GPD and TMD Studies at HERMES
Frank Ellinghaus
University of Colorado
October 2007
DNP 2007, Newport News, USA
Generalized Parton Distributions (GPDs)
Simplest/cleanest hard exclusive process:
e p -> e’ p’ g , Deeply-Virtual Compton Scattering (DVCS)
scattered
electron
real photon
• Longitudinal momentum
fractions:
x  [1,1] (not accessible)
electron
  xB / (2  xB )
• t  (q  q ')2
proton
2
2
• Q  q
recoiling
proton
Experimental challenges:
• Measurements as a function of xB, Q2, AND t !
• Exclusive -> detect full final state!
q
q
q
Access to the four leading quark GPDs H , E , H , E
in real photon (DVCS) and Meson production !
q
Azimuthal Asymm. in BH-DVCS Interference
d DVCS
|  BH |2  | Bethe-Heitler
 DVCS |2  (BH)
I
Calculable in
QED with
knowledge of FFs
Small at
HERMES, JLab
kinematics
Indistinguishable processes
interfere with each other!
2
 I 3 I

I   c0   cn cos(n )    snI sin(n ) 
n 1
n 1


Access to real part of Access to imaginary part
DVCS amplitude
of DVCS amplitude
e/ e
LU
A
d ( )  d ( )
( ) 
d ( )  d ( )
d  ( )  d  ( )
AC ( ) 
d  ( )  d  ( )
 s1I sin 
|  BH |2
Needs polarized (electron) beam
(other asymmetries with pol. Target!)
c1I cos 
|  BH |2
Needs both beam charges
(e+ and e-) beam
(simplest approx.)
The HERA accelerator at DESY (Hamburg)
7/1/07@ 1:09:56 am
27.6 GeV e+ and e<P> about 35-55%
Event Selection at HERMES
pol. and unpol. Gas targets -> H, D, He, N, Ne, Kr, Xe
All data in the following taken before installation of Recoil Detector !
Recoil Detector Overview
1 Tesla Superconducting Solenoid
Photon Detector
–
–
–
3 layers of Tungsten/Scintillator
PID for higher momentum
detects Δ+pp0
Scintillating Fiber Detector
–
–
–
–
2 Barrels
2 Parallel- and 2 Stereo-Layers in each
barrel
10° Stereo Angle
Momentum reconstruction & PID
Silicon Detector
Target Cell
–
–
–
–
–
16 double-sides sensors
10×10 cm2 active area each
2 layers
Inside HERA vacuum
momentum reconstruction & PID
First physics signals
Data taking with the recoil detector in 2006 and 2007
• p / p PID
• Promising first physics signals…
Exclusivity for DVCS via Missing Mass
elastic BH: e p -> e p g
assoc. BH: e p -> e D g (mainly)
semi-incl. : e p -> e p0 X (mainly)
• Exclusive p0 (e p -> e p p0 ) not shown (small)
• DVCS process not simulated (DVCS c.s. unknown, c.s. << BH)
• Radiative corrections to BH not simulated (-> Excl. Peak
overestimated, BG underestimated)
About 15 % BG in exclusive bin (-1.5 < Mx < 1.7 GeV)
BCA versus -t (PRD 75, 2007)
d  ( )  d  ( )
AC ( ) 
d  ( )  d  ( )
c1I cos 
|  BH |2
( simplest approx.)
HERMES,
(PRD 75, 2007)
Model by Vanderhaeghen, Guichon, Guidal (VGG),
based on double-distributions (Radyushkin)
Guzey/Teckentrup, PRD 74, 2006
Analysis based on tiny e- p sample (~ 700 events),
Now about 20 times more data on disk!
 BCA has high sensitivity to GPD models!
Beam-Spin Asymmetry (BSA)
Simplest approx. :
e/ e
LU
A
1
N ( )  N ( )
( ) 
| PB | N ( )  N ( )
 s1I sin 
|  BH |2
HERMES preliminary
•
•
•
Compare to model calculations at
average kinematics per bin
Flat kinematic dependence
(kinematics correlated !)
described by models
Too large absolute asymmetries
Model by Vanderhaeghen, Guichon, Guidal (VGG),
based on double-distributions (Radyushkin)
BSA: Model comparison II
Model (Guzey, Teckentrup) based on dual-parametrization (Polyakov, Shuvaev)
are in agreement with “all other” DVCS data so far:
-> Cross sections from H1/ZEUS (used for normalization)
-> BCA at HERMES
-> Published (PRL, 2001) AVERAGE BSA values from HERMES and CLAS
Size and kinematic dependence of the asymmetry is reproduced
More data with improved systematics to come, but BSA not very sensitive to
models.
New BSAs can be defined and measured
Fourier expansion for unpolarized Hydrogen target:
|  BH |  c
2
BH
0
|  DVCS |  c
2
DVCS
0
2
  cnBH cos(n )
n 1
2
  cnDVCS cos(n )   s1DVCS sin( )
<- Let’s not neglect it…
n 1
2
 I 3 I

