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Transverse Partonic Structure of the Proton

Transverse Partonic Structure of the Proton. Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory. Transverse spin physics. RHIC. RHIC. Bunce, Lambda. E704, pp to Pi. JLab. COMPASS. HERMES. …. BELLE. BHS. Factorization. unify. (non)Universality.

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Transverse Partonic Structure of the Proton

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  1. Transverse Partonic Structure of the Proton Feng Yuan Lawrence Berkeley National Laboratory RBRC, Brookhaven National Laboratory

  2. Transverse spin physics RHIC RHIC Bunce,Lambda E704,pp to Pi JLab COMPASS HERMES … BELLE BHS Factorization unify (non)Universality Efremove-Teryav CSS Sivers Jaffe-Ji Collins Mulders et al. Ralston-Soper Collins-Soper Collins Qiu-Sterman BJY

  3. Transverse spin physics • Goal • Quark transversity distributions • Orbital motion of quarks and gluons? • Transverse partonic structure of proton • Various transverse momentum dependent physics (additional information on nucleon structure) • Sivers function (PDF) • Collins function (FF) • …

  4. Transverse Momentum Dependent Parton Distributions • Nucleon Structure, connection to GPDs, quantum phase space distribution • Single spin asymmetry phenomena • Nontrivial QCD dynamics, and fundamental test of the factorization, and the universality of PDFs, FFs,…

  5. Connection between TMD and GPD • Wigner distributions After integrating over r, one gets TMD After integrating over k, one gets Fourier transform of GPDs Ji: PRL91,062001(2003)

  6. 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(k,r) “Mother” Wigner distributions d3r d2kT dr|| GPDs Hpu(x,x,t), GDAs Fudp+(x,x) FT TMD PDFs fpu(x,kT), TMD FFs Dup+(kT,z) IPDs Wpu(x,rT),… x=0 GPD d2r x=0,t=0 dx d2kT 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),… FFs Dup+(z) Some PDFs same in exclusive and semi-inclusive analysis H.Avakian, Nov 19, 2004

  7. TMD Distribution: the definition Gauge Invariance requires the Gauge Link Brodsky,Hwang,Schmidt 02’ Collins 02’ Belitsky,Ji,Yuan 02’ Boer,Mulders,Pijlman, 03’

  8. Polarized TMD Quark Distributions Nucleon Unpol. Long. Trans. Quark Unpol. Long. Trans. Boer, Mulders, Tangerman (96&98)

  9. Three classes in the view of a quark model • S-wave • Unpolarized, helicity, transversity • S-P interference • g_1T,h_1L • f_1T^\perp, h_1^\perp • P-P or S-D interference • h_1T^\perp • Miller 07, Burkardt 07, Avakian et al 08. EIC Meeting 2008

  10. Lz≠0 Amplitude and Sivers Function • All distributions can be calculated using the wave function. Sivers function: • Similar expressions for others Lz=1 Lz=0 Ji, Ma, Yuan, Nucl. Phys. B (2003)

  11. Where can we learn TMDs • Semi-inclusive hadron production in deep inelastic scattering (SIDIS) • Drell-Yan lepton pair production in pp scattering • Relevant e+e- annihilation processes • Many others… EIC Meeting 2008

  12. Inclusive and Semi-inclusive DIS Inclusive DIS: Partonic Distribution depending on the longitudinal momentum fraction Q Semi-inclusive DIS: Probe additional information for partons’ transverse distribution in nucleon Q

  13. Azimuthal Dependence in SIDIS • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations

  14. SIDIS Cross Section At leading power of 1/Q The structure functions depend on Q2, xB, z, PhT

  15. ST kT Two major contributions • Sivers effect in the distribution • Collins effect in the fragmentation • Other contributions… ST (PXkT) P (zk+pT) (k,sT) ~pTXsT

  16. Universality of the Collins Fragmentation

  17. Collins effects in e+e- • Reliable place to extract the information on the Collins fragmentation function Belle Col., PRL 06

  18. Collins asymmetry in pp collisions Collins Fragmentation function Quark transversity distribution FY, arXiv:0709.3272 [hep-ph]

  19. e+e- annihilation Semi-inclusive DIS Hadron in a jet in pp Simple model a la Collins 93 Phase information in the vertex or the quark propagator Collins-93 Universality of the Collins Function!!

