1. The GPD program at COMPASS
Andrzej Sandacz
Sołtan Institute for Nuclear Studies, Warsaw
on behalf of the COMPASS collaboration
XIII Workshop on High Energy Spin Physics
September 1-5, Dubna, Russia

2. Generalized Parton Distributions and DVCS
Factorisation:
Q2 large, -t<1 GeV2
hard
x+x
x-x
soft
GPDs
P1,h1 t
P2,h2
Pi, hi – proton momentum
and helicity ~ ~
depending on 3 variables: x, x, t
4 Generalised Parton Distributions : H, E, H, E
for each quark flavour and for gluons
for DVCS gluons contribute at higher orders in αs

3. GPDs and Hard Exclusive Meson Production
4 Generalised Parton Distributions (GPDs)
for each quark flavour and for gluons
factorisation proven only for σL
σT suppressed by 1/Q2
necessary to extract longitudinal contribution to observables (σL , …)
allows separation and wrt quark flavours
conserve flip nucleon helicity
H E Vector mesons (ρ, ω, φ)
H E Pseudoscalar mesons (π, η) ~
Flavour sensitivity of HEMP on the proton p0
2Du+Dd h
2Du-Dd
quarks and gluons enter at the same order of αS ρ0
2u+d, 9g/4 ω
2u-d, 3g/4 f
s, g ρ+
u-d
J/ψ g
at Q2 ≈ few GeV2 power corrections/higher order
pQCD terms are essential
wave function of meson (DA Φ)
additional input

4. GPDs properties, links to DIS and form factors
for P1 = P2 recover usual parton densities
no similar relations; these GPDs decouple for P1 = P2
needs orbital angular momentum between partons
Dirac
axial
pseudoscalar
Pauli
Ji’s sum rule
total angular momentum carried by quark flavour q
(helicity and orbital part)

5. ½ = ½ ΔΣ + ΔG + < Lzq > + < Lzg >
‘Holy Grails’ of the GPD quest
Contribution to the nucleon spin puzzle
E related to the angular momentum
2Jq =  x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx
½ = ½ ΔΣ + ΔG + < Lzq > + < Lzg > t p q E
 GPD= a 3-dimensional picture of the partonic nucleon structure
or spatial parton distribution in the transverse plane
H(x, =0, t) → H(x,, rx,y )
probability interpretation
Burkardt
x P x y r z

6. generalised parton distributions (GPDs)
Structure of the Nucleon
form factors
location of partons in nucleon
parton distributions
longitudinal momentum fraction x
FF: transverse location of partons in the nucleon (independently of their long momentum): local operator, initial/finale states different  non-forward matrix element
Pdf: longitudinal momentum distributions (no info on transverse location): bilocal operator, initial/final states identical  forward matrix element
GPD: longitudinal momentum fraction x at transverse location b_perp: bilocal operator, initial/final states different  non-forward matrix element
generalised parton distributions (GPDs)
transverse location b and longitudinal momentum fraction x T
embody 3D picture of hadrons

7. Nucleon tomography from fits to elastic form factors
from GPD fits to Diehl, Feldmann, Jakob, Kroll – (2005)
unpolarized proton uV dV

8. Nucleon tomography from fits to elastic form factors
from GPD fits to Diehl, Feldmann, Jakob, Kroll – (2005)
in ┴ polarized proton uV dV

9. Observables and their relationship to GPDs
(at leading order:)
Beam charge asymmetry contains ReT,
integrated GPDs over x
Beam or target spin asymmetry
contains ImT,
therefore GPDs at x = x and -x
Intro

10. μ’  μ p’ Future GPD program @ COMPASS primary physics goal is DVCS,
The GPDs program is part of the COMPASS Phase II ( ) proposal to be submitted to CERN in 2009.
The first stage of this program requires a 4 m long recoil proton detector (RPD) together with a 2.5 m long LH2 target. Upgrades of electromagnetic calorimeters to enlarge coverage at large xB and reduce bkg. μ  p’ μ’
The second stage requires either a new transversely polarized NH3 target (with a thin superconductiong coil) inserted in the RPD or a new SciFi (?) RPD inserted in the existing NH3 target system.
primary physics goal is DVCS,
meson production will be done
at the same time
Stage 1 (~2012) to constrain H
dσ/dt → t-slope parameter b
d(+, ) + d(-, )  Im(F1 H) sin 
d(+, ) - d(-, )  Re(F1 H) cos 
Stage 2 (~2014) to constrain E
d(, S) - d(, S+π)  Im(F2 H – F1 E) sin (- S) cos 

