1. Prospects for Generalized Parton Distributions studies at
GPDs
Experimental Setup
Prospects
F.-H. Heinsius (Universität Freiburg/CERN)
on behalf of the COMPASS collaboration
DIS 2006, Tsukuba,

2. GPDs – a 3-D picture of the partonic nucleon structurePx
ep eX
Deep Inelastic Scattering
Q²xBj x p g*
Parton Density q ( x )
x boost
x P z 1 y
Hard Exclusive Scattering
Deeply Virtual Compton Scattering
Burkardt,Belitsky,Müller,Ralston,Pire
Generalized
Parton Distribution H( x,,t )
ep ep p
GPDs * Q²
x+
x-  t
x P y z r
x boost
( Px, ry,z )

3. What do we learn from the 3 dimensional picture (Px,ry,z)?
Lattice calculation (unquenched QCD):
J.W. Negele et al., NP B128 (2004) 170
M. Göckeler et al., NP B140 (2005) 399
 fast parton close to the N center
 small valence quark core
 slow parton far from the N center
 widely spread sea q and gluons
mp=0.87 GeV
xav
measure H(x,0,t) as function of t
2. Chiral dynamics: Strikman et al., PRD69 (2004)
at large distance, the gluon density
is generated by the pion cloud
significant increase of
the N transverse size
if xBj < mπ/mp=0.14
COMPASS domain

4. Generalized Parton Distributions
µp µp (µpr) p
GPDs * Q²
x+
x-
,r t
GPDs depend on 3 variables:
x: longitudinal quark momentum fraction ≠ xBj
2: longitudinal momentum transfer: =xBj/(2-xBj)
t: momentum transfer squared to the target nucleon (fourier conjugate to the transverse impact parameter r)
Deep Virtual Compton Scattering
GPD: H, H̃, E, Ẽ
Hard Exclusive Meson Production
Vektormeson: E, H
Pseudoscalar: Ẽ, H̃
H nucleon no spin flip
E nucleon spin flip
H,E: quark spin averaged
Tilde: quark spin differences
x P y z r
x boost

5. GPDs and Relations to Physical Observables
factorization
x+ξ
x-ξ t
The observables are some integrals of GPDs over x
Dynamics of partons
in the Nucleon Models:
Parametrization
Fit of Parameters to the data
H, H̃, E, Ẽ(x,ξ,t)
“ordinary” parton density
Elastic Form Factors
Ji’s sum rule
2Jq =  x(Hq+Eq)(x,ξ,0)dx x x
H(x,0,0) = q(x) H̃(x,0,0) = Δq(x)
 H(x,ξ,t)dx = F(t)

6. Measurement of GPDs g* g* g g g * Collins et al.
Deeply Virtual Compton Scattering (DVCS): g g* Q2 p p’
GPDs
x + ξ
x - ξ
t =Δ2
meson
Gluon contribution L g* Q2 g
hard
x + ξ
x - ξ
soft
GPDs
Q2 large
t << Q2
+ g* p p’
t =Δ2
Hard Exclusive Meson Production (HEMP):
meson p p’
GPDs
g *
x + ξ
x - ξ
hard
soft L Q2 L
t =Δ2
Quark contribution

7. DVCS and Bethe Heitler φ θ μ’ μ *  p BH calculable μ μ p p
High energy muon beam
at COMPASS:
Higher energy: DVCS >> BH
 DVCS Cross section
Smaller energy: DVCS ≈ BH
Interference term will provide
the DVCS amplitude φ θ μ’ μ *  p

8. Advantage of µ+ and µ- for DVCS (+BH)
t, ξ~xBj/2 fixed
dσ(μpμp) = dσBH + dσDVCSunpol + Pμ dσDVCSpol
+ eμ aBH Re ADVCS eμ Pμ aBH Im ADVCS
 cos nφ  sin nφ φ θ μ’ μ *  p
Pμ+=-0.8 Pμ-=+0.8
Diehl

9. Advantage of µ+ and µ- for DVCS (+BH)
t, ξ~xBj/2 fixed
dσ(μpμp) = dσBH + dσDVCSunpol + Pμ dσDVCSpol
+ eμ aBH Re ADVCS eμ Pμ aBH Im ADVCS
 cos nφ  sin nφ φ θ μ’ μ *  p
Pμ+=-0.8 Pμ-=+0.8
Diehl

10. Advantage of µ+ and µ- for DVCS (+BH)
t, ξ~xBj/2 fixed
dσ(μpμp) = dσBH + dσDVCSunpol + Pμ dσDVCSpol
+ eμ aBH Re ADVCS eμ Pμ aBH Im ADVCS
 cos nφ  sin nφ φ θ μ’ μ *  p
Pμ+=-0.8 Pμ-=+0.8
Diehl

