Deeply Virtual Compton Scattering with CLAS12

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by  Latifa Elouadrhiri

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Deeply Virtual Compton Scattering with CLAS12.
n
a
J L.Elouadrhiri∗

8 Jefferson Lab
2 Newport News, VA 23606, USA
∗E-mail: [email protected]
]
h
p AnoverviewisgivenaboutthecapabilitiesprovidedbytheJLab12GeVUp-
- grade to measure deeply virtual exclusive processes with high statistics and
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covering a large kinematics range in the parameters that are needed to allow
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h reconstruction of a spatial image of the nucleon’s quark structure. The mea-
[ surements planned with CLAS12 willcross section asymmetries with polarized
beamsandwithlongitudinallyandtransverselypolarizedprotontargetsinthe

1 constrainedkinematicsx=±ξ.Inaddition,unpolarizedDVCScrosssections,
v and doubly polarized beam target asymmetries will be measured as well. In
8 thistalkonlythebeam andtargetasymmetrieswillbediscussed.
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1 Keywords: GPDs,DVCS
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.
1 1. Introduction
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8 The concept of GPDs1–3 has led to completely new methods of “spatial
0 imaging” of the nucleon. The mapping of the nucleon GPDs, and a de-
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v tailed understanding of the spatial quark distribution of the nucleon, have
i been widely recognized are a key objectives of nuclear physics of the next
X
decade, and is a key justification for the JLab energy upgrade to 12 GeV.
r
a GPDs also allow to quantify how the orbital motion of quarks in the nu-
cleoncontributesto the nucleonspin–a questionofcrucialimportancefor
our understanding of the “mechanics” underlying nucleon structure. This
requires a comprehensive program, combining results of measurements of
a variety of processes in electron–nucleon scattering with structural infor-
mation obtained from theoretical studies, as well as with expected results
from future lattice QCD simulations.
It is well recognized4–6 that exclusive processes can be used to probe
the GPDs and construct 2-dimensional and 3-dimensional images of the
quarkcontentofthenucleon.DeeplyvirtualComptonscatteringanddeeply
virtual meson production are identified as the processes most suitable to
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0.5 0.5
0.4 0.45
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-0 0.25
-0.1 0.2
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-0.3 0.1
-0.4 0.05
-0.5 0
0 3600 0.2 0.4 0.6 0.8 1 0.2 0.3 0.4 0.5 0.6
ϕ -t (GeV 2 ) xB
Fig.1. ThebeamspinasymmetryshowingtheDVCS-BHinterferencefor11GeVbeam
energy from the VGG model14 with uncertainties projected for 11 GeV.13 Many other
binswillbemeasuredsimultaneously.
map out the twist-2 vector GPDs H, E and the axial GPDs H˜, E˜ in
x, ξ, t, where x is the momentum fraction of the struck quark, ξ the
longitudinalmomentumtransfertothequark,andtthemomentumtransfer
to the nucleon.Havingaccesstoa3-dimensionalimageofthe nucleon(two
dimensions in transverse space, one dimension in longitudinal momentum)
opensupcompletelynewinsightsintothecomplexstructureofthenucleon.
For example, the nucleon matrix element of the energy-momentum tensor
contains3formfactorsthatencode informationonthe angularmomentum
distribution Jq(t) of the quarks with flavor q in transverse space, their
mass-energy distribution Mq(t), and their pressure and force distribution
2
dq(t).TheseformfactorsalsoappearasmomentsofthevectorGPDs,7thus
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offering prospects of accessing these quantities through detailed mapping
of GPDs. The quark angular momentum in the nucleon is given by
+1
Jq(t)= dxx[Hq(x,ξ,t)+Eq(x,ξ,t)] ,
Z
−1
and the mass-energy and pressure distribution
+1
Mq(t)+4/5dq(t)ξ2 = dxxHq(x,ξ,t) .
2 1 Z
−1
The mass-energyandforce-pressuredistributionofthe quarksaregivenby
the secondmomentofGPDH,andtheirrelativecontributioniscontrolled
by ξ. The separation of Mq(t) and dq(t) requires measurement of these
2 1
moments in a large range of ξ.
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AUL0.6 a) jsinAUL0.6 b) jsinAUL0.6 c)
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-0.6
-150 -100 -50 0 50 1j00 (d1e50g) 00 0.10.2 0.30.40.50.6-t0 .(7G0e.8V20).9 00.2 0.25 0.3 0.35 0.4 0.45 x0B.5
Fig. 2. The longitudinal target spin asymmetry beam spin asymmetry showing the
DVCS-BHinterferencefor11GeVbeamenergyfromtheVGGmodel14 withuncertain-
tiesprojectedfor11GeV.13 Otherbinswillbemeasuredsimultaneously
2. GPDs and DVCS
DVCShasbeenshown8–11 tobethecleanestprocesstoaccessGPDsatthe
kinematics accessible today. It is also a relatively rare process and requires
high luminosities for the required high statistics measurements. The beam
helicity-dependent cross section asymmetry is given in leading twist as
ALU ≈sinφ[F1(t)H +ξ(F1(t)+F2(t))H˜]dφ ,
