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, 21.4.2006

GPDs – a 3-D picture of the partonic nucleon structure Px 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 )

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) 054012 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

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

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)

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

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

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

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

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

Experimental Setup: Beam Polarized beam: Ep=110 GeV → Eµ=100 GeV P(µ+) = -0.8 2.108/spill P(µ-) = +0.8 2.108/spill Muon section 400m Hadron decay section 600m Compass target scrapers Be absorbers Protons 400 GeV T6 primary Be target Collimators 1 2 3 4 H V H V 2.108 muons/spill 1.3 1013 protons/spill

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 = 1.3 1032 cm-2 s-1

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 250-750 MeV/c ToF with 200 ps resolution required 2 concentric barrels of 24 scintillators read out at both sides, fast multi-hit ADC

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

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

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) 094017

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=1.3 1032 cm-2s-1 150 days efficiency=25%

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

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. (PRD56 1997): 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

Roadmap for GPDs at COMPASS 2005: Expression of interest SPSC-EOI-005 2006: Test of recoil detector prototype Proposal 2007-2009: 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

SPARE

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)

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°

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