and deep inelastic scattering
(DIS) of leptons off the nucleon measures parton dis-
tribution functions, which determine longitudinal momen-
tum distributions. The demonstration by Ji [1], Radyushkin
[2], and Mueller et al. [3], of a formalism to relate the
spatial and momentum distributions of the partons al-
lows the exciting possibility of determining spatial distri-
butions of quarks and gluons in the nucleon as a func-
tion of the parton wavelength. These new structure func-
tions, now called generalized parton distributions (GPD),
became of experimental interest when it was shown [1]
that they are accessible through deeply virtual Compton
scattering (DVCS) and its interference with the Bethe-
Heitler (BH) process (Fig. 1). Figure 1 presents our kine-
matic nomenclature. DVCS is defined kinematically by the
PRL 97, 262002 (2006)
PHYSICAL REVIEW LETTERS
week ending
31 DECEMBER 2006
0031-9007=06=97(26)=262002(5) 262002-1 © 2006 The American Physical Society
limit t Q
2
and Q
2
much larger than the quark con-
finement scale.
The factorization proofs [4,5] confirmed the connection
between DVCS and DIS. Diehl et al. [6] showed that the
twist-2 and twist-3 contributions in the DVCS-BH inter-
ference terms (the first two leading orders in 1=Q) could be
extracted independently from the azimuthal dependence of
the helicity-dependent cross section. Burkardt [7] showed
that the t dependence of the GPDs is the Fourier conjugate
to the transverse spatial distribution of quarks in the infinite
momentum frame as a function of momentum fraction.
Ralston and Pire [8], Diehl [9], and Belitsky et al. [10]
extended this interpretation to the general case of skewness
0. The light-cone wave function representation by
Brodsky et al. [11] allows GPDs to be interpreted as
interference terms of wave functions for different parton
configurations in a hadron.
These concepts stimulated an intense experimental ef-
fort in DVCS. The H1 [12,13] and ZEUS [14]
Collaborations measured the cross section for x
Bj
10
3
. The HERMES Collaboration measured relative
beam helicity [15] and beam-charge asymmetries
[16,17]. Relative beam helicity [18] and longitudinal target
[19] asymmetries were measured at the Thomas Jefferson
National Accelerator Facility (JLab) by the CLAS
Collaboration.
Extracting GPDs from DVCS requires the fundamental
demonstration that DVCS is well described by the twist-2
diagram of Fig. 1 at finite Q
2
. This Letter reports the first
strong evidence of this cornerstone hypothesis, necessary
to validate all previous and future GPD measurements
using DVCS. We present the determination of the cross
section of the
~
ep ! ep reaction for positive and negative
electron helicity in the kinematics of Table I.
The E00-110 [20] experiment ran in Hall A [21] at JLab.
The 5.75 GeVelectron beam was incident on a 15 cm liquid
H
2
target. Our typical luminosity was 10
37
=cm
2
=s with
76% beam polarization. We detected scattered electrons in
one high resolution spectrometer (HRS). Photons above a
1 GeV energy threshold (and coincidences from
0
decay) were detected in a 11 12 array of 3 3
18:6cm
3
PbF
2
crystals, whose front face was located
110 cm from the target center. We calibrated the PbF
2
array by coincident elastic He; e
0
Calo
p
HRS
data. With
(elastic) k
0
4:2 GeV=c, we obtain a PbF
2
resolution of
2.4% in energy and 2 mm in transverse position (one-).
The calibration was monitored by reconstruction of the
0
! mass from He; e
0
0
X events.
We present in Fig. 2 the missing mass squared obtained
for He; e
0
X events, with coincident electron-photon
detection. After subtraction of an accidental coincidence
sample, we have the following competing channels in
addition to He; e
0
p: ep ! e
0
p, ep ! e
0
N, ep !
eN, ep ! eN .... From symmetric (lab-frame)
0
decay, we obtain a high statistics sample of
He; e
0
0
X
0
events, with two photon clusters in the PbF
2
calorimeter. From these events, we determine the statistical
sample of (asymmetric) He; e
0
X
0
events that must be
present in our He; e
0
X data. The solid M
2
X
spectrum
displayed in Fig. 2 was obtained after subtracting this
0
yield from the total (stars) distribution. This is a 14%
average subtraction in the exclusive window defined by
M
2
X
cut in Fig. 2. Depending on the bin in
and t, this
subtraction varies from 6% to 29%. After our
0
subtrac-
tion, the only remaining channels, of type He; e
0
N,
N, etc. are kinematically constrained to M
2
X
> M
m
2
. This is the value (M
2
X
cut in Fig. 2) we chose for
truncating our integration. Resolution effects can cause the
inclusive channels to contribute below this cut. To evaluate
this possible contamination, we used an additional proton
array (PA) of 100 plastic scintillators. The PA subtended a
solid angle (relative to the nominal direction of the q
vector) of 18
<
p
< 38
and 45
<
p
180
< 315
, arranged in 5 rings of 20 detectors.
For He; e
0
X events near the exclusive region, we can
predict which block in the PA should have a signal from a
proton from an exclusive He; e
0
p event. Open crosses
TABLE I. Experimental ep ! ep kinematics, for incident beam energy E 5:75 GeV.
q
is the central value of the q-vector
direction. The PbF
2
calorimeter was centered on
q
for each setting. The photon energy for q
0
k q is E
.
