Generalized Parton Distributions and Nucleon Structure

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1 Generalized Parton Distributions and Nucleon Structure Volker D. Burkert Jefferson Lab With pqcd established we have the tool to understand matter at a deeper level. Nobel prize D. Gross, D. Politzer, F. Wilzcek GPDs - a unifying framework of hadron structure DVCS and DVMP at 12 GeV Extracting GPDs from polarization measurements 3D Imaging of the Nucleon Quark Structure Transverse momentum dependent PDFs A five year program with CLAS12 Summary DOE Science Review for the JLab Upgrade to 12 GeV, Jefferson Lab, April 6-8, 2005

2 Fundamental questions in hadron physics? : Does the proton have finite size and structure? Elastic electron-proton scattering the proton is not a point-like particle but has finite size charge and current distribution in the proton, G E /G M Nobel prize R. Hofstadter : What are the internal constituents of the nucleon? Deeply inelastic scattering discover quarks in scaling of structure function and measure their momentum and spin distributions Nobel prize J. Friedman, H. Kendall, R. Taylor Today: How are the nucleon s charge & current distributions related to the quark momentum & spin distributions?

3 Beyond form factors and quark distributions Generalized Parton Distributions (GPDs) X. Ji, D. Mueller, A. Radyushkin, M. Burkardt, Interpretation in impact parameter space Proton form factors, transverse charge & current densities Correlated quark momentum and helicity distributions in transverse space - GPDs Structure functions, quark longitudinal momentum & helicity distributions

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

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

6 Link to DIS and Elastic Form Factors ),, ( ~, ~,, t x E H E H q q q q ξ [ ] ξ + ξ J G = = 1 1,0), (,0), ( x E x xdx H J q q q Quark angular momentum (Ji s sum rule) X. Ji, Phy.Rev.Lett.78,610(1997) DIS at ξ=t=0 ) ( ), (,0,0) ( ~ ) ( ), (,0,0) ( x q x q x H x q x q x H q q = = Form factors (sum rules) [ ) ( ),, ( ~ ), ( ),, ( ~ ) Dirac f.f. ( ),, (, 1 1, t G t x dx E t G t x dx H t F 1 t x H dx P q q A q q q q = ξ = ξ = ] ξ [ ) Pauli f.f. ( ),, ( 1 t F 2 t x E dx q q = ] ξ

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

8 DVCS Kinematics ep epγ γγ*p plane S y e - ee γ* plane e - γ* Θ γγ γ p φ φ s x z A LU : Beam Longitudinally polarized, Target Unpolarized A UL : Beam Unpolarized, Target Longitudinally polarized A UT : Beam Unpolarized, Target Transversely polarized

9 Accessing GPDs through DVCS GPDs are universal, they can be determined in any suitable 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 DVCS BH BH T BH : given by elastic form factors T DVCS : determined by GPDs DVCS A LU ~ (BH) Im(DVCS) sinφ + h.t. BH-DVCS interference generates beam and target asymmetries that carry the nucleon structure information. DVCS/BH comparable, allows asymmetry, cross section measurements

10 Measuring GPDs through polarization A = σ + σ σ + + σ = σ 2σ Polarized beam, unpolarized target: ~ σ LU ~ sinφim{f 1 H + ξ(f 1 +F 2 )H +kf 2 E}dφ Unpolarized beam, longitudinal target: ~ Kinematically suppressed σ UL ~ sinφim{f 1 H+ξ(F 1 +F 2 )(H +ξ/(1+ξ)e) -.. }dφ H(ξ,t) ξ = x B /(2-x B ) k = t/4m 2 ~ H(ξ,t), H(ξ,t) Unpolarized beam, transverse target: Kinematically suppressed σ UT ~ sinφim{k(f 2 H F 1 E) +.. }dφ H(ξ,t), E(ξ,t) Kinematically suppressed

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

12 DVCS interpreted in pqcd at Q 2 > 1 GeV 2 Pioneering DVCS experiments First GPD analyses of HERA/CLAS/HERMES data in LO/NLO consistent with α ~ A. Freund (2003), A. Belitsky et al. (2003) Full GPD analysis needs high statistics and broad coverage CLAS preliminary A LU E=5.75 GeV A UL = αsinφ + βsin2φ twist-2 twist-3 twist-3 contributions are small <Q 2 > = 2.0GeV 2 <x> = 0.3 <-t> = 0.3GeV 2 φ [rad]

