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Outline

This paper discusses the investigation of nucleon structure using the 12 GeV upgrade, focusing on areas such as elastic form factors and Feynman parton distributions. It also explores the potential of measuring generalized parton distributions (GPDs) and the importance of deep exclusive processes. The 12 GeV upgrade offers the opportunity for comprehensive studies in this field.

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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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