Kin k
0
(GeV=c)
e
(
) Q
2
(GeV
2
) x
Bj
q
(
) W (GeV) E
(GeV)
1 3.53 15.6 1.5 0.36 22:3 1.9 2.14
2 2.94 19.3 1.9 0.36 18:3 2.0 2.73
3 2.34 23.8 2.3 0.36 14:8 2.2 3.33
k
k'
electron
DVCS
p
p'
proton
q'
++
Bethe-Heitler
FIG. 1. Lowest-order QED diagrams for the process ep !
ep, including the DVCS and Bethe-Heitler (BH) amplitudes.
The external momentum four-vectors are defined on the dia-
gram. The virtual photon momenta are q k k
0
in the DVCS-
and q q
0
in the BH-amplitudes. The invariants are: W
2
q p
2
, Q
2
q
2
> 0, t
2
, x
Bj
Q
2
=2p q, and the
DVCS scaling variable
q
2
=
q Px
Bj
=2 x
Bj
, with
q q q
0
=2 and P p p
0
.
PRL 97, 262002 (2006)
PHYSICAL REVIEW LETTERS
week ending
31 DECEMBER 2006
262002-2
show the X p y missing mass squared distribution
for He; e
0
py events in the predicted PA block, with a
signal above an effective threshold 30 MeV. Squares show
our inclusive yield, obtained by subtracting the normalized
triple coincidence yield from the He; e
0
X yield. The
dotted curve shows our simulated He; e
0
p spectrum,
including radiative and resolution effects, normalized to
fit the data for M
2
X
M
2
. Triangles show the estimated
inclusive yield obtained by subtracting the simulation from
the data. Squares and triangles are in good agreement, and
show that our exclusive yield has less than 3% contamina-
tion from inclusive processes.
To order twist-3 the DVCS helicity-dependent (d) and
helicity-independent (d) cross sections are [22]:
d
4
d
4
1
2
d
4
d
4
d
4
d
4
d
4
jDVCSj
2
d
4
sin
Im
1
ImC
I
F
sin2
Im
2
ImC
I
F
eff
; (1)
d
4
d
4
1
2
d
4
d
4
d
4
d
4
d
4
jDVCSj
2
d
4
d
4
jBHj
2
d
4
Re
0;
ReC
I
C
I
F
Re
0
ReC
I
F
cos
Re
1
ReC
I
F
cos2
Re
2
ReC
I
F
eff
; (2)
where d
4
dQ
2
dx
Bj
dtd
and the azimutal angle
of the detected photon follows the ‘‘Trento Convention’’
[23]. The
Re;Im
n
are kinematic factors with a
depen-
dence that arises from the electron propagators of the BH
amplitude. The C
I
and C
I
angular harmonics depend on
the interference of the BH amplitude with the set F
fH ; E;
~
H ;
~
Eg of twist-2 Compton form factors (CFFs) or
the related set F
eff
of effective twist-3 CFFs:
C
I
F F
1
H G
M
~
H
t
4M
2
F
2
E; (3)
C
I
F
eff
F
1
H
eff
G
M
~
H
eff
t
4M
2
F
2
E
eff
; (4)
C
I
C
I
F F
1
H
t
4M
2
F
2
E
2
G
M
H E:
(5)
F
1
t, F
2
t, and G
M
tF
1
tF
2
t are the elastic
form factors. CFFs are defined in terms of the GPDs H
f
,
E
f
,
~
H
f
, and
~
E
f
, defined for each quark flavor f.For
example, (f 2fu; d; sg):
H ; t
X
f
e
f
e
2
iH
f
; ; tH
f
; ; t
P
Z
1
1
dx
2x
2
x
2
H
f
x; ; t
: (6)
Thus, the DVCS helicity-dependent and helicity-
independent cross sections provide very distinct and com-
plementary information on GPDs. On one hand, d mea-
sures the imaginary part of the BH-DVCS interference
terms and provides direct access to GPDs at x .On
the other hand, d determines the real part of the BH-
DVCS interference terms and measures the integral of
GPDs over their full domain in x. This real part of the
BH-DVCS interference term is the same interference term
that can be obtained by measurements of the difference of
electron and positron (or
) DVCS cross sections.
The twist-2 and twist-3 CFFs are matrix elements of
quark-gluon operators and are independent of Q
2
(up to
logarithmic QCD evolution). Their Q
2
variation measures
the potential contamination from higher twists.
The helicity-independent cross section also has a
cos3
twist-2 gluon transversity term. We expect this
term to be small, and do not include it in our analysis. We
neglect the DVCS
2
terms in our analysis. Therefore, our
results for ImC
I
and ReC
I
may contain, respectively,
twist-3 and twist-2 DVCS
2
terms, which enter with similar
dependence. However, the DVCS
2
terms in both d
and d are kinematically suppressed by at least an order of
magnitude in our kinematics [22], because they are not
enhanced by the BH amplitude. In any case, the terms we
neglect do not affect the cross sections we extract, which
are accurately parametrized, within statistics, by the con-
tributions we included.
Our simulation includes internal bremsstrahlung in the
scattering process and external bremsstrahlung and ioniza-
tion straggling in the target and scattering chamber win-
FIG. 2 (color online). Missing mass squared for He; e
0
X
events (stars) at Q
2
2:3 GeV
2
and t 20:12; 0:4 GeV
2
,
integrated over the azimuthal angle of the photon
. The
solid histogram shows the data once the He; e
0
X
0
events
have been subtracted. The other histograms are described in the
text.
PRL 97, 262002 (2006)
PHYSICAL REVIEW LETTERS
week ending
31 DECEMBER 2006
262002-3
