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Decoding Nucleon Spin: Journey through Quark Tomography

Explore the cutting-edge research on nucleon spin structure using state-of-the-art techniques and theoretical frameworks. Delve into the complexities of quark and gluon interactions at various energy scales, shedding light on the fundamental aspects of Quantum Chromodynamics (QCD). Unravel the mysteries of nucleon tomography and the role of transverse momentum-dependent parton distributions in understanding the inner workings of protons and neutrons. Stay updated with the latest developments in the field, from experimental probes to theoretical calculations, paving the way for a deeper understanding of subatomic physics.

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Decoding Nucleon Spin: Journey through Quark Tomography

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  1. Nucleon Spin: Final Solution at the EIC Feng Yuan Lawrence Berkeley National Laboratory

  2. Next Big Thing in QCD

  3. References: • INT-Write-Up, “Gluons and the quark sea at high energies: distributions, polarization, tomography”, 500 pages, e-Print: arXiv:1108.1713 [nucl-th]. • EIC-White Paper, “Electron-Ion Collider: Next QCD Frontier”,150 pages, e-Print: arXiv:1212.1701 [nucl-ex]

  4. Clay Mathematics Institute Millennium Prize Problem QCD and Strong-Interactions • QCD: Non-Abelian gauge theory • Building blocks: quarks (spin ½, mq, 3 colors; gluons: spin 1, massless, 32-1 colors) • Asymptotic freedom and confinement Short distance hard, perturbative Long distance:? Soft, non-perturbative ~1/Length Nonperturbative scale QCD~1GeV

  5. Understanding the nucleon • Solving QCD • Numeric simulation: Lattice QCD BMW, Science, 2008 LHPC, 2011

  6. Understanding the nucleon • Experimental probes • Study the quark and gluon structure through low and high-energy scattering • Matrix elements of local operators (e.g., form factors) or operators on the light-cone (parton distributions) • High energy experiments • perturbative QCD, factorization, universality • Sum rules: • Momentum • Bjorken • Nucleon spin • …

  7. Deep Inelastic Scattering Friedman Kendall Taylor Bjorken Scaling: Q2Infinity Feynman Parton Model: Point-like structure in Nucleon

  8. In particular • DIS (Virtual Photon Q>>∧QCD) Leading Born Diagram P • Higher Order Corrections: • Gluon Momentum (divergence) • Collinear: xP, x-finite • Soft: xP+kt, x-small

  9. Factorization is essential to study nucleon structure • Universality of the parton distributions • Predictive power of QCD Collins-Soper-Sterman 85, Bodwin 85, … Ji-Ma-Yuan 04, Dominguez-Xiao-Yuan 10,…

  10. EIC Proposals in US

  11. Basics • Inclusive DIS • Parton distributions • Semi-inclusive DIS, measure additional hadron in final state • Kt-dependence • Exclusive Processes, measure recoiled nucleon • Nucleon tomography • Parity violating process Luminosity requirement

  12. Big questions

  13. QCD Phase structure of cold nuclei • kt-dependence crucial to the saturation

  14. Comprehensive study of small-x saturation at the EIC Inclusive observable Two-particle correlations xiao@EIC-Whitepaper

  15. Diffractions

  16. Hadronization in cold nuclei vs hot matter

  17. Intensity Frontier (EW Physics) √S = 140GeV, 200fb-1

  18. Ultimate goal of spin physics? • Spin sum rule Jaffe-Manohar, 90 Ji, 96 Quark spin, Best known Gluon spin, Start to know Orbital Angular Momentum of quarks and gluons, Little known

  19. EMC experiment at CERN • Polarized muon + p deep inelastic scattering, • Virtual photon can only couple to quarks with opposite spin, because of angular momentum conservation • Select q+(x) or q-(x) by changing the spin direction of the nucleon or the incident lepton • The polarized structure function measures the quark spin density

  20. Summary of the polarized DIS data

  21. EIC kinematics

  22. Back to DIS With EIC

  23. In particular

  24. gluon spin Quark spin x2

  25. Where is the rest of spin • Back to the angular momentum density • Energy-momentum tensors in quark and gluon

  26. Spin sum rule Ji, 1996 • Taking forward limit,

  27. Q2 t ( H + E) x dx =Jq Quark OAM: Lq = 1/2 DS+ Lz (Ji 96) Generalized Parton Distributions in hard exclusive processes: • A new type of parton “distributions” contains much more information • Comprehensive program at JLab,HERMES,COMPASS and future EIC Mueller et al.,94;Ji,96; Radyushkin,96

  28. Extract the GPDs • The theoretical framework has been well established • Perturbative QCD corrections at NLO, some at NNLO Mueller, et al., 1310.5394 Ju, Jd, Jg

  29. EIC kinematics coverage

  30. Further decomposition of Jq • Quark spin explicitly • OAM, twist-three nature Ji, Xiong, Yuan, PRL109, 152005 (2012); PRD 13; Hatta, Yoshita, JHEP 2012; Liuti, et al., 1310.5157

  31. Related to the parton’s phase space Wigner Distributions Phase space distribution: Projection onto p (x) to get the momentum (probability) density Quark orbital angular momentum Well defined in QCD: Ji, Xiong, Yuan, PRL, 2012; PRD, 2013 Lorce, Pasquini, Xiong, Yuan, PRD, 2012

  32. Quark imaging from EIC Mueller, et al., 1304.0077

  33. Gluon Tomography toward small-x

  34. Nucleon tomography

  35. Transverse momentum dependent parton distribution • Straightforward extension • Spin average, helicity, and transversity distributions • PT-spin correlations • Nontrivial distributions, STXPT • In quark model, depends on S- and P-wave interference

  36. Alex Prokudin @EIC-Whitepaper Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane

  37. Where can we learn TMDs • Semi-inclusive hadron production in deep inelastic scattering (SIDIS) • Drell-Yan lepton pair, photon pair productions in pp scattering • Dijet correlation in DIS • Relevant e+e- annihilation processes • …

  38. Semi-inclusive DIS • Novel Single Spin Asymmetries Collins: U: unpolarized beam T: transversely polarized target Sivers:

  39. EIC kinematics

  40. Precision of 3-D PDFs at EIC

  41. all order factorization Similar calculations for pp collisions: Zhu HX, et al., PRL110 (2013) 082001

  42. Conclusions: EIC • Great opportunities in nuclear science • Ultimate machine for nucleon spin physics • Unique place to investigate gluon saturation • Potential discovery in BSM physics

  43. TMDs in valence region Alex Prokudin @EIC-Whitepaper Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane

  44. Current Research Focused on QCD: Factorization, Universality, Evolution, Lattice, … Nucleon Spin Long. Momentum distributions 3D imaging Transverse-momentum-dependent and Generalized PDFs

  45. Access the GPDs • Deeply virtual Compton Scattering (DVCS) and deeply virtual exclusive meson production (DVEM) GPD In the Bjorken limit: Q2>>(-t),∧2QCD,M2 Mueller, et al., hep-ph/0112108, 1310.5394

  46. Nucleon tomography and Orbital angular momentum Coordinate BT Momentum PT Factorization: Ji-Ma-Yuan 2004

  47. 1310.0461

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