Probing Generalized Parton Distributions in Exclusive Processes with CLAS Volker D. Burkert Jefferson Lab The nucleon: from structure to dynamics First GPD related results in DVCS and DVMP Experimental DVCS program at 6 GeV Prospects for the JLab energy upgrade Conclusions N*2002 Workshop, Pittsburgh, October 8-11, 2002
A real 3-dimensional Scotty z y x Scotty reduced to one dimension probablity Water Calcium Carbon Carbon x
Snapshot of a Nucleon (taken through a low resolution microscope) meson cloud quark spin valence quarks sea quarks A one-dimensional slice of the nucleon from DIS experiments correlations orbital angular momentum We need to map out the full nucleon wave function to understand its internal dynamics q + q 0 0.5 Longitudinal parton momentum and helicity distribution q - q x 1
Deeply Virtual Exclusive Processes Inclusive Scattering Forward Compton Scattering θ = 0 Deeply Virtual Compton Scattering (DVCS) t Probes the internal nucleon dynamics at the amplitude level. H(x, ξ, t),.
Modeling of the Generalized Parton Distributions Cross section difference Quark distribution q(x) Cross section qq distribution
GPDs may be accessed in Deeply Virtual Exclusive Processes DVCS DVMP hard gluon Scaling cross sections for photon and meson production hard vertices 1/Q 6 1/Q 6 1/Q 4 DVCS depends on all 4 GPDs and u, d quarks DVMP allow separation of un(polarized) H, E (H, E) GPDs, and contributions of u, d quarks M = ρ, ω H, E γ M = π, η, Κ H, E In hard scattering, photons dominate at high Q 2 Need to isolate γ * L
DVCS in the Interference with the Bethe-Heitler (BH) Measures DVCS in the interference with the known BH process: d 4 σ dq 2 dx B dtdφ ~ T DVCS + T BH 2 E o = 11 GeV E o = 6 GeV E o = 4 GeV BH DVCS Beam helicity cross section difference in twist-2: σ + σ ~ sinφim{(f 1 H+ k 1 (F 1 +F 2 )H+k 2 F 2 E }dφ
Measurement of exclusive DVCS with CLAS 2000 data, E=4.8GeV Beam Spin Asymmetry 1999 data, E=4.2GeV p ary n i relim A. Belitsky et al. S. Stepanyan et al. Phys. Rev. Lett. 87 (2001) Α(φ) = αsinφ + βsin2φ g g α = 0.202 ± 0.028stat ± 0.013sys β = -0.024 ± 0.021stat ± 0.009sys AJM ansatz for GPDs in L.O. α = 0.20 A. Feund, M. McDermott, M. Strikman, hep-ph/0208160 g g α = 0.218 ± 0.017stat β = -0.009 ± 0.013stat fit gives very small twist-3 contributions β/α g
Total cross section for γ*p p ρ 0 CLAS E = 4.2 GeV σ (γ*p->pρ 0 ) (µb) Comparison to world data CLAS DESY Cornell
Separation of σ L /σ T in γ*p pρ 0 π + π angular distribution d dn 3 = 1 + 0 0 4 3 0 0 4 1 cos 2 ( ϑ) cos( ϑ r r ) 4 (r 0 0 4 : probablity that ρ o has helicity 0) With SCHC, Q 2 = 2.4 GeV 2 from the shape of the angular distribution σ L /σ T cos(θ π)
Total, longitudinal, transversal cross section CLAS γ*p p ρ 0 1999 data p r e l i m i n a r y GPDs (frozen coupling constant + k perp effects) Regge/VDM (Laget) 1 Q 2 (GeV 2 ) 2001 data at 5.75 GeV more than 10 times statistics
Dedicated DVCS Program with CLAS at 6 GeV Measure the beam spin asymmetry and helicity-dependent cross section difference for several Q 2 bins x B -dependence Φ - dependence t dependence o Imaginary part of DVCS amplitude o Kinematical dependence of DVCS observables and GPDs o Relative importance of twist-2 and higher twist contributions, QCD corrections o Improve modeling of GPDs
DVCS - Expected Kinematical Dependencies sensitivity to twist 3 probes ξ dependency t=-0.325 x B =0.22 φ = 90 ο x B =0.22 ~ 380 bins in φ, x B, t
Prospects for GPD at 12 GeV
L = 10 35 cm -2 s -1 The CLAS ++ Detector Forward Cerenkov Forward DC Forward EC Inner Cerenkov Central Detector Preshower EC Torus Cold Ring Inner Calorimeter Forward TOF
DVCS with CLAS ++ at 11 GeV Q 2,x B, t, ranges measured simultaneously
DVCS with CLAS ++ at 11 GeV 2% of all data points that are measured simultaneously.