  20. One-gluon exchange (gauge link)? Metz 02, Collins-Metz 02: Gamberg-Mukherjee-Mulders, 08 Universality of the Collins function!!

  21. By using the Ward Identity: same Collins fun. Similar arguments for pp collisions Conjecture: the Collins function will be the same as e^+e^- and SIDIS

  22. Key observations • Final state interactions DO NOT provide a phase for a nonzero SSA • Eikonal propagators DO NOT contribute to a pole • Ward identity is applicable to warrant the universality arguments

  23. Sivers effect is different • It is the final state interaction providing the phase to a nonzero SSA • Ward identity is not easy to apply • Non-universality in general • Only in special case, we have “Special Universality”

  24. DIS and Drell-Yan • Initial state vs. final state interactions • “Universality”: fundamental QCD prediction * * DIS Drell-Yan HERMES

  25. Experiment SIDIS vs Drell Yan HERMES Sivers Results RHIC II Drell Yan Projections 0 Markus Diefenthaler DIS Workshop Munich, April 2007 0 0.1 0.2 0.3 x http://spin.riken.bnl.gov/rsc/

  26. Study QCD dynamics at different PT Region • Integrate out PT (w/o weight) -- normal factorization, similar to inclusive DIS • Large PT (>>QCD) -- hard gluon radiation, can be calculated from perturbative QCD • Low PT (~QCD) -- nonperturbative information: TMD factorization formula

  27. A unified picture for SSA • In DIS and Drell-Yan processes, SSA depends on Q and transverse-momentum P • At large P, SSA is dominated by twist-3 correlation effects • At moderate P, SSA is dominated by the transverse-momentum-dependent parton distribution/fragmentation functions • The two mechanisms at intermediate P generate the same physics! Ji-Qiu-Vogelsang-Yuan,Phys.Rev.Lett.97:082002,2006

  28. A difficulty at next-leading-power (1/Q) • Mismatch at low and high transverse momentum SIDIS at 1/Q • Bacchetta-Boer-Diehl-Mulders, 0803.0227 • The factorization needs to be carefully examined at this order • Earlier works indicates possible problems • Afanasev-Carlson, PRD, 2006 • Gamberg-Hwang-Metz-Schlegel, PLB, 2006

  29. Final PT Distribution • PT dependence • Which is valid for all Pt range • SSA is suppressed by 1/Pt at large Pt Sivers function at low Pt Qiu-Sterman Twist-three

  30. Extend to all other TMDs: large Pt power counting • kt-even distributions have the same dependence on kt • kt-odd distributions are suppressed at large kt • Power Counting Rule kt-even: 1/kt2 kt-odd: 1/kt4

  31. SIDIS cross sections at large Pt 1/Pt2 1/Pt4 1/Pt3 1/Pt5

  32. Transition from Perturbative region to Nonperturbative region? • Compare different region of PT Nonperturbative TMD Perturbative region

  33. pp scattering experiments • RHIC and RHIC II • Collins effects, quark transversity • Drell-Yan, quark Sivers • Heavy flavor, gluon Sivers • JPARC (pp collision at low energy) • Drell-Yan, quark Sivers effects • GSI-FAIR (ppbar collision) • Drell-Yan, quark transversity • Quark Sivers effects

  34. Summary • We are in the early stages of a very exciting era of transverse spin physics studies, where the future JLAB, RHIC, and EIC experiments will certainly play very important roles • We will learn more about QCD dynamics and nucleon structure from these studies, especially for the quark orbital motion • More work needs to be done

  35. y • Quark distribution is deformed when nucleon is transversely polarized, because of the orbital motion • This deformation will lead to a single transverse spin asymmetry (SSA), because of final state interactions Burkardt, 2003 x y z

  36. Semi-Inclusive DIS • Transverse Momentum Dependent (TMD) Parton Distributions and Fragmentations • Novel Single Spin Asymmetries U: unpolarized beam T: transversely polarized target

  37. What’s Single spin asymmetry? Transverse plane Final state particle is Azimuthal symmetric Single Transverse Spin Asymmetry (SSA)

  38. SSAs in Modern era : RHIC, JLab, HERMES, … STAR Central rapidity!! BRAHMS Large SSA continues at DIS ep and collider pp experiments!!