13 Deeply Virtual Exclusive Processes - Kinematics Coverage of the 12 GeV Upgrade overlap with other experiments H1, ZEUS unique to JLab High x B only reachable with high luminosity JLab Upgrade Upgraded JLab has complementary & unique capabilities

14 DVCS/BH- Beam Asymmetry E e = 11 GeV A LU With large acceptance, measure large Q 2, x B, t ranges simultaneously. A(Q 2,x B,t) σ(q 2,x B,t) σ (Q 2,x B,t)

15 CLAS12 - DVCS/BH- Beam Asymmetry E e = 11 GeV Q 2 =5.5GeV 2 x B = t = 0.25 GeV 2

16 CLAS12 - DVCS/BH Beam Asymmetry e p epγ E = 11 GeV σ LU ~sinφim{f 1 H+..}dφ Sensitive to GPD H Selected Kinematics L = 1x10 35 T = 2000 hrs Q 2 = 1 GeV 2 x = 0.05

17 CLAS12 - DVCS/BH Target Asymmetry e p epγ Longitudinally polarized target ~ σ~sinφim{f 1 H+ξ(F 1 +F 2 )H...}dφ E = 11 GeV L = 2x10 35 cm -2 s -1 T = 1000 hrs Q 2 = 1GeV 2 x = 0.05 CLAS preliminary A UL E=5.75 GeV <Q 2 > = 2.0GeV 2 <x> = 0.2 <-t> = 0.25GeV 2

18 CLAS12 - DVCS/BH Target Asymmetry e p epγ E = 11 GeV Sample kinematics Q 2 =2.2 GeV 2, x B = 0.25, -t = 0.5GeV 2 Transverse polarized target σ ~ sinφim{k 1 (F 2 H F 1 E) + }dφ A UTx Target polarized in scattering plane A UTy Target polarized perpedicular to scattering plane Asymmetry highly sensitive to the u-quark contributions to proton spin.

19 From Observables to GPDs Procedures to extract GPDs from experimental data are currently under intense development. Approximations for certain kinematics (small ξ, t), allow extraction of dominant GPDs directly. Fit parametrizations of GPDs to large sets of DVCS/DVMP cross section and SSA data. Constraint by forward parton distribution Polynomiality conditions Elastic form factors Meson distribution amplitudes Partial wave expansion techniques. GPDs are given by sum over t-channel exchanges See: talk by M. Vanderhaeghen

20 GPDs H from expected DVCS A LU data Q 2 =3.5 GeV 2 b val =b sea =1 MRST02 NNLO distribution Other kinematics measured concurrently

21 GPDs Flavor separation DVCS DVMP long. only hard gluon hard vertices Photons cannot separate u/d quark contributions. M = ρ/ω select H, E, for u/d flavors M = π, η, K select H, E

22 Exclusive ep epρ 0 production L CLAS (4.3 GeV) x B =0.38 HERMES (27GeV) W=5.4 GeV Q 2 (GeV 2 ) GPD formalism approximately describes CLAS and HERMES data Q 2 >1.5 GeV 2

23 CLAS12 L/T Separation ep epρ ο (π + π ) x B = t = GeV 2 Projections for 11 GeV (sample kinematics) σ L Other bins measured concurrently σ T

24 Exclusive ρ 0 production on transverse target Α UT = 2 (Im(AB*))/π T Α 2 (1 ξ 2 ) Β 2 (ξ 2 +t/4m 2 ) - Re(ΑΒ )2ξ 2 ρ 0 A~ 2H u + H d B~ 2E u + E d A UT ρ + A~ H u -H d B ~ E u -E d Asymmetry depends linearly on the GPD E, which enters Ji s sum rule. ρ 0 CLAS12 K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 x B

25 3D Images of the Proton s Quark Content M. Burkardt PRD 66, (2002) b - Impact parameter T u(x,b ) T u X (x,b ) transverse polarized target T d X (x,b ) T d(x,b ) T quark flavor polarization Needs: H u E u Accessed in Single Spin Asymmetries. E d H d

26 Transverse Momentum Dependent GPDs (TMDs) TMD W pu (x,k,r) Parent Wigner distributions d 3 r (FT) d 2 k T GPD Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k TMD PDFs: f pu (x,k T ),g 1,f 1T, h 1L GPDs: H pu (x,ξ,t), E pu (x,ξ,t), Measures momentum transfer to quark. d 2 k T ξ=0,t=0 dx Measure momentum transfer to nucleon. PDFs f pu (x), g 1, h 1 FFs F 1pu (t),f 2pu (t)..