DVCS with CLAS ++ at 11 GeV sinφ-moment of A LU: t - dependence
Deeply Virtual ρ 0 Production at 11 GeV CLAS ++ σ L Separation of σ L /σ T by analysis of angular distribution of the π + π system, and use of SCHC. 400 hrs @ 10 35 cm -2 s -1
Separated Cross section for ep eπ + n Rosenbluth separation for σ L /σ T x B = 0.4-0.5 + many other bins at -t = 0.2-0.4GeV 2 the same time σ L Measure pπ 0, pη, KΛ, KΣ,.. simultaneously σ TOT σ T
Summary g First exclusive DVCS measurement with CLAS at 4 GeV g New 6 GeV data in hand for DVCS and DVMP g Some 6 GeV DVCS data with longitudinal polarized target g Dedicated setup under design in Hall B and in Hall A for a DVCS measurement at 6 GeV with complete event reconstruction and large kinematic coverage High luminosity data at 6 GeV and 12 GeV will allow to map the Q 2,x B and t dependences necessary for extracting information about the GPDs in the essentially unexplored kinematical region: W > 2 GeV, Q 2 > 1.5 GeV 2, 0.1 < x B <0.7 Elevate the study of nucleon dynamics to a new level
First Measurement with CLAS Data (March 1999) CEBAF Large Acceptance Spectrometer Beam polarization (~70%) E beam = 4.2 GeV Integrated L tot = 1.4x10 39 cm -2 (1.4fb -1 ) Corresponds to 3 days of beam time DVCS: Exclusive measurement: ep e'p(γ)
Hall A DVCS at 6 GeV Experimental Setup http://www.jlab.org/~sabatie/dvcs High Resolution Hall A spectrometer for electron detection 100-channel scintillator array for proton detection 150-block PbF 2 electromagnetic calorimeter for photon detection Detection of all 3 final-state particles ensures exclusivity
Hall A DVCS at 6 GeV Methods and goals Unique characteristics: Very high luminosity (10 37 cm -2 s -1 ) Well defined kinematics (high resolution detection of e - and γ) Very high statistics for Q 2 up to 2.5 GeV 2 at fixed x B =0.35 Method: Measure weighted cross-section differences ( purer than asymmetries) as function of ϕ angle. Deduce Q 2 dependence and relative importance of twist-2 and higher twists. Test factorization of DVCS Measure linear combinations of GPD s One of three bins at Q 2 =2.5GeV 2
Experimental Setup: Modified CLAS Configuration Increase luminosity to 2 x10 34 cm -2 s -1 45 ο 8 ο Replace the mini-torus shield with a solenoidal magnetic field. Exclusivity of DVCS event by event PbWO 4 crystal array for the detection of high-energy photons at small lab angles.
Complete Photon Detection 430 crystals, 15x15x160mm 3, pointing geometry, APD readout γ γ 4GeV/c π 0 at 65 cm distance (symmetric decay)
W > 2 and E = 6 GeV CLAS Kinematical coverage in Q 2, t, and x B
DVCS and Generalized Parton Distributions (GPDs) ~ ~ GPDs: H, E unpolarized, H, E polarized γ γ e.g. H(ξ, t, Q 2 ) = Hq (x, ξ, t, Q 2 )dx x-ξ + iε H q (x, ξ, t, Q 2 )dx = x-ξ 10/8/2002 real part + iπh q (ξ, ξ, t, Q 2 ) imaginary part ~ ~ P ( x + ξ ) P( x ξ ) GPD s cross section difference d 3 σ dq 2 dx B dt ~[ah(ξ, t, Q2 )+be(ξ, t, Q 2 )+ch(ξ, t, Q 2 )+de(ξ, t, Q 2 )] 2 H q : Probability amplitude for N to emit a parton q with x+ξ and N to absorb it with x- ξ. Latifa Elouadrhiri - DVCS at 6 GeV with CLAS 31
CLAS 4.3 GeV - Kinematical Coverage
DVCS: Beam Spin Dependence The imaginary part of the DVCS amplitude can be accessed with longitudinally polarized beam: d 4 σ + dq 2 dx B dtdφ - d 4 σ - dq 2 dx B dtdφ Im(TDVCS )T BH a ImM 1,1 sinφ + b ImM 0,1 sin2φ + O(1/Q 2 ) The leading term (twist-2) has a sinφ modulation. dσ + - dσ - = - 16(2 y) 1- x 1- yx - 2 Q 2 sinφim{f 1 H+ ~ x 2 - x (F 1 + F 2 )H - 2 4M 2 F 2E}dM The twist-3 term has sin2φ modulation
Measurements to extract all twist-2 and twist-3 Compton Form Factors. polarized beam polarized target - longitudinal - transverse e - /e + beam beam target observed experiment e + /e unpol Re C I unp?/e1-dvcs pol long. Re C I LP EG1 pol trans. Re C I TP+/-? pol unpol Im C I unp E1/E1-DVCS unpol long. Im C I LP EG1 unpol trans. Im C I TP+/-? Fourier components cosφ, cos2φ,cos3φ 1, cosφ, cos2φ cosφ,cos2φ sinφ, sin2φ sinφ, sin2φ,sin3φ Σ = 10 (13) x B C I unp = F 1 H + (F 1 +F 2 )H - 2 2-x B 4M 2 F 2 E H = dxc(ξ,x)h(x,ξ) -1 +1
Total cross section for γ*p p π + π Comparison to world data @ W ~ 2GeV σ ( B) * µ γ p pππ CLAS DESY Cornell p r e l i m i n a r y
ep e'px - Missing Mass Analysis Radiative eleastic events Exclusive ep e'pγγ For DVCS kinematics ep e'p(γ) ep e'pπ o Exclusive ep e'pγ
Expected Results ep e'pγ (DVCS + BH) at 6 GeV 60 days of beam time at luminosity L = 2x10 34 cm -2 sec -1 Q 2 =1 Q 2 = 2 φ= 90 o t= -0.325 Q 2 =3
Expected t Dependence φ= 90 o x B = 0.22
Expected Φ Dependence t = -0.325 x B = 0.22
Expected CLAS DVCS Results at 11 GeV Expected Kinematical Coverage
Measurement of exclusive DVCS/BH with CLAS Beam Spin Asymmetry g CLAS Data g First Measurement of the beam spin asymmetry in fully exclusive DVCS process gthe measured asymmetry: α = 0.202 ± 0.028 stat ± 0.013 sys Α(φ) = αsinφ + βsin2φ S. Stepanyan et al. Phys. Rev. Lett. 87 (2001) g From the recent calculation CLAS data are consistent with antiquark-gluon-quark correlation in the twist-3 GPDs