  39. Naïve parton model fails • If the underlying scattering mechanism is hard, the naïve parton model generates a very small SSA: (G. Kane et al, 1978), • It is in general suppressed byαSmq/Q • We have to go beyond this naïve picture

  40. ST kT Two mechanisms in QCD • Spin-dependent transverse momentum dependent (TMD) function • Sivers 90 • Brodsky,Hwang,Schmidt, 02 (FSI) • Gauge Property: Collins 02;Belitsky-Ji-Yuan,NPB03 Boer-Mulders-Pijlman,03 • Factorization: Ji-Ma-Yuan,PRD04;Collins,Metz,04 • Twist-3 quark-gluon correlations (coll.) • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98 Sivers function ~ ST (PXkT) . P

  41. What can we learn from SSA • Quark Orbital Angular Momentum e.g, Sivers function ~ the wave function amplitude with nonzero orbital angular momentum! Vanishes if quarks only in s-state! Ji-Ma-Yuan, NPB03 Brodsky-Yuan, PRD06

  42. Take Drell-Yan as an example(with non-zero transverse momentum q?) • We need a loop to generate a phase + + + + - - + + • Twist-three Correlations • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98 Kane et al., hard parton model

  43. Further factorization (q?<<Q) • The collinear gluons dominate q?<<Q • Transverse Momentum Dependent distributions • Sivers, 90, Collins, 93,02 • Brodsky-Hwang-Schmidt,02 • Ji-Qiu-Vogelsang-Yuan,06 • Twist-three Correlations • Efremov-Teryaev, 82, 84 • Qiu-Sterman, 91,98

  44. Quantum Phase Space Distribution • Wigner operator • Wigner distribution: “density” for quarks having position r and 4-momentum k(off-shell) a la Saches 7-dimensional distribtuion No known experiment can measure this!

  45. Custom-made for high-energy processes • In high-energy processes, one cannot measure k= (k0–kz) and therefore, one must integrate this out. • The reduced Wigner distribution is a function of six variables [r,k=(k+k)]. • After integrating over r, one gets transverse-momentum dependent parton distributions • Alternatively, after integrating over k, one gets a spatial distribution of quarks with fixed Feynman momentum k+=(k0+kz)=xM.

  46. Collins from HERMES • Large, positive p+ asymmetries: no surprise from u-quark dominance • Large, negative p- asymmetries: first a surprise, now understood by large, negative disfavored Collins function

  47. Collins from COMPASS • Smaller asymmetries than in proton case PRL 94, 202002 (2005) and Nucl.Phys.B765:31-70,2007

  48. First extraction of Collins functions and transversity distributions from fitting HERMES + COMPASS + BELLE data By Anselmino et al., PRD 75 (07)

  49. Comparison with some models [1] Soffer et al. PRD 65 (02) [2] Korotkov et al. EPJC 18 (01) [3] Schweitzer et al., PRD 64 (01) [4] Wakamatsu, PLB 509 (01) [5] Pasquini et al., PRD 72 (05) [6] Anselmino et al., PRD 75 (07)

  50. Non-universality: Dijet-correlation at RHIC • Proposed by Boer-Vogelsang • Pheno. studies: Vogelsang-Yuan 05; Bomhof-Mulders-Vogelsang-Yuan 07 • Initial state and/or final state interactions? • Bacchetta-Bomhof-Mulders-Pijlman: hep-ph/0406099, hep-ph/0505268, hep-ph/0601171, hep-ph/0609206 • Qiu-Vogelsang-Yuan, arXiv:0704.1153; 0706.1196 • Collins-Qiu, arXiv:0705.2141  • Voglesang-Yuan, arXiv:0708.4398 • Collins, arXiv:0708.4410 • Bomhof-Mulders, arXiv:0709.1390 • Factorization? Universality?

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