Prospects for GPD and TMD studies at the JLab Upgrade Volker D. Burkert Jefferson Lab Introduction JLab Upgrade and CLAS12 GPDs from DVCS and DVMP TMDs from SIDIS and SSA Summary SIR Workshop – Jefferson Lab, May 17-20, 2005

GPDs, TMDs & PDFs z z y x x x 3-D Scotty 2-D Scotty 1-D Scotty probablity Calcium Water Carbon This Workshop – GPDs, TMDs Deeply Inelastic Scattering, PDFs

JLab Upgrade to 12 GeV Energy Add new hall 12 GeV CHL-2 Enhance equipment in existing halls Beam polarization Pe > 80% E= 2.2, 4.4, 6.6, 8.8, 11 GeV

Design luminosity = 1035cm-2s-1 CLAS12 Nearly full angle coverage for tracking and g, n detection High luminosity, 1035 cm-2s-1 Concurrent measurement of deeply virtual exclusive, semi-inclusive, and inclusive processes. EC Cerenkov Drift Chambers TOF Cerenkov Torus Central Detector Beamline IEC Design luminosity = 1035cm-2s-1

CLAS12

High Q2, low t ep eK+S0(gL(pp-)) event CLAS12 - Central Detector High Q2, low t ep eK+S0(gL(pp-)) event Silicon tracker, calorimetry, ToF Solenoid magnet, Bcenter = 5 T K+ e- g p- p g e-

CLAS 12 - Expected Performance Forward Detector Central Detector Angular coverage: Tracks (inbending) 8o - 40o 40o - 135o Tracks (outbending) 5o - 40o 40o - 135o Photons 2o - 40o 40o - 135o Track resolution: dp (GeV/c) 0.003p + 0.001p2 dpT=0.03pT dq (mr) < 1 (>2.5 GeV/c) 8 (1 GeV/c) df (mr) < 3 (> 2.5 GeV/c) 2 (1 GeV/c) Photon detection: Energy range > 150 MeV > 60 MeV dE/E 0.09(EC)/0.04(IEC) 0.06 (1 GeV) dq (mr) 4 (1 GeV) 15 (1 GeV) Neutron detection: heff 0.5 (EC), 0.1 (TOF) 0.04 (TOF) Particle id: e/p >>1000 ( < 5 GeV/c) - >100 ( > 5 GeV/c) - p/K (4s) < 3 GeV/c (TOF) 0.65 GeV/c 3 - 10 GeV/c (CC) p/p (4s) < 5 GeV/c (TOF) 1.2 GeV/c 3 - 10 GeV/c (CC) K/p(4s) < 3.5 GeV/c (TOF) 0.9 GeV/c

Deeply Virtual Exclusive Processes - Kinematics Coverage of the 12 GeV Upgrade H1, ZEUS H1, ZEUS 11 GeV 27 GeV 200 GeV 11 GeV JLab Upgrade JLab @ 12 GeV COMPASS W = 2 GeV HERMES Study of high xB domain requires high luminosity 0.7

Acceptance for DVCS, SIDIS Q2 > 2.5 GeV2 Forward Detector Central Detector ep egp qg xB = 0.35 EC IEC Q2 ep ep+X

Separating GPDs through polarization ep epg x = xB/(2-xB) k = t/4M2 A = Ds 2s s+ - s- s+ + s- = Polarized beam, unpolarized target: ~ ~ DsLU ~ sinf{F1H + x(F1+F2)H +kF2E}df H, H, E Kinematically suppressed Unpolarized beam, longitudinal target: ~ ~ H, H DsUL ~ sinf{F1H+x(F1+F2)(H + … }df Unpolarized beam, transverse target: H, E DsUT ~ sinf{k(F2H – F1E) + ….. }df

DVCS/BH- Beam Asymmetry ~ ~ DsLU ~ sinf{F1H + x(F1+F2)H +kF2E}df Ee = 11 GeV ALU ALU CLAS preliminary E=5.75 GeV <Q2> = 2.0GeV2 <x> = 0.3 <-t> = 0.3GeV2 f [rad] B

CLAS12 - DVCS/BH- Beam Asymmetry Ee = 11 GeV Q2=5.5GeV2 xB = 0.35 -t = 0.25 GeV2 Luminosity = 720fb-1

CLAS12 - DVCS/BH Beam Asymmetry e p epg E = 11 GeV DsLU~sinfIm{F1H+..}df Sensitive to GPD H Selected Kinematics L = 1x1035 T = 2000 hrs DQ2 = 1 GeV2 Dx = 0.05

GPDs H from expected DVCS ALU data bval=bsea=1 MRST02 NNLO distribution Q2=3.5 GeV2 Other kinematics measured concurrently p

CLAS12 - DVCS/BH Target Asymmetry E = 11 GeV L = 2x1035 cm-2s-1 T = 1000 hrs DQ2 = 1GeV2 Dx = 0.05 e p epg Longitudinally polarized target ~ Ds~sinfIm{F1H+x(F1+F2)H...}df CLAS preliminary E=5.75 GeV AUL <Q2> = 2.5GeV2 <x> = 0.25 <-t> = 0.25GeV2

CLAS12 - DVCS/BH Target Asymmetry Q2=2.2 GeV2, xB = 0.25, -t = 0.5GeV2 E = 11 GeV Sample kinematics e p epg Transverse polarized target Ds ~ sinfIm{k1(F2H – F1E) +…}df AUTx Target polarization in scattering plane AUTy Target polarization perpedicular to scattering plane Asymmetry highly sensitive to the u-quark contributions to proton spin.

