GPD and TMD Studies at HERMES

Frank Ellinghaus

University of Colorado

October 2007

DNP 2007, Newport News, USA

Generalized Parton Distributions (GPDs)

• Longitudinal momentum fractions: (not accessible)

•

•

Simplest/cleanest hard exclusive process:e p -> e’ p’ , Deeply-Virtual Compton Scattering (DVCS)

Experimental challenges:• Measurements as a function of xB, Q2, AND t !

electron

scattered electron

real photon

recoiling proton

proton

2( ')t q q 2 2Q q

/ (2 )B Bx x

[ 1,1]x

• Exclusive -> detect full final state!

, , ,q q q qH E H EAccess to the four leading quark GPDs in real photon (DVCS) and Meson production !

Azimuthal Asymm. in BH-DVCS Interference

3 2

01 1

cos( ) sin( )I I In n

n n

I c c n s n

2 2| | | |BH DVCSd I

/ 12

( ) sin( )( )

| |( ) ( )

Ie eLU

BH

sd dA

d d

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Access to real part of DVCS amplitude

Access to imaginary part of DVCS amplitude

Calculable in QED with

knowledge of FFs

Small at HERMES, JLab

kinematics

12

( ) ( )( )

( ) ( |

c

) |

osI

CBH

cd dA

d d

Needs polarized (electron) beam(other asymmetries with pol. Target!)

Needs both beam charges (e+ and e-) beam

Indistinguishable processesIndistinguishable processesinterfere with each other!interfere with each other!

DVCS Bethe-Heitler (BH)

(simplest approx.)

The HERA accelerator at DESY (Hamburg)

27.6 GeV e+ and e-<P> about 35-55%

7/1/07@ 1:09:56 am

Event Selection at HERMESpol. 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

Photon Detector– 3 layers of Tungsten/Scintillator

– PID for higher momentum

– detects Δ+p0

Scintillating Fiber Detector– 2 Barrels

– 2 Parallel- and 2 Stereo-Layers in each barrel

– 10° Stereo Angle

– Momentum reconstruction & PID

Silicon Detector– 16 double-sides sensors

– 10×10 cm2 active area each

– 2 layers

– Inside HERA vacuum

– momentum reconstruction & PID

Target Cell

1 Tesla Superconducting Solenoid

First physics signals

Data taking with the recoil detector in 2006 and 2007

• p / PID• Promising first physics signals…

Exclusivity for DVCS via Missing Mass

About 15 % BG in exclusive bin (-1.5 < Mx < 1.7 GeV)

elastic BH: e p -> e p assoc. BH: e p -> e (mainly)semi-incl. : e p -> e 0 X (mainly)

• Exclusive 0 (e p -> e p 0 ) 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)

BCA versus -t (PRD 75, 2007)

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!

12

( ) ( )( )

( ) ( |

c

) |

osI

CBH

cd dA

d d

( simplest approx.)

HERMES, (PRD 75, 2007)

Model by Vanderhaeghen, Guichon, Guidal (VGG), based on double-distributions (Radyushkin)

Beam-Spin Asymmetry (BSA)

• 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)

/ 12

sin1 ( ) ( )( )

| | | |( ) ( )

Ie eLU

B BH

sN NA

P N N

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Simplest approx. :

HERMES preliminary

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

3 2

01 1

sin(cos( ))I I In n

n n

I c c n s n

22

0 11

| | cos( ) sin( )DVCS DVCS DVCSDVCS n

n

c c n s

22

01

| | cos( )BH BHBH n

n

c c n

Fourier expansion for unpolarized Hydrogen target:

/ 1 12

0 1 0 1

1 ( ) ( )( )

| | | |

sin sin

cos cos( ) ( )

I DVCSe eLU DVCS DVCS I I

B BH

s sN NA

P c c c cN N

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/ 12

sin1 ( ) ( )( )

| | | |( ) ( )

Ie eLU

B BH

sN NA

P N N

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���������������������������� Zero Order approximation:

More realistic approximation:

<- Let’s not neglect it…

New BSAs

/ 1 12

0 1 0 1

1 ( ) ( )( )

| | | |

sin sin

cos cos( ) ( )

