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Generalized Parton Distributions and the Structure of the Nucleon

1.5. 1. 0. 0. -1.5. -1. Generalized Parton Distributions and the Structure of the Nucleon. x=0.4. x=0.9. Volker D. Burkert Jefferson Lab. fm. fm. April Meeting. Today: How are these representations of the proton, charge/current distributions and quark momentum/spin

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Generalized Parton Distributions and the Structure of the Nucleon

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  1. 1.5 1 0 0 -1.5 -1 Generalized Parton Distributions and the Structure of the Nucleon x=0.4 x=0.9 Volker D. Burkert Jefferson Lab fm fm April Meeting

  2. Today: How are these representations of the proton, charge/current distributions and quark momentum/spin distributions fundamentally connected? 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)

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

  4. A. Belitsky, B. Mueller, NPA711 (2002) 118 An Apple A Proton detector From Holography to Tomography mirror mirror 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”).

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

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

  7. 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

  8. DVCS BH FF GPDs plane gg*p f d4 e-’ g ~ |DVCS + BH|2 dQ2dxBdtd Qgg* ~|DVCS|2 + |BH|2 + BH*Im(DVCS) g* e- p ee’g* plane BH:given by elastic form factors DVCS: determined by GPDs DsLU~ BHIm(DVCS)sinf+ higger twist. Accessing GPDs through DVCS ep epg

  9. Ds 2s s+ - s- s+ + s- A = = x = xB/(2-xB) k = t/4M2 Separating GPDs through polarization 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

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

  11. CLAS 4.3 GeV HERMES 27 GeV 0 -180 +180 f(deg) First observation of DVCS/BH beam asymmetry e+p e+gX 2001 e-p e-pX Q2=1.5 GeV2 Q2=2.5 GeV2 A(f) = asinf + bsin2f GPD analysis of CLAS/HERMES/HERAdata in LO/ NLOshows 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

  12. e p epg ~ AUL~sinf{F1H+x(F1+F2)H...}df DVCS/BH target asymmetry CLAS preliminary AUL E=5.75 GeV Longitudinally polarized target <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

  13. B Twist-2 + twist-3: Kivel, Polyakov, Vanderhaeghen (2000) First DVCS experiment with GPDs in mind CLASpreliminary 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.

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

  15. x H (x, , t ) dx q ò x ) ( , t H = x x- DVCS/BH Beam-Charge Asymmetry HERMES The e+- e- beam asymmetry measures real part of convolution integral for GPDs. • 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

  16. 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

  17. HERMES (27GeV) W=5.4 GeV GPD formalism approximately describes CLAS and HERMES data Q2 > 2 GeV2 Exclusiveep epr0production L CLAS (4.3 GeV) xB=0.38 Q2 (GeV2)

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

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

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

  21. 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)

  22. 1 Q2=5.5GeV2 xB = 0.35 -t = 0.25 GeV2 ALU -1 CLAS12 - DVCS/BH- Beam Asymmetry Ee = 11 GeV

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

  24. AUT r0 xB Exclusiver production on transverse target A~ 2Hu + Hd r0 AUT ~ Im(AB*) B~ 2Eu + Ed A~ Hu - Hd B ~ Eu - Ed r+ Asymmetry depends linearly on the GPDEin Ji’s sum rule. r0and r+ measurements allow separation of Eu, Ed CLAS12 projected K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001

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

  26. 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.

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