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GPD and TMD Studies at HERMES. Frank Ellinghaus University of Colorado October 2007 DNP 2007, Newport News, USA. scattered electron. real photon. electron. recoiling proton. proton. Generalized Parton Distributions (GPDs). Simplest/cleanest hard exclusive process:

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gpd and tmd studies at hermes

GPD and TMD Studies at HERMES

Frank Ellinghaus

University of Colorado

October 2007

DNP 2007, Newport News, USA

generalized parton distributions gpds



real photon





Generalized Parton Distributions (GPDs)

Simplest/cleanest hard exclusive process:

e p -> e’ p’ g , Deeply-Virtual Compton Scattering (DVCS)

  • Longitudinal momentum
  • fractions:
  • (not accessible)
  • Experimental challenges:
  • Measurements as a function of xB, Q2, AND t !
  • 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


Bethe-Heitler (BH)

Indistinguishable processes

interfere with each other!

Azimuthal Asymm. in BH-DVCS Interference

Small at



Calculable in

QED with

knowledge of FFs

Access to real part of

DVCS amplitude

Access to imaginary part of DVCS amplitude

Needs polarized (electron) beam

(other asymmetries with pol. Target!)

Needs both beam charges

(e+ and e-) beam

(simplest approx.)

the hera accelerator at desy hamburg
The HERA accelerator at DESY (Hamburg)

7/1/[email protected] 1:09:56 am

27.6 GeV e+ and e-

<P> about 35-55%

event selection at hermes
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

  • 16 double-sides sensors
  • 10×10 cm2 active area each
  • 2 layers
  • Inside HERA vacuum
  • momentum reconstruction & PID

Target Cell

Recoil Detector Overview
first physics signals
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
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
BCA versus -t (PRD 75, 2007)

( simplest approx.)


(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
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

Simplest approx. :

HERMES preliminary

Model by Vanderhaeghen, Guichon, Guidal (VGG),

based on double-distributions (Radyushkin)

bsa model comparison ii
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)


-> 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


new bsas can be defined and measured
New BSAs can be defined and measured

Fourier expansion for unpolarized Hydrogen target:

<- Let’s not neglect it…

Zero Order approximation:

More realistic approximation:

new bsas
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

what about j q
What about Jq?

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 target-spin asymmetry TTSA:

dvcs ttsa and model calculations
DVCS TTSA and model calculations

Result from data taken on transversely polarized Hydrogen:

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 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
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
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 only

(Collins, Frankfurt, Strikman PRD 56, 1997)

  • Event selection:
  • r0 -> p+p-
  • No recoil detection -> Missing energy
transverse target spin asymmetry ttsa
Transverse Target Spin Asymmetry (TTSA)

(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
Exclusive Pseudo-Scalar Meson Production
  • Access to and :
  • Exclusive p+ production:

Factorization proof for 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
Exclusivity for e p -> e n p+

N(p+) – N(p-) versus

  • 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
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
The Sivers function

“tranverse momentum distribution of unpolarized quarks in a transversely polarized proton

  • non-zero Sivers function implies non-zero orbital angular momentum



sivers amplitudes
Sivers amplitudes
  • 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
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
Contribution from different processes from MC

Task: Find for each target upper (lower) -t

cut in order to compare the BSA for the

coherent (incoherent) production at similar

average kinematics:

Coherent BH

Incoherent BH

Semi-Inclusive BG


82% coherent for heavier targets at –t =0.018 GeV2

and very similar average x and Q2

a dependence of bsa
A-Dependence of BSA
  • No obvious A-dependence seen.
  • sin(2f) moment consistent with zero for all targets
bsa ratios nuclei hydrogen
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 hydrogen1
BSA Ratios Nuclei/Hydrogen

Guzey/Siddikov (J. Phys. G, 2006)

Promising, more data needed…

Guzey/Strikman (Phys.Rev. C, 2003)

  • 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 !)