27 SIDIS at leading twist e Boer e p Mulders e p Sivers transversity 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)

28 Semi-Inclusive Deep Inelastic Scattering (SIDIS) Main focus of SIDIS studies: Give access to quark distributions weighted by fragmentation function Probes orbital motion of quarks through quark transverse momentum distribution Access to new PFDs not accessible in inclusive DIS. parton distributions at large x (Z.E. Meziani) orbital angular momentum of quarks through SSA in inclusive meson production.

29 Azimuthal Asymmetry Sivers Effect Originates in the quark distribution. It is measured in the azimuthal asymmetry with transverse polarized target. sin(φ φ A UT ~ s ) kf 1T D 1 T f 1T = Requires: non-trivial phase from the FSI + interference between different helicity states (S. Brodsky)

30 SIDIS Azimuthal Asymmetry - Sivers effect sin(φ φ A s ) UT Probes orbital angular momentum of quarks by measuring the imaginary part of s-p-wave interference in the amplitude. Extraction of Sivers function f 1T from asymmetry. T

31 CLAS12 - Sivers function from A UT (π 0 ) In large Nc limit: f 1T u = -f 1T d F 1T =1/2 q e q2 f 1T q Efremov et al (large x B behavior of f 1T from GPD E) CLAS12 projected CLAS12 projected x B x B Sivers function extraction from A UT (π 0 ) does not require information on fragmentation function. It is free of HT and diffractive contributions. A UT (π 0 ) on proton and neutron will allow flavor decomposition w/o info on FF.

32 Azimuthal Asymmetry - Collins Effect h 1 = sin(φ+φ σ UT ~ s ) k h 1 H 1 T Access to transversity distribution and fragmentation of polarized quarks.

33 Collins Effect and Kotzinian-Mulders Asymmetry KM σ UL ~ k h 1L H 1 T T Measures the Collins fragmentation with longitudinally polarized target. Access to the real part of s-p wave interference amplitudes.

34 What can be achieved in the first five years? Precision measurements of DVCS/BH and DVMP, beam asymmetry, target asymmetries, and cross section differences in kinematics Q 2 = GeV 2, x B = , -t = GeV 2 Precision measurements of beam and target asymmetries for π +,π,π 0 in current fragmentation region and SIDIS kinematics Determine GPDs H(ξ,ξ,t), H(ξ,ξ,t), E(ξ,ξ,t) Flavor separated E u/d, H u/d from ρ 0, ρ + production Probe the orbital motion of quarks in the nucleon through spin asymmetries. Precision measurement of the Sivers distribution function. Determine transversity in a variety of channels. Confront moments of GPDs with Lattice QCD calculations

35 CLAS12 Large angle coverage, High luminosity, cm -2 s -1 Concurrent measurement of deeply virtual exclusive, semi-inclusive, and inclusive processes, for same target, polarized or unpolarized. The CLAS upgrade is essential to the physics mission of the 12 GeV Upgrade. (PAC27, January 2005)

36 Summary A program to study the nucleon Generalized Parton Distributions has been developed for the CEBAF 12 GeV upgrade covering a broad range of kinematics and reactions. This program will provide fundamentally new insights into the internal quark dynamics through the measurement of polarization observables of exclusive and semi-inclusive deep inelastic processes. It will determine: quark orbital angular momentum contributions to the proton spin, quark flavor contributions to the spin sum rule, quark flavor polarization in polarized nucleons, recently discovered new quark distribution functions, and project 3D images of the nucleon in the infinite momentum frame.

37 The program of Deeply Exclusive and Semi- Inclusive Experiments at the JLab 12 GeV Upgrade constitutes the next step in the breakthrough experiments to study the internal nucleon structure at a deeper level. It has the potential to revolutionize hadronic physics with electromagnetic probes.