11. COMPASS kinematical coverage for DVCS
CERN SPS high energy muon beam 100/190 GeV
with a 2.5m long LH2 target
L = 1032 cm-2 s-1
Q2 → 8 GeV2
→ 12 GeV2 if luminosity increased by factor 4
~10-2 < x < ~10-1
x → with upgrade of present calorimetry

12. The GPDs in the next several years
H1, ZEUS, HERMES, JLab 6 GeV are providing the first results
significant increase of statistics expected after
full data sets analysed
The energy upgrade of the CEBAF accelerator will allow access
to the high xB region which requires large luminosity.
The GPD project at COMPASS will explore intermediate xB ( )
and large Q2 (up to ~8(12) GeV2) range
COMPASS will be the only experiment in this range before
availability of new colliders

13.  θ μ’ μ *  p
DVCS + BH with + and - beams
and unpolarized proton target
dσ(μpμp) = dσBH + dσDVCSunpol + Pμ dσDVCSpol
+ eμ aBH ReTDVCS eμ Pμ aBH ImTDVCS
Beam Charge & Spin Difference
DU,CS
 d( +) - d( -) 
2(eμ aBH ReTDVCS + Pμ dσDVCSpol )
Beam Charge & Spin Sum
SU,CS
 d( +) + d( -) 
2(dσBH + dσDVCSunpol + eμPμ aBH ImTDVCS)

14. Using SU,CS , integrating over  dDVCS/dt ~ exp(-B|t|)
t-slope measurement; relevant for nucleon ‘tomography’
Using SU,CS , integrating over 
dDVCS/dt ~ exp(-B|t|)
and subtracting BH
1<Q2<8
‘tomography’: B(x) ~ <rT2>(x)
FFS model
adapted for COMPASS by A.S.
assumed
B(x) = b0 + 2 α’ ln(x0/x)
with
α’ =0.125 GeV-2
160 GeV muon beam
2.5m LH2 target
global = 10%, 140 days
L = 1222pb-1
for gluons, from J/Ψ at HERA α’ ~ GeV photoproduction (Q2 ≈0)
α’ ~ 0.02 GeV DIS (Q2=2-80 GeV2)
for valence quarks, from fits to FF α’ ~ 1 GeV-2

15. Comparison to different models
Beam Charge and Spin Asymmetry
from DU,CS / SU,CS :
Comparison to different models
160 GeV muon beam
2.5m LH2 target
global = 10%, 140 days
L = 1222pb-1
D.Mueller-hep-ph/
fit to world data

16. If Lumi × 4  more bins up to Q2 = 12 GeV2
Beam Charge and Spin Asymmetry in various kinematic bins
Q2 = 12 GeV2
VGG model
4 < Q2 < 8
160 GeV muon beam
2.5m LH2 target
global = 10%, 140 days
L = 1222pb-1
x = 0.15
2 < Q2 < 4
0°   360°
1 < Q2 < 2
0.005< x < 0.01
0.01< x < 0.02
0.02 < x < 0.03
0.03< x < 0.07
If Lumi × 4  more bins up to Q2 = 12 GeV2 16

17. DT,CS ADT,CS ≡ DT,CS/d σ0 ST,CS AST,CS ≡ ST,CS/d σ0
Single γ production with transversely polarised target
dσ(μpμpγ) = dσU(μpμp) + dσT(μpμpγ)
unpolarized target
transversely polarized target
dσT(μpμp) = ST Pμ dσTBH + ST dσTDVCS + ST Pμ dσTDVCSpol
+ ST eμ aTBH TTDVCS ST eμ Pμ aTBH TTDVCSpol
to isolate TTS part measurements at opposite target polarisations needed
dσT = ½ {dσ (ST=+PT) - dσ(ST=−PT)}
to disentangle DVCS and Interference terms having the same azimuthal dependence
cf. the next slide
both + and - beams needed
DT,CS
 dT( +) - dT( -)
ADT,CS ≡ DT,CS/d σ0
measure
or/and
ST,CS
AST,CS ≡ ST,CS/d σ0
 dT( +) + dT( -)
dσ0 is unpolarised, charge averaged cross section

18. Harmonics decomposition of TTS-dependent 1 γ production cross section
Belitsky,Müller,Kirchner
ST Pμ 
ST 
ST Pμ 
ST eμ 
ST eμ Pμ 
not shown are terms with sin(kφ) and cos(kφ) (k=2,3) dependence
twist-2 terms
those are twist-3 and NLO twist-2 gluon helicity flip terms

19. An ‘appetizer’ – HERMES measurements of DVCS
from Transverse Target Spin asymmetry AUTsin(ϕ-ϕs)cosϕ  c1,T-Int
for proton sensitive to Ju (not to Jd) => allows model dependent constraints
study of azimuthal asymmetries from transversely polarized NH3 target is a part of Phase 2 of COMPASS proposal, simulations are in progress

