Generalized Parton Distributions and the Structure of the Nucleon x=0.4 x=0.9 1.5 -1.5 1 -1 Volker D. Burkert Jefferson Lab fm fm April Meeting

Fundamental questions in hadron physics? 1950-1960: Does the proton have finite size and structure? Elastic scattering the proton is not a point-like particle charge and current distribution in the proton, F1/F2 1960-1990: What is the internal structure of the proton? Deep inelastic scattering discover quarks quark momentum and spin distributions q(x), Dq(x) We can soon celebrate a half century of electron scattering. So, we can ask what are the most fundamental questions that have been addressed in electron scattering. Today: How are these representations of the proton, charge/current distributions and quark momentum/spin distributions fundamentally connected?

Beyond charge and quark distributions – Generalized Parton Distributions (GPDs) X. Ji, D. Mueller, A. Radyushkin (1994-1997), … M. Burkardt, A. Belitsky (2000) … Infinite momentum frame Transverse charge & current densities Quark longitudinal momentum & helicity distributions Correlated distributions in transverse space - GPDs

From Holography to Tomography An Apple A. Belitsky, B. Mueller, NPA711 (2002) 118 mirror mirror detector A Proton mirror mirror By varying the energy and momentum transfer to the proton we probe its interior and generate tomographic images of the proton (“femto tomography”).

Deeply Virtual Exclusive Processes & GPDs “handbag” mechanism x Deeply Virtual Compton Scattering (DVCS) hard vertices g x – longitudinal quark momentum fraction x+x x-x 2x – longitudinal momentum transfer –t – Fourier conjugate to transverse impact parameter t H(x,x,t), E(x,x,t), . . xB x = 2-xB

[ ] ò Link to DIS and Elastic Form Factors [ ] ò ) ( ), , ~ q H - D = Form factors (sum rules) [ ) ( , ~ ) Dirac f.f. 1 t G x E dx H F1 q P A = ] ò - ) Pauli f.f. F2 DIS at x =t=0 ) ( ), , ~ q H - D = ) , ( ~ t x E H [ ] ò - x + - JG = = 1 ) , q( 2 E H xdx Jq Quark angular momentum (Ji’s sum rule) X. Ji, Phy.Rev.Lett.78,610(1997)

GPDs A Unified Description of Hadron Structure Elastic form factors Parton momentum distributions GPDs Real Compton scattering at high t Deeply Virtual Compton Scattering Deeply Virtual Meson production

Accessing GPDs through DVCS dQ2dxBdtd ~ |DVCS + BH|2 BH : given by elastic form factors DVCS: determined by GPDs DsLU ~ BH Im(DVCS)sinf + higger twist. ~ |DVCS|2 + |BH|2 + BH*Im(DVCS) DVCS BH GPDs FF ep epg e-’ f Qgg* p g e- g* plane ee’g* plane gg*p

Separating GPDs through polarization 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

Access GPDs through x-section & asymmetries DIS measures at x=0 Quark distribution q(x) -q(-x) Accessed by cross sections Accessed by beam/target spin asymmetry t=0

First observation of DVCS/BH beam asymmetry e+p e+gX 2001 e-p e-pX CLAS 4.3 GeV HERMES 27 GeV -180 +180 f(deg) Q2=2.5 GeV2 Q2=1.5 GeV2 A(f) = asinf + bsin2f GPD analysis of CLAS/HERMES/HERA data in LO/ NLO shows results consistent with handbag mechanism and lowest order pQCD A. Freund, PRD 68,096006 (2003), A. Belitsky, et al. (2003) b/a << 1 twist-3 << twist-2

e p epg DVCS/BH target asymmetry ~ AUL E=5.75 GeV CLAS preliminary e p epg AUL E=5.75 GeV Longitudinally polarized target AUL~sinf{F1H+x(F1+F2)H...}df ~ <Q2> = 2.0GeV2 <x> = 0.2 <-t> = 0.25GeV2 Asymmetry observed at about the expected magnitude. Much higher statistics, and broad kinematical coverage are needed. HERMES data on deuterium target

First DVCS experiment with GPDs in mind Twist-2 + twist-3: Kivel, Polyakov, Vanderhaeghen (2000) B CLAS preliminary ALU E=5.75 GeV <Q2> = 2.0GeV2 <x> = 0.3 <-t> = 0.3GeV2 f [rad] Model with GPD parametrization and quark kT corrections describes data.

CLAS Hall A First Dedicated DVCS Experiments at JLab => Full reconstruction of all final state particles e, p, g => High luminosity Hall A x, t, Q2 - dependence of Im(DVCS) in wide kinematics. Constrain GPD models. PbWO4 Electromagnetic calorimeter s.c. solenoid CLAS Currently taking data Azimuthal and Q2 dependence of Im(DVCS) at fixed x. Test Bjorken scaling. Data taking completed

ò DVCS/BH Beam-Charge Asymmetry HERMES ~ The e+- e- beam asymmetry measures real part of convolution integral for GPDs. H ( x , t ) x- = ò q (x, dx ~ Improved statistics and control of systematic expected in future run Measurements proposed for COMPASS experiment at CERN in m+-m-. DsC ~ cosf{F1H + x(F1+F2) H +kF2E}df

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

Exclusive ep epr0 production W=5.4 GeV HERMES (27GeV) CLAS (4.3 GeV) xB=0.38 Q2 (GeV2) GPD formalism approximately describes CLAS and HERMES data Q2 > 2 GeV2

JLab Upgrade to 12 GeV Energy A much better machine for GPD studies …. Add new hall CHL-2 Enhance equipment in existing halls

Deeply Virtual Exclusive Processes - Kinematics Coverage of the 12 GeV Upgrade unique to JLab High xB only reachable with high luminosity H1, ZEUS JLab Upgrade

CLAS12 Luminosity > 1035cm-2s-1 EC Cerenkov Drift Chambers TOF Torus Central Detector Beamline IEC Luminosity > 1035cm-2s-1

DVCS/BH- Beam Asymmetry Ee = 11 GeV ALU With large acceptance, measure large Q2, xB, t ranges simultaneously. A(Q2,xB,t) Ds(Q2,xB,t) s (Q2,xB,t)

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

CLAS12 - DVCS/BH Beam Asymmetry Projected data: e p epg E = 11 GeV DsLU~sinfIm{F1H+..}df Integrated luminosity ~ 720 fb-1 L = 1x1035 T = 2000 hrs DQ2 = 1 GeV2 Dx = 0.05

Exclusive r production on transverse target A ~ 2Hu + Hd AUT ~ Im(AB*) r0 B ~ 2Eu + Ed AUT r0 xB A ~ Hu - Hd B ~ Eu - Ed r+ Asymmetry depends linearly on the GPD E in Ji’s sum rule. r0 and r+ measurements allow separation of Eu, Ed CLAS12 projected K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001

quark flavor separation Images of the Proton’s Quark Content M. Burkardt (2002) b - Impact parameter T u(x,b ) by bx x=0.3 x=0.5 x=0.1 transverse polarized target uX(x,b ) T dX(x,b ) T d(x,b ) T quark flavor separation Hu Eu Hd Ed Target polarization

Summary The discovery of Generalized Parton Distributions has opened up a new and exciting area of hadron physics that needs exploration in dedicated experiments. Moderate to high energy, very high luminosity, and large acceptance spectrometers are needed to measure GPDs in deeply virtual exclusive processes. The JLab 12 GeV Upgrade will provide the tools to do this well and explore the nucleon at a deeper level.