Generalized Parton Distributions

1
Generalized Parton Distributions
Harut Avakian Jefferson Lab

• GPD studies in hard exclusive processes
• Photons (DVCS)
• Pseudoscalar mesons
• Vector mesons
• Exclusive processes with strangeness
• Summary Conclusions

2
Physics Motivation
Describe the complex nucleon structure in terms
of partonic degrees of freedom
Probability to find a quark u in a nucleon P with
a certain polarization in a position r and
momentum k
Wpu(k,r) Mother Wigner distributions
d2kT
IPDs Wpu(x,rT),
FT
x
d2r
3
Quark Angular Momentum Sum Rule
GPDs Hu, Hd, Eu, Ed provide access to total
quark contribution to proton angular momentum.
½ ½ (DuDdDs) Lq Jg
Protons spin
J q
1
1


ò
x

x
)
0
,
,
q(
)
0
,
,
q(
x
E
x
H
xdx

J q
2
-
1
X. Ji, Phy.Rev.Lett.78,610(1997)
Large x contributions important.
4
Hard Exclusive Processes and GPDs
DVMP
DVCS
long. only
hard vertices
DVCS for different polarizations of beam and
target provide access to different combinations
of GPDs H,H, E,E
DVMP for different mesons is sensitive to flavor
contributions (r0/r/K select H, E, for u/d
flavors, p, h, K select H, E)
5
Electroproduction Kinematics
6
Deeply Virtual Exclusive Processes Kinematics
Coverage
HERA

• collider experiments
• H1, ZEUS (EIC)
• 10-4ltxBlt0.02 (0.3) gluons (and quarks) in the
  proton
• fixed target experiments
• COMPASS, HERMES
• ? 0.006/0.02ltxBlt0.3 gluons/valence and sea
  quarks
• JLab/JLab_at_12GeV
• ? 0.1ltxBlt0.7 valence quarks

27 GeV
Q2
EIC
JLab (upgraded)
compass
hermes
JLab_at_6GeV
Study of high xB domain requires high luminosity
7
Deeply Virtual Compton Scattering ep?epg
Polarized beam, unpolarized target

DsLU sinfF1H( x,x,t) x(F1F2)H kF2E
Kinematically suppressed
Unpolarized beam, longitudinal target

DVCS
DsUL sinfF1Hx(F1F2)(H ..
BH
Kinematically suppressed
Unpolarized beam, transverse target
DsUT sinfk(F2H F1E) ..
x xB/(2-xB ),k t/4M2
Kinematically suppressed
GPD combinations accessible as azimuthal moments
of the total cross section.
8
DVCS Experiments
CLAS at 4.3 GeV
ALU(f)
ALU(f)
HERMES 27 GeV
A(f) asinf bsin2f
S. Stepanyan et al. Phys. Rev. Lett. 87 (2001)
A. Airapetian et al. Phys. Rev. Lett. 87 (2001)
9
GPDs from ep ?epg
Requirements for precision (lt15) measurements
of GPDs from DVCS SSA

• Define the procedure to extract GPDs
• from ALU
• effect of finite bins (prefactor variations) 10
• other moments

• Traget mass corrections, dynamic and kinematic HT

• A complete MC simulation of the whole chain
• Generator (signalbackground)
• Detector response (GEANT)
• Extraction of GPDs from measured exclusive events
  (cleaned from background)

10
DVCS p0 background
ep ? epp0

• Use epgg(p0) to estimate the contribution of p0
  in the epg sample.

p0 CLAS(2003/4)
ALU
p0 CLAS(2005)

• Corrections of DVCS SSA
• contamination by p0 photons
• p0 beam SSA.

CLAS preliminary
? p0 Asymmetry is 1/3 of DVCS-BH asymmetry!
350000 exclusive p0s
11
GPD extraction from Beam SSAMC
GPDs MC-input
corrected for p0
epg
Hx(F1F2)H kF2E
raw asymmetry
0.3ltxlt0.4
only H
2ltQ2lt3
Divide the ALU by the kinematic factor cLU
extracted from event by event sum
Extraction procedure tested with GEANT based MC
with realistic cross sections for DVCS and
exclusive pions, recover input GPDs

12
DVCS Beam SSA from CLAS

• High luminosity, polarized CW beam.
• Wide physics acceptance
• Wide geometric acceptance, allowing detection of
  multi-particle final states.