I DVCSe eLU DVCS DVCS I I

B BH

s sN NA

P c c c cN N

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12

0 1

1 ( ) ( ) ( ) ( )( )

| | | | cos( ) ( ) (

si

( )

n

)

IILU DVCS DVCS

B BH

sN N N NA

P c cN N N N

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12

0 1

1 ( ) ( ) ( ) ( )( )

| | | | cos( ) ( ) (

si

) ( )

nDVCSDVCSLU DVCS DVCS

B BH

sN N N NA

P c cN N N N

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“Usual” BSA is not only sensitive to interference term but gets contribution fromDVCS term. “Usual” BSA depends on beam charge and size of the BCA.

New asymmetries can disentangle (both charges needed) the contributionsfrom the interference and the DVCS term

Define:

What about Jq?

'

'

( , ) ( , )( , )

( , ) ( , )s s

UT s

s s

d dA

d d

~ ~

2 1 2 1sin( )cos cos( )sins sIM F F IM F H FE EH

GPD E (on a proton target) is always kinematically suppressed except in the transverse target-spin asymmetry TTSA:

So far: Access to GPD H using unpolarized hydrogen targets

1

01

1lim ( , , ) ( , , )

2q

qt

qJ dxx x t x tH E

X. Ji, 1997

How to get to GPD E ?

DVCS TTSA and model calculations

2 1 sin( ) cos( , ) ...sUT s H EA IM F F

Result from data taken on transversely polarized Hydrogen:

sin( )cos :sUTA

Largely independent on all model parameters but Ju

First model dependent extraction of Ju possible!

(F.E., Nowak, Vinnikov, Ye, EPJ C46 2006, hep-ph/0506264)

First constraint on quark angular momentum

First model dependent constraint on total quark angular momentum!

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!

Similar Method used by JLab Hall-A; “neutron” data has higher sensitivity to Jd

What about the other model?

Second comparison to model calculations (Guzey/Teckentrup, PRD 2006) suggest small/negative value for Ju if Jd=0.

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).

Model uncertainty bigger than uncertainties from measurements!

Exclusive Vector-Meson ProductionThe (only) other (promising) accessto the GPD E (J) on a p target :AUT in excl. 0 production

Factorization proof for only(Collins, Frankfurt, Strikman PRD 56, 1997)

Event selection:• 0 -> + -

*L

• No recoil detection -> Missing energy

Transverse Target Spin Asymmetry (TTSA)'

'

( , ) ( , )( , ) sin( )

( , ) ( , )s s

UT s s

s s

d dA

d Hd

E

• L / T separation done via angular dist. in 0 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

(strongly simplified)

• Positive Ju suggested by both models• Additional model unc. due to gluons when compared to DVCS

Exclusive Pseudo-Scalar Meson Production

Access to and :• Exclusive + production:

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)….

~

H~

E

Factorization proof for only(Collins, Frankfurt, Strikman PRD 56, 1997)

*L

Exclusivity for e p -> e n +

'

2 2( )X p e eM P P P P N(+) – N(-) versus

• No excl. - production on p target -> Excl. + survive• Some BG contributions not (well) described by MC cancel, e.g., excl. 0 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: * 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

1Tf

)ehX 2

1 1

21 1

2 sin( )q q

qqS q q

qq

e h H

e f D

S

2

1

1 1

21

sin( )2q

qqT

Sq

q qqq

e D

e D

f

f

S

CollinsSivers (UTA ep

Sivers amplitudes

1 1sin( )S TUTf D • Published (PRL 94, 2005) results

for + and - confirmed with full statistics:• + clearly positive -> Non-zero Sivers fct. -> Non-zero orbital ang. momentum• Additional 0 measurement -> Isospin symmetry for Sivers amplitudes fulfilled

Prelim. kaon results comfirmed with full statistics:• K+ clearly positiveUnexpected result: • K+ amplitude (still) > + 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 BHIncoherent BH

Semi-Inclusive BGResonances

Task: Find for each target upper (lower) -tcut in order to compare the BSA for thecoherent (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 G 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 !)