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Outline. Introductory Remarks Major areas of nucleon structure investigations with 12 GeV upgrade Conclusion. Introduction. Nucleons are the basic building blocks of atomic nuclei.

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Outline

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  1. Outline • Introductory Remarks • Major areas of nucleon structure investigations with 12 GeV upgrade • Conclusion

  2. Introduction • Nucleons are the basic building blocks of atomic nuclei. • Their internal structure, arising from the underlying quark and gluon constituents, determines their mass, spin, and interactions. • These, in turn, determine the fundamental properties of the nuclei and atoms. • Nucleon physics represents one of the most important frontiers in modern nuclear physics.

  3. The Two Traditional Observables • Elastic Form Factors • Low Q: charge and current distributions. High Q: light-cone parton distribution amplitudes, underlying pQCD reaction mechanism, • Starting from Hofstadter’s work in 1950’s • Well-measured for some, not so for others • Neutron form factors • Large Q2 • …

  4. The Two Traditional Observables • Feynman Parton Distributions • Distributions of quarks in momentum space. • Starting from Freedman, Kendall and Taylor’s DIS experiments at SLAC • Well-measured in some kinematics. But some key aspects are missing • Parton distributions as x1 • Spin-flavor dependence • …

  5. 12 GeV Kinematic Coverage

  6. Three Major Areas of Nucleon Structure Studies With 12 GeV • Major New Direction: 3D mapping of the quark structure of the nucleon • Comprehensive Study of nucleon spin structure (also Avakian’s talk) • Definitive Investigation of quarks at highest x, resonances, duality, and higher twists.

  7. A Major New Direction:3D Quark and Gluon Structure of the Nucleon

  8. GPDs • Detailed mapping of the structure of the nucleon using the Generalized Parton Distributions (GPDs) A proton matrix element which is a hybrid of elastic form factor and Feynman distribution J(x): bilocal quark operator along light-cone

  9. x1P x2P' P' P A Cartoon for the GPD x: average fraction of the longitudinal momentum carried by parton, just like in the Feynman parton dis. t=(p’-p)2: t-channel momentum transfer squared, like in form factor ξ: skewness parameter ~ x1-x2 Recent Review: M. Diehl, Phys. Rep. 388, 41 (2003)

  10. Physical Meaning of GPDs at ξ=0 • Form factors can be related to charge densities in the 2D transverse plane in the infinite-momentum frame • Feynman parton distribution is a quark density in the longitudinal momentum x, • The Fourier transformation of a GPD H(x,t, ξ=0) give the density of quarks in the “combined” 2+1 space! by bx

  11. Mixed Coordinate and Momentum “3D” Picture • Longitudinal Feynman momentum x + Transverse-plane coordinates b = (bx,by) b A 3D nucleon

  12. by bx Tomographic Pictures From Slicing the x-Coordinates (Burkardt) x 0.1 0.3 0.5 up down

  13. Physical meaning of GPDs: Wigner function • For one-dim quantum system, Wigner function is • When integrated over x (p), one gets the momentum (probability) density. • Not positive definite in general, but is in classical limit. • Any dynamical variable can be calculated as Short of measuring the wave function, the Wigner function contains the most complete (one-body) info about a quantum system.

  14. Simple Harmonic Oscillator N=5 N=0 Husimi distribution: positive definite!

  15. Quark Wigner Distributions • Functions of quark position r, and its Feynman momentum x. • Related to generalized parton distributions through t= – q2  ~ qz

  16. Phase-Space Charge Density and Current • Quark charge density at fixed Feynman x • Quark current at fixed Feynman x in a spinning nucleon (spinning around the spatial x-direction) * Quark angular momentum sum rule:

  17. Imaging quarks at fixed Feynman-x • For every choice of x, one can use the Wigner distributions to picture the nucleon in 3-space; This is analogous to viewing the proton through the x (momentum) filters! z by bx

  18. How to Measure GPDs • Deep exclusive processes: Deeply-exclusive meson production Deeply-virtual Compton scattering

  19. What 12 GeV can do • The first machine in the world capable of studying these novel exclusive processes in a comprehensive way • High luminosity! • Large acceptance! • What do we need? small t, large x-range, high Q2 12 GeV upgrade will deliver these!

  20. What one can measure (also V. Burkert’s talk) • Beam spin asymmetry, longitudinal and transverse single target-spin asymmetries for DVCS and meson production (measuring imaginary part of the amplitudes, x= ξ) • Separation of different GPDs (E, H, H-tilde, etc.) • Absolute cross section measurements (get real part of Compton amplitude (principal value)) • Exploration of double DVCS process to map x and ξ independently. • …

  21. e p epg L = 2x1035 T = 1000 hrs DQ2 = 1 GeV2 Dx = 0.05 CLAS12-DVCS/BH Beam Asymmetry E = 11 GeV Selected Kinematics

  22. CLAS12-DVCS/BH Target Asymmetry E = 11 GeV Selected Kinematics Longitudinal polarized target L = 1x1035 T = 1000 hrs DQ2 = 1GeV2 Dx = 0.05

  23. Spin-dependent DVCS Cross Section Leading twist Twist-3/Twist-2

  24. Rho production to measure the fraction of quark angular momentum

  25. From observables to GPDs • Direct extraction GPDs from cross sections and asymmetries at certain kinematics. • Global fits with parameterizations. • Partial wave analysis (expand in a certain basis) • Lattice QCD calculations can provide additional constraints. • Effective field theory (large Nc and chiral dynamics) constraints • Phenomenological models