GPDs – Flavor separation DVMP DVCS long. only hard gluon hard vertices Photons cannot separate u/d quark contributions. M = r0/r+ select H, E, for u/d flavors M = p, h, K select H, E

CLAS12 – L/T Separation ep epro (p+p-) sT xB = 0.3-0.4 -t = 0.2-0.3GeV2 Other bins measured concurrently Projections for 11 GeV (sample kinematics) Test of Bjorken scaling Power corrections?

Exclusive r0 production on transverse target 2D (Im(AB*))/p T AUT = - |A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2 A ~ 2Hu + Hd r0 Q2=5 GeV2 B ~ 2Eu + Ed Eu, Ed needed for angular momentum sum rule. r0 K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 B

Exclusive r+ with transverse target Strong sensitivity to d-quark contributions. A ~ Hu - Hd B ~ Eu - Ed r+ CLAS 5.7 GeV n AUT r+

[ ] ò Quark Angular Momentum Sum Rule With GPDs Hu, Hd, Eu, Ed obtain access to total quark contribution to proton angular momentum. Large x contributions important. [ ] ò - x + - J G = = 1 ) , q( 2 E H xdx J q X. Ji, Phy.Rev.Lett.78,610(1997)

Transverse Momentum Dependent PDFs (TMDs) Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k Wpu(x,k,r) “Parent” Wigner distributions TMD PDFs: fpu(x,kT),g1,f┴1T, h┴1L d3r Measure momentum transfer to quark. TMD d2kT (FT) GPD GPDs: Hpu(x,x,t), Epu(x,x,t),… Measure momentum transfer to nucleon.

SIDIS at leading twist e Boer e p Mulders e p transversity Sivers Off-diagonal PDFs vanish if quarks only in s-state! In addition T-odd PDFs require FSI (Brodsky et al., Collins, Ji et al. 2002)

Azimuthal Asymmetry – Sivers Effect Originates in the quark distribution. It is measured in the azimuthal asymmetry with transverse polarized target. sin(f-fs) f1T D1 T AUT ~ k Requires: non-trivial phase from the FSI + interference between different helicity states (S. Brodsky)

SIDIS Azimuthal Asymmetry - Sivers effect (P /M)AUT sin(f-fs) T Probes orbital angular momentum of quarks by measuring the imaginary part of s-p-wave interference in the amplitude. Extraction of Sivers function f1T from asymmetry. T

CLAS12 - Sivers function from AUT (p0) Efremov et al (large xB behavior of f1T from GPD E) In large Nc limit: F1T=∑qeq2f1T┴q f1Tu = -f1Td CLAS12 projected CLAS12 projected xB xB

Azimuthal Asymmetry - Collins Effect sUT ~ k h1H1 sin(f+fs) T Access to transversity distribution and fragmentation of polarized quarks.

Tomographic Images of the Nucleon x=0.4 1.5 -1.5 fm x=0.9 1 -1 X. Ji u-quark charge density distribution y z dX(x,b ) T uX(x,b ) T CAT scan slice of human abdomen flavor polarization M. Burkardt Ed(x,t) Eu(x,t)

Double DVCS (DDVCS) e-p e-pe+e- DDVCS DVCS asymmetry Cross section DDVC rates reduced by more than factor 200

CLAS12 – Acceptance for DDVCS

Summary The JLab 12 GeV Upgrade is essential for the study of nucleon structure in the valence region with high precision: - deeply virtual exclusive processes (DVCS, DVMP) - semi-inclusive meson production with polarized beam and polarized targets Provide new and deeper insight into - quark orbital angular momentum contributions to the nucleon spin - 3D structure of the nucleon’s interior and correlations - quark flavor polarization - ….. CLAS12 will be world wide the only full acceptance, general purpose detector for high luminosity electron scattering experiments, and is essential for the GPD/TMD program.

New Collaborators are welcome!

Additional Slides

Sivers effect in the target fragmentation xF>0 (current fragmentation) xF<0 (target fragmentation) xF - momentum in the CM frame Wide kinematic coverage of CLAS12 allows studies of hadronization in the target fragmentation region

Collins Effect and Kotzinian-Mulders Asymmetry sUL ~ k h1LH1 KM T Measures the Collins fragmentation with longitudinally polarized target. Access to the real part of s-p wave interference amplitudes.

Collins Effect and Kotzinian-Mulders Asymmetry sUL ~ (1-y) h1LH1 KM T Measures the Collins fragmentation with longitudinally polarized target. Access to the real part of s-p wave interference amplitudes.

CLAS12 - L(1115) Polarization ` CLAS12 - L(1115) Polarization E = 11 GeV ep eL(pp-)X (SIDIS) K K*(892)

L polarization in the target fragmentation Λ 1 2