CLAS DVCS data sets

1. epg 1 photon in Calorimeter 150000 (2003/4)
2. epX no photons in CLAS 2M events (2003/4)
   tight cuts on PID,missing mass MX, no other tracks

VGG with TM
CLAS PRELIMINARY
CLAS PRELIMINARY

• ALU corrected for p0 (bin by bin)
• H ALU / cLU calculated for all events in a bin
  related to GPDs

The ratio of the ALU and the cLU (H) extracted
for two non-overlapping data sets epX(ep0g) and
epg consistent
13
Dedicated DVCS experiment at JLab Hall-A
JLab/Hall A, (2004 2005)
Detection of 3 particles e, ? and (p)
nucl-ph/0607029
HRS PbF2 H(e,egp), D(e,egN)
BH
confirm scaling ( Q2 1.5- 2.5 GeV2),
?x-section difference measured for the first time
? Data consistent with large real part for CFFs.

p0 background crucial for the real part (studies
underway)
Talk by F.Sabatie
14
Dedicated CLAS DVCS experiment
? Detection of 3 particles e, p and ? in final
state ? Large kinematical coverage in xB and t
CLAS_at_5.7 GeV (2005)
Calorimeter and superconducting magnet within
CLAS torus
400K events
CLAS PRELIMINARY
Hall-A
dedicated calorimeter (424 PbWO4 crystals)
detect photons from 5o
CLAS_at_4
Talk by F.Sabatie
New data consistent within error bars with
published data and also CLAS 2003/4 data at 5.7
GeV for epg and epX
15
CLAS12 - DVCS/BH Beam Asymmetry
Projected results
E 11 GeV
DsLUsinfImF1H..df
Selected Kinematics
16
JLab12 Hall A unpolarized target
Absolute measurements d?(?e1)
H(e,e?)p
250K setup
Twist 2 Twist 3 separation. ImDVCSBH?DVCS2
ReDVCSBH ?DVCS2
100 days
17
DVCS Beam Charge Asymmetry
DsC cosf Re H
(projected)
e/- p ? e/- p g (MXlt1.7 GeV) (in HERMES
acceptance)
Regge, D-term Regge, no D-term fac.,
D-term fac., no D-term
Most sensitive to different GPD models. With
increased statistics asymmetries may constrain
GPD models
talk by D.Neyret
18
Target Spin Asymmetry (LTSA) t- dependence
Unpolarized beam, longitudinal target

CLAS 2001 HERMES (PRELIMINARY) CLAS 2007-2008
(projected)
DsUL sinfF1Hx(F1F2)(H ..
Kinematically suppressed
g
a0.2520.042 0.020 b-0.0220.045 0.021
First data available(5 CLAS days), more(60 days)
to come at 6 GeV
Measurements with polarized target will constrain
the polarized GPDs and combined with beam SSA
measurements would allow precision measurement of
unpolarized GPDs.
19
HERMES Transverse target spin asymmetry

AUT sin(f-fS) cos(f) Im H - E cos(f-fS)
sin(f) ImH
L 64 pb-1
? First (model dependent) constraints on Ju and
Jd !
talk by W-D.Nowak
20
CLAS12 - DVCS/BH Target Asymmetry
e p epg
Transversely polarized target
Sample kinematics
E 11 GeV
Q22.2 GeV2, xB 0.25, -t 0.5GeV2
DsUT sinfImk1(F2H F1E) df
AUTx Target polarization in scattering plane
AUTy Target polarization perpendicular to
scattering plane

• Asymmetry highly sensitive to the u-quark
  contributions to the proton spin.

21
HERMES r0 longitudinal cross sections
EPJC17,2000
L 106 pb-1
GPD model calculations for sL H
Diehl et.al. (2005)
Vanderhaegen et.al. (1999)

• no indication of a large gluon contribution.

--- 2-gluon exchange --- quark exchange
corrections to LO quark transverse momenta

• quark exchange dominates

• more data to come r, f, w, r

Talk by E.Kinney
22
Exclusive ? meson production gp ? p?0
GPD formalism (beyond leading order) describes
approximately data for xBlt0.4, Q2 gt1.5 GeV2
CLAS (5.75 GeV)
Analysis in progress
GPD (MG-MVdh)
Decent description in pQCD framework already at
moderate Q2
23
HERMES p cross section measurement
L250 pb-1
sT suppressed by 1/Q2
? at large Q2, sL dominates
Q2 dependence is in general agreement with the
theoretical expectation Corrections to LO (k- and
soft overlap) calculations overestimate the data
24
Exclusive r0 production on transverse target
2D (Im(AB))/p
T
AUT -
A2(1-x2) - B2(x2t/4m2) - Re(AB)2x2
A 2Hu Hd
r0
B 2Eu Ed
A Hu - Hd B Eu - Ed
r
r0
Eu, Ed needed for angular momentum sum rule.
Talk by Ed Kinney
K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001
Asymmetry is a more appropriate observable for
GPD at Q2lt10GeV2 as possible corrections to the
cross section are expected to cancel
B
25
GPDs from cross sections and ratios
M.Diehl et al. hep-ph/0506171
Eides,Frankfurt,Strikman 1998
Talk by K.Joo

• Study ratio observables p/h/K/K/r,polarization
  transfer
• Different final state mesons filter out different
  combinations of unpolarized (H,E) and polarized
  (H,E) GPDs.