  26. GPD Constraints from Form Factors • The first moments of GPDs are related to electroweak form factors. • Compton form factors Measurable from large angle Compton scattering

  27. Why one needs high-t form factors • High resolution for quark distributions in impact parameter space • Testing pQCD predictions, • helicity conservation • mechanisms for high-t reactions (soft vs. hard reaction mechanisms) • 12 GeV capabilities • proton charge FF ~ 14 GeV2 • neutron magnetic FF ~ 14 GeV2 • neutron electric FF ~ 8 GeV2 • Compton FF: s ~ 20 GeV2, t ~ 17 GeV2

  28. Proton Form Factors with 12 GeV upgrade

  29. Neutron and Pion Form Factors Testing pQCD calculations

  30. Nucleon-Delta Transition From Factors

  31. Compton form factor at 12 GeV

  32. A Comprehensive Study of the Nucleon Spin Structure (see also Avakian’s talk)

  33. Spin Structure of the Nucleon • The spin was thought to be carried by the spin of the three valence quarks • Polarized deep-inelastic scattering found that only 20-30% are in these. • A host of new questions: • Flavor-dependence in quark helicity distributions? Polarization in sea quarks? • Transversity distributions? • Transverse-momentum-dependent (TMD) parton distributions(Single spin asymmetry and T-odd distributions, Collins and Sivers functions) • Orbital angular momentum of the quarks?

  34. Semi-Inclusive Deep Inelastic Scattering • Has been explored at Hermes and other expts with limited statistics • Jlab 12 GeV could make the definitive contribution! (Avakian’s talk) • Measuring mostly meson (pion, kaon) production • longitudinal momentum fractionz • transverse momentump~ few hundred MeV TMD parton distributions

  35. Quantum Phase-Space Distributions of Quarks Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k Wpu(x,kT,r) “Mother” Wigner distributions d3r d2kT (FT) GPD TMD PDFs: fpu(x,kT),… GPDs: Hpu(x,x,t), … d2kT x=0,t=0 dx Measure momentum transfer to target Direct info about spatial distributions Measure momentum transfer to quark Direct info about momentum distributions Form Factors F1pu(t),F2pu(t ).. PDFs fpu(x),…

  36. Inclusive measurement: g2 structure function

  37. Inclusive Measurements: Quark helicity at large x

  38. A Definitive Investigation of Quarks at Highest x, Resonances, Duality and Higher twists

  39. Parton Distributions at large x • Large-x quark distribution directly probes the valence quark configurations. • Better described, we hope, by quark models. • Standard SU(6) spin-flavor symmetry predictions • Rnp = Fn/Fp=2/3, Ap = g/F=5/9, An=0 • Symmetry breaking (seen in parton distribution at x>0.4) • One-gluon (or pion) exchange  higher effective mass for vector diquark. Rnp = ¼, Ap=An = 1 • Instanton effects? Ap = – 1, An = 0

  40. Perturbative QCD prediction at large x • Perturbative QCD prediction q(x) ~ (1-x)3 Farrar and Jackson, 1975 the coefficient, however, is infrared divergent! • The parton distribution at x1 exhibits the following factorization • Total di-quark helicity zero. Rnp3/7 Ap & An -> 1.

  41. Why is large-x perturbative? Example: Pion • Leading-order diagram contributing to parton distribution at large x As x->1, the virtuality of these lines goes to infinity Farrar & Jackson On-shell quark with longitudinal momentum 1-x

  42. Lattice QCD calculations • Parton structure of the nucleon can best be studied through first-principle, lattice QCD calculations of their moments. • Mellin moments emphasize large x-parton distributions 1 Weighting in forming moments x x5 x2 x3 x4 0 0.6 1

  43. Large-x Distributions are hard to access experimentally • Low rates, because parton distributions fall quickly there • need high luminosity • No free neutron target: • Nuclear effects are important at large x • Scaling?(duality)

  44. What 12 GeV Upgrade Can Do • Tag neutron through measuring spectator proton • DIS from A=3 mirror nuclei

  45. Duality and Resonances • As x->1 the scaling sets in later and later in Q, as the final-state invariant mass is W2 = M2 + Q2(1-x)/x • Resonance production is dominant! • However, the resonance behaviors are not arbitrary. Taken together, they reflect, on an average sense, the physics of quark and gluons => (global) parton-hadron duality. • Studied quantitatively at Jlab 6 GeV.

  46. Extended exploration at 12 GeV • What 12 GeV can do • Separation of L/T responses • Duality in spin observables? • Duality in semi-inclusive processes? • What is duality good for? • Accessing the otherwise inaccessible • Resonances partons, as in QCD sum rules, • Exploring limitations of QCD factorizations • Studying quark-gluon correlations and higher-twists

  47. Parton Distributions at large x from Duality • Examples

  48. Duality allows precise extraction of higher-twists • Higher-twist matrix elements encode quark-gluon correlations. • They are related to the deviation of the average resonance properties from the parton physics, and mostly reside at large-x. • Studies of resonances and duality allow precision extraction of higher-twist matrix elements.

  49. Conclusion • The Jlab 12 GeV upgrade will support a great leap forward in our knowledge of hadron structure through major programs in three areas: • Generalized parton distribution and 3D structure of the nucleon. • Spin structure of the nucleon via semi-inclusive DIS processes. • Parton, resonance, and duality physics at large-x. • And

  50. Let’s DO IT!

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