11. Experimental Setup: Beam
Polarized beam: Ep=110 GeV → Eµ=100 GeV
P(µ+) = /spill
P(µ-) = /spill
Muon section 400m
Hadron decay section 600m
Compass
target
scrapers
Be absorbers
Protons
400 GeV
T6 primary
Be target
Collimators
H V H V
2.108 muons/spill
protons/spill

12. Experimental Setup: Target & Detektor
all COMPASS trackers:
SciFi, Si, MM, GEM, DC, Straw, MWPC
2.5 m Liquid H2 target
to be designed and built μ’ 
ECAL1/2
  12°
COMPASS equipment
with additional calorimetry
at large angle (p0 bkg) μ p’
Recoil detector to insure exclusivity
to be designed and built
L = cm-2 s-1

13. Recoil Detector Design
30°
ECAL0
12°
scintillator: Inner 4 mm (2.8m), outer 5cm (4m)
Neutral detection: layers of lead and scintillators 4m
Detect protons of MeV/c
ToF with 200 ps resolution required
2 concentric barrels of 24 scintillators
read out at both sides, fast multi-hit ADC

14. Recoil Detector Prototype
4 m
30° sector design
Test at COMPASS beam this year
Funded by EU FP6 (Bonn, Mainz, Saclay, Warsaw)

15. Prospects: Kinematical Range
if Nμ  2  Q2 < 11 GeV2
for DVCS
Limitation by luminosity
now Nμ= 2.108μ per SPS spill
Q2 < 7.5 GeV2 
if Nμ  5  Q2 < 17 GeV2
Limit for r (DVMP)
2 times higher Q²
100GeV
E=190,
At fixed xBj, study in Q2

16. Simulations with two Models
Parametrizations of GPDs
Model 1: H(x,ξ,t) ~ q(x) F(t)
Model 2: Chiral quark-soliton model: Goeke et al., NP47 (2001) 401
H(x,0,t) = q(x) e t <b2> = q(x) / xα’t (α’slope of Regge traject.)
<b2> = α’ln 1/x transverse extension of partons in hadronic collisions
considers fast partons in the small valence core
and slow partons at larger distance (wider meson cloud)
includes correlation between x and t
Vanderhaeghen et al., PRD60 (1999)

17. DVCS Simulations for COMPASS at 100 GeV
x = 0.05 ± 0.02
x = 0.10 ± 0.03
BCA φ
Q2=40.5 GeV2
Model 1: H(x,ξ,t) ~ q(x) F(t)
Model 2: H(x,0,t) = q(x) e t <b2>
= q(x) / xα’t
6 bins in Q2 from 1.5 to 7.5 GeV2 (1 shown)
3 bins in xBj=0.05,0.1,0.2 (2 shown)
Assumptions
L= cm-2s-1
150 days
efficiency=25%

18. Advantage of COMPASS kinematics
Model 1: H(x,ξ,t) ~ q(x) F(t)
model 1
Model 2: H(x,0,t) = q(x) e t <b2>
= q(x) / xα’t
model 2
COMPASS
sensitive to different spatial distributions at different x

19. Hard Exclusive Meson Production (ρ,ω,…,π,η… )
GPDs g*
x + ξ
x - ξ
t =Δ2 L
Scaling predictions:
hard
soft
1/Q6
1/Q4
Collins et al. (PRD ):
1. factorization applies only for g*
2. σT << σL L
vector mesons pseudo-scalar mesons
ρ0 largest production present study
ρ0  π+ π with COMPASS

20. Roadmap for GPDs at COMPASS
2005: Expression of interest SPSC-EOI-005
2006: Test of recoil detector prototype
Proposal
: construction of
recoil detector
LH2 target
ECAL0
≥ 2010: Study of GPDs at COMPASS
In parallel present COMPASS studies with polarised target
Complete analysis of ρ production
Other channels: , 2π …
GPD E/H investigation with the transverse polarized target

22. SPARE

23. Complementarity of Experiments
100GeV
E=190,
At fixed xBj,
study in Q2
0.0001< xBj < 0.01
Gluons
Valence and sea quarks
and Gluons
Valence quarks
JLab
PRL87(2001)
Hermes PRL87(2001)
COMPASS plans
H1 and ZEUS
PLB517(2001) PLB573(2003)

24. Competing reactions to DVCS Selection DVCS/DIS
DVCS: μp  μp
HEπ°P: μp  μpπ°
 
Dissociation of the proton:
μp  μN*π°
 Nπ
DIS: μp μpX
with 1, 1π°, 2π°,η…
Beam halo
with hadronic contamination
Beam pile-up
Secondary interactions
External Bremsstrahlung
Selection DVCS/DIS
with PYTHIA 6.1
Tune parameters:
-maximum angle for photon detection 30°
-threshold for photon detection 50MeV
-maximum angle for charged particle
detection 30°

26. Cross-section measurement and beam charge asymmetry (ReT)
integrate GPDs over x
Beam or target spin asymmetry
contain only ImT,
therefore GPDs at x = x and -x
Quark distribution q(x), -q(-x)
M. Vanderhaeghen