20. AUTsin(ϕ-ϕs) compatible with 0
TTS asymmetry AUTsin(ϕ-ϕs) for ρ0 production on protons from COMPASS
2007 data from transversely polarised NH3 COMPASS target
transverse spin dep. VM cross section
access to GPD E
related to orbital momentum
HM , EM
are weighted sums of integrals
of the GPDs Hq,g , Eq,g
< Q2 > ≈ 2.2 (GeV/c) < xBj > ≈ < pt2 > ≈ 0.18 (GeV/c)2
AUTsin(ϕ-ϕs) compatible with 0
in progress: L/T γ* separation (using ρ0 decay angular distribution)

21. Comparison to a GPD model
Goloskokov-Kroll
‘Hand-bag model’; GPDs from DD using CTEQ6
[EPJ C53 (2008) 367]
power corrections due to kt of quarks included
both contributions of γ*L and γ*T included ρ0 ω
K*0 ρ+
W = 10 GeV
t’ integrated
COMPASS p↑ preliminary
predictions for protons
AUT(ρ) ≈
AUT(ω) ≈

22. Detectors to be built
Large Proton Recoil Detector and a long LH2 target (Phase 1)
with dedicated read out electronics with 1 GHz sampling
Proton Recoil Detector for a transversely polarized ammonia target (Phase 2)
Large Q2 trigger
Monitoring of muon flux
ECAL1 and ECAL2 to be extended and upgraded
ECAL0 to be designed and build to increase range in xBj
and to reduce background
sketch, not to the scale

23. 2008 DVCS test run
Goal: evaluate feasibility to detect DVCS/BH in the COMPASS setup
μ p → μ p γ
Use COMPASS ‘hadron’ set-up
proton γ μ’
in EMCals
LH cm
in the small RPD
1.5 days of 160 GeV muon beam (μ+ and μ-)

24. LH target region in 2008 DVCS test run
Ring A
Ring B

25. Recoil Proton Detector
Small 1 m long Recoil Proton Detector
and a 40cm LH2 target available in 2008/2009
Proton identification in RPD
Elastic scattering with pion beam (2008)

26. Selection of exclusive single γ events
Selection of events :
- one vertex with μ and μ’
- no other charged tracks
- only 1 high energy photon
- 1 proton in RPD with p< 1. GeV/c
DVCS
Bethe-Heitler
σ ≈ 1 ns
σ ≈ 4.5 cm
Timing difference :
z position difference :
tμ- tRPD
zμμ’- zRPD

27. Kinematic constraints in the transverse plane
proton γ μ’
μ’+γ Δϕ
Δp =|Pμ’+γ|-|PRPD|
Δpperp< 0.2 GeV
Δϕ=ϕmiss- ϕRPD
Δϕ< 36 deg

28. Azimuthal distribution for single photon eventsφ θ μ’ μ *  p
After cuts
All Q2
Before cuts
All Q2
A flat background contribution in φ suppressed
The peak at φ=0 remains =>identified as BH

29. Azimuthal distribution for exclusive single photon eventsφ θ μ’ μ *  p
Monte-Carlo simulation
of BH (dominant) and DVCS
DVCS
Bethe-Heitler
After all cuts,
Q2>1GeV2
Data & MC =>
global = 13%±5%
Clear signature of dominant BH events

30. 2009 DVCS pilot run 2 weeks of DVCS pilot run in 2009 approved by SPSC
to start September 17
‘Hadron setup’ as in 2008 with the small RPD and 40 cm LH target
+ operational BMS for momentum measurements of beam μ’s
+ beam flux measurement
Both μ+ and μ- beams
Goals : observe DVCS (~100 ev.)
measure BH (~1000 ev.) to precisely verify global efficiency
observe exclusive π0 events, estimate background to DVCS
demonstrate feasibility of beam flux measurements at a few % level
measure other channels of exclusive meson prod. (ρ0)

31. Conclusion & prospects
Possible physics ouput
Sensitivity to transverse size of parton distributions inside the nucleon
Sensitivity to the GPD E and total angular momentum
Working on a variety of models to quantify the physics impact
of GPD measurements at COMPASS
Experimental requirements
Recoil detection with long LH target or polarized target
Good calorimetry and Extension at larger angles
Roadmap
A global COMPASS proposal for the period /2017
including GPD will be submitted to SPSC in 2009
2008-9: The small RPD and liquid H2 target are available for the hadron program  tests of DVCS feasibility
from 2012: The complete GPD program at COMPASS with a long RPD
+ liquid H2 target (2012)
+ transversely polarized ammonia target (2014)