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 x B, Q 2, AND t ! electron scattered electron real photon recoiling proton Exclusive -> detect full final state! Access to the four leading quark GPDs in real photon (DVCS) and Meson production !

Azimuthal Asymm. in BH-DVCS Interference 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 Needs polarized (electron) beam (other asymmetries with pol. Target!) Needs both beam charges (e+ and e-) beam Indistinguishable processes interfere with each other! DVCSBethe-Heitler (BH) (simplest approx.)

The HERA accelerator at DESY (Hamburg) 27.6 GeV e+ and e- about 35-55% 1:09:56 am

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 Photon Detector –3 layers of Tungsten/Scintillator –PID for higher momentum –detects Δ +  p  0 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 cm 2 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 < M x < 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! ( 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) 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 Fourier expansion for unpolarized Hydrogen target: Zero Order approximation: More realistic approximation: <- Let’s not neglect it…

New BSAs “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. New asymmetries can disentangle (both charges needed) the contributions from the interference and the DVCS term Define:

What about J q ? 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 X. Ji, 1997 How to get to GPD E ?

DVCS TTSA and model calculations Result from data taken on transversely polarized Hydrogen: Largely independent on all model parameters but J u First model dependent extraction of J u possible! (F.E., Nowak, Vinnikov, Ye, EPJ C , hep-ph/ )

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 J d

What about the other model? Second comparison to model calculations (Guzey/Teckentrup, PRD 2006) suggest small/negative value for J u if J d =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 (J u,J d ). Model uncertainty bigger than uncertainties from measurements!

Exclusive Vector-Meson Production The (only) other (promising) access to the GPD E (J) on a p target : A UT in excl.  0 production Factorization proof for only (Collins, Frankfurt, Strikman PRD 56, 1997) Event selection:  0 ->  +  - No recoil detection -> Missing energy

Transverse Target Spin Asymmetry (TTSA) 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 J u 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 A UT predicted Also sensitive to different pion distribution amplitudes TTSA not yet available, but final result for cross section available (hep-ex/ )…. Factorization proof for only (Collins, Frankfurt, Strikman PRD 56, 1997)

Exclusivity for e p -> e n  + 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 mass 2 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’ 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 Collins Sivers

Sivers amplitudes 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 positive Unexpected result: K + amplitude (still) >  + amplitude role of sea-quarks?

DVCS on Nuclei? First measurement of DVCS on Neon (F.E. et al, hep-ex/ ) 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 GeV 2 and very similar average x and Q 2

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 !)