where F1 and F2 are the Dirac and Pauli form factors, φ is the azimuthal
angle between the electron scattering plane and the hadronic plane. The
kinematically suppressedtermwith GPD E is omitted. For nottoo largeξ
the asymmetry is mostly sensitive to the GPD H(x=ξ,ξ,t).
The asymmmetry with a longitudinally polarized target is given by
AUL ≈sinφ[F1(t)H˜ +ξ(F1(t)+F2(t)H] .
ThecombinationofA andA allowsaseparationofGPDH(x=ξ,ξ,t)
LU UL
and H˜(x=ξ,ξ,t).
Using a transversely polarized target the asymmetry
AUT ≈sinφt/4M2[F2(t)H −F1(t)E]
can be measured, which depends in leading order on GPD E and is highly
sensitive to orbital angular momentum contributions of quarks.
Clearly, determining moments of GPDs for different t will require mea-
surement in a large range of x, in particular at largex. The reconstruction
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ofthetransversespatialquarkdistributionrequiresmeasurementinalarge
range in t, and the separationof the dq(t) and Mq(t) form factors requires
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a large span in ξ.
CLAS12
3. Upgrade of CLAS to .
To meetthe requirementsofhighstatistics measurementsofrelativelyrare
exclusive processes such as DVCS at high photon virtuality Q2, large t
andξ, the CLAS detector willbe upgradedandmodified to CLAS12.16 The
main new features of CLAS12 over the current CLAS detector include a
high operational luminosity of 1035cm−2sec−1, an order of magnitude in-
crease over CLAS.15 Improved particle identification will be achieved with
additional threshold gas Cerenkov counter, improved timing resolution of
the forward time-of-flight system, and a finer granularity electromagnetic
preshowercalorimeterthat,inconjunctionwiththexistingCLAScalorime-
ter will provide much improved γ/π0 separation for momenta up to 10
GeV.Inaddition,anew centraldetectorwillbe built thatusesahigh-field
solenoid magnet for particle tracking and allows the operation of dynami-
cally polarized solid state targets. With these upgrades CLAS12 will be the
workhorseforexclusiveelectroproductionexperimentsinthe deepinelastic
kinematics.
CLAS12
4. Projected results at 12 GeV with .
The12GeVupgradeoffersmuchimprovedcapabilitiestoaccessGPDs.Fig-
ure1showstheexpectedstatisticalprecisionofthebeamDVCSasymmetry
for some sample kinematics. At the expected luminosity of 1035cm−2sec−1
and for a run time of 2000 hours, high statistics measurements in a very
large kinematics range are possible.
Using a dynamically polarized NH3 target we can also measure the
longitudinaltargetspinasymmetryA withhighprecision.Theprojected
UL
results are shown in Fig. 2. The statistical accuracy of this measurement
will be less than for the A asymmetry due to the largedilution factor in
LU
the target material, but it will still be a very significant measurement.
Polarizingthe target transverse to the beam direction will access a dif-
ferentcombinationofGPDs,andprovidedifferentsensitivityforthey-and
x-components of the target polarization. The expected accuracy for one of
the polarization projections is shown in Fig. 3. Here the target is assumed
to be a frozen HD-Ice target, which has different characteristics from the
NH3 target.
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Q2=2.6,x =0.25
B
0.6
fs HERMES
o
s)c0.5 CLAS12
f-
fn(0.4
si
UT0.3
A Ju=0.12
0.2
0.1 Ju=0.34
0
-0.1
Ju=0.50
-0.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
t
Fig.3. Projected transverse target asymmetry AUT forDVCSproduction off protons
at 11 GeV beam energy. The curves represent different assumptions on the u-quark
contributions toJ(t).
x = 0.45
3
x = 0.35
3 2
x = 0.25
3 2 1
0
2 1 0 0.5 1
0
1
0 0.5 1
0
x 0 0.5 1
b [fm]
Fig.4. Theu-quarkdistributionintransversespaceasextractedfromprojectedDVCS
datawithCLAS12.
Ameasurementofall3asymmetrieswillallowaseparatedetermination
ofGPDsH, H˜ andE attheabovespecifiedkinematics.ThroughaFourier
transformation the t-dependence of GPD H can be used to determine the
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u−quarkdistributionintransverseimpactparameterspace.Figure4shows
projected results for such a transformation assuming a model parameteri-
zation for the kinematical dependences of GPD H. Knowledge of GPD E
willbeparticularlyinterestingasitisdirectlyrelatedtotheorbitalangular
momentum distribution of quarks in transverse space.
Acknowledgment
We thank the members of the CLAS collaboration who contributed to
the development of the exciting physics program for the JLab upgrade to
12 GeV, and the CLAS12 detector. Much of the material in this report is
takenfromtheCLAS12TechnicalDesignReportVersion3,October2007.16
This work was supported in part by the U.S. Department of Energy
and the National Science Foundation, the French Commisariat ´a l’Energie
Atomique, the Italian Instituto Nazionale di Fisica Nucleare, the Korea
ResearchFoundation, and a researchgrantof the Russian Federation. The
Jefferson Science Associates, LLC, operates Jefferson Lab under contract
DE-AC05-060R23177.
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