26
? production
e
e
K,K
1
p
?
2
p
Accessing polarized and strange GPDs with
unpolarized target ! (no gluons)
(ud)-diquark is a spin and isospin singlet
s-quark carries whole spin of L
6
CLAS 5.7 GeV
27
Chiral-odd GPDs
First introduced
X.Ji, P.Hoodbhoy 1987
28
Chiral-odd GPDs with exclusive r,r
Long distance part described by GPD HT
hard

• Large momentum
• transfer, large rapidity gap
• Virtual photon replaced with 2 gluons

pT
hard
GPD
Smaller rapidity gap r selects quark antiquark
exchange with the nucleon
Ivanov et al. Phys.Part.Nucl.35S67-S70,2004 Enber
g et al. Eur.Phys.J.C4787-94,2006
Ratio of r0LrTn/ r0LrLn directly related to
ratio of GPDs HT/H (EIC,JLab)
29
Summary

• The new data are just the first trickle of a
  great wealth of upcoming information on GPDs

Measurement of GPDs require global analysis of
different exclusive final states measured in a
wide range of kinematics at different facilities.
30

• Support slides.

31
g MC vs Data

• Region where BH totally dominates (small t, small
  photon qLAB)
• Negligible DVCS x-section, small p0 contamination
• Rapidly changing prefactors, mainly small f, hard
  to detect photons
• Large angles
• Uniform coverage in angle f, photon measurement
  less challenging
• DVCS x-section non negligible introduce some
  model dependence)
• p0 dominates the single photon sample (in
  particular at low Q2 and large t )

• MC Kinematic distributions in x,Q2,t consistent
  with the CLAS data

32
DVCS BH propagators

• Strong dependence on kinematics of prefactor
  f-dependence, at ttcol P1(f)0 require special
  attention in interpretation of beam averaged beam
  SSA and in particular x-section differences
• Fraction of pure DVCS increases with t and f

33
Exclusive pp- and pp0 from CLAS
e p e p ?
p p-
n
r
r0

• Provide access to different combinations of
  orbital momentum contributions Ju,Jd r0 -gt 2Ju
  Jd, r -gt Ju Jd
• Measurements of ratios r / r0 , r / p

34
Exclusive 2 pion production MX (epX)
CLAS (5.75 GeV)
D ,N
f2
f0
r
Significant background from exclusive 2 pion
production
35
CLAS12 JLab Energy Upgraded to 12 GeV

• High luminosity polarized (80) CW beam
• Wide geometric acceptance
• Wide physics acceptance

Beamline
- quark orbital angular momentum contributions
- 3D structure of the nucleons interior and
correlations - quark flavor polarization
36
COMPASS r0 longitudinal cross sections
37
Comparing ALU for different sets
e16-epg
e1DVCS-epg
e16-epX

• Kinematical averages are different for different
  data sets for the same bin

38
p0 MC vs Data
1.0ltQ2lt2.0, 0.1ltxlt0.3

• Exclusive p0 production simulated using a
  realistic MC (PDF based)
• Kinematics distributions in x,Q2 and t tuned to
  describe the CLAS data (b1)
• Define contribution to the single photon sample
  from p0

39
p0 contamination of DVCS sample
Use realistic event generators for single g and
p0 that reproduce the measured yields.
g
CLAS forward Calo
single photons from p0
p0
BH-DVCS g
q (photon lab. angle)

• Cut on the direction of the measured photon
  significantly reduces the p0 contamination.
• Contamination strongly dependent on kinematics,
  and p0 contribution must be subtracted bin by bin.

40
Exclusive r0 production on transverse target
2D -(Im(AB))/p

AUT -
A2(1-x2) - B2(x2t/4m2) - Re(AB)2x2
A 2Hu Hd B 2Eu Ed
r0
A Hu - Hd B Eu - Ed
r
r0
Eu, Ed needed for angular momentum sum rule.
K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001
Asymmetry is a more appropriate observable for
GPD studies at JLab energies as possible
corrections to the cross section are expected to
cancel
41
Transversity GPDs with exclusive r,r
hard

• Large momentum
• transfer, large rapidity gap
• Virtual photon replaced with 2 gluons

hard
(courtesy M. Vanderhaeghen)
GPD
Smaller rapidity gap r selects quark antiquark
exchange with the nucleon.
Long distance part described by GPD HT
Ivanov et al. Phys.Part.Nucl.35S67-S70,2004