I   c0   cn cos(n )    snI sin(n ) 
n 1
n 1


1
N ( )  N ( )
e/ e
Zero Order approximation: ALU ( ) 
| PB | N ( )  N ( )
 s1I sin 
|  BH |2
More realistic approximation:
e / e
LU
A
1
N ( )  N ( )
( ) 
| PB | N ( )  N ( )
|  BH
 s1I sin   s1DVCS sin 
|2 c0DVCS  c1DVCS cos   c0I  c1I cos 
New BSAs
e / e
LU
A
1
N ( )  N ( )
( ) 
| PB | N ( )  N ( )
|  BH
 s1I sin   s1DVCS sin 
|2 c0DVCS  c1DVCS cos   c0I  c1I cos 
“Usual” BSA is not only sensitive to interference term but gets contribution from
DVCS term.
“Usual” BSA depends on beam charge and size of the BCA.
Define:
1
N  ( )  N  ( )  N  ( )  N  ( )
A ( ) 
| PB | N  ( )  N  ( )  N  ( )  N  ( )
I
LU
DVCS
LU
A
1
N  ( )  N  ( )  N  ( )  N  ( )
( ) 
| PB | N  ( )  N  ( )  N  ( )  N  ( )
|  BH
|  BH
 s1I sin 
|2 c0DVCS  c1DVCS cos 
s1DVCS sin 
|2 c0DVCS  c1DVCS cos 
New asymmetries can disentangle (both charges needed) the contributions
from the interference and the DVCS term
What about Jq?
1
J q  lim
t 0 2
1

1
dxx  H q ( x,  , t )  E q ( x,  , t ) 
X. Ji, 1997
So far: Access to GPD H using unpolarized hydrogen targets
How to get to GPD E ?
GPD E (on a proton target) is
always kinematically suppressed
except in the transverse targetspin asymmetry TTSA:
d  ( , s )  d  ( , s' )
AUT ( , s ) 
d  ( , s )  d  ( , s' )
~
 ~

 IM  F2 H  F1 E  sin(  s ) cos   IM  F2 H  F1 E  cos(  s ) sin 


DVCS TTSA and model calculations
Result from data taken on transversely polarized Hydrogen:
AUT ( , s )  IM  F2 H  F1E  sin(  s )cos   ...
sin( s )cos 
AUT
: Largely independent on all model parameters but Ju
(F.E., Nowak, Vinnikov, Ye, EPJ C46 2006, hep-ph/0506264)

First model dependent extraction of Ju possible!
First constraint on quark angular momentum
First model dependent constraint
on total quark angular momentum!
Similar Method used by
JLab Hall-A; “neutron” data
has higher sensitivity to Jd
Value to be taken with care, since VGG does not seem to describe the
available BSA data, but it is important to have a (first) method!
What about the other model?
Second comparison to model calculations
(Guzey/Teckentrup, PRD 2006) suggest
small/negative value for Ju if Jd=0.
Model uncertainty bigger than uncertainties from measurements!
The way to go:
Constrain models for GPD H first by BSA/BCA.
(some model parameters might be the same for GPD E)
Compare remaining models to asymmetries sensitive to GPD E (Ju ,Jd).
Exclusive Vector-Meson Production
The (only) other (promising) access
to the GPD E (J) on a p target :
AUT in excl. r0 production
Factorization proof for g L only
*
(Collins, Frankfurt, Strikman PRD 56, 1997)
Event selection:
• r0 -> p+ p• No recoil detection -> Missing energy
Transverse Target Spin Asymmetry (TTSA)
d  ( , s )  d  ( , s' )
E
AUT ( , s ) 

sin(



)
s
H
d  ( , s )  d  ( , s' )
(strongly simplified)
• L / T separation done via angular dist. in r0 decay, SCHC assumed
• Data in agreement with earlier calc. (at higher –t ) based on quark
production only (Goeke, Polyakov, Vanderhaeghen, Prog. Part. Nucl. P. 47, 2001)
• Data in agreement with theoretical calc. including gluons
(F.E., Nowak, Vinnikov, Ye, EPJ C46, 2006)
• Additional gluon contr. dilutes asymmetry -> decreases sensitivity
• Positive Ju suggested by both models
• Additional model unc. due to gluons when compared to DVCS
Exclusive Pseudo-Scalar Meson Production
~
~
Access to H and E :
• Exclusive p+ production:
*
g
Factorization proof for L only
(Collins, Frankfurt, Strikman PRD 56, 1997)
Frankfurt, Pobylitsa, Polyakov, Strikman,
PRD 60 (1999)
• Large amplitudes for AUT predicted
• Also sensitive to different pion distribution amplitudes
• TTSA not yet available,
but final result for cross section available (hep-ex/0707.0222)….
Exclusivity for e p -> e n p+
N(p+) – N(p-)
versus
M X2  ( Pp  Pe  Pe'  Pp )2
• No excl. p- production on p target
-> Excl. p+ survive
• Some BG contributions not (well)
described by MC cancel, e.g.,
excl. r0 and resonances (partially)
• Excl. peak at neutron mass2
after BG subtraction by MC
• Agreement with excl. MC based on
GPD model (VGG, PRD 60, 1999)
• suggests little remaining contr.
from resonances
Cross section: g* p -> p+ n
• GPD model (VGG, PRD 60, 1999) including power corrections
applicable only at low values of –t’ << Q2 -> agreement with data
• Good description by Regge model (Laget, PRD 70, 2004)
except maybe at small –t’
The Sivers function
“tranverse momentum distribution of unpolarized quarks in a transversely
polarized proton
• non-zero Sivers function implies non-zero orbital angular momentum
f1T 
AUT (ep ehX ) 
2 S  sin(  S )
Sivers
Collins
2 q
q
e
f

D
 q q 1T
1

e f D
2 q
q q 1
q
1
2 S  sin(  S )
2
q
q
e
h

H
q q 1 1
2
q
q
e
f

D
q q 1 1
Sivers amplitudes
sin(  S )
UT
 f1T  D1
• Published (PRL 94, 2005) results
for p+ and p- confirmed with
full statistics:
• p+ clearly positive
-> Non-zero Sivers fct.
-> Non-zero orbital ang. momentum
• Additional p0 measurement
-> Isospin symmetry for Sivers
amplitudes fulfilled
Prelim. kaon results comfirmed with
full statistics:
• K+ clearly positive
Unexpected result:
• K+ amplitude (still) > p+ amplitude
• role of sea-quarks?
DVCS on Nuclei?
First measurement of DVCS on Neon (F.E. et al, hep-ex/0212019) triggered
first calculations for DVCS on Nuclei.
->Opens possibility to explore nuclear structure in terms of quarks and gluons,
EMC effect, (Anti-)Shadowing, CT, ….
Contribution from different processes from MC
Coherent BH
Incoherent BH
Semi-Inclusive BG
Resonances
Task: Find for each target upper (lower) -t
cut in order to compare the BSA for the
coherent (incoherent) production at similar
average kinematics:
82% coherent for heavier targets at –t =0.018 GeV2
and very similar average x and Q2
A-Dependence of BSA
• No obvious A-dependence seen.
• sin(2) moment consistent with zero for all targets
BSA ratios Nuclei/Hydrogen
• Coherent enriched: 2 sigma above unity.
Prediction of R=5/3 for Spin-0 and Spin ½ tragets (Kirchner, Mueller,
EPJ 2003).
R=1-1.1 for 4-He (Liuti, Taneja, PRC 2005), but large stat. error,
calculations for heavier targets underway/promised
• Incoherent enriched Consisten with unity as expected
BSA Ratios Nuclei/Hydrogen
Guzey/Siddikov (J. Phys. G, 2006)
Promising, more data needed…
Guzey/Strikman (Phys.Rev. C, 2003)
Summary
• Indications for small DG stress the importance of the
investigation of the quark orbital angular momentum via
GPDs <- 3 Dim structure
• HERA /HERMES shut down, but much more to come for
GPDs (e.g., all data taken with the recoil detector !)