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Transversity and Transverse-Momentum-Dependent Partonic Functions

Transversity and Transverse-Momentum-Dependent Partonic Functions. Alessandro Bacchetta. Outline. Theoretical framework Transversity Sivers function Boer-Mulders function. Theoretical framework. Semi-inclusive Deep Inelastic Scattering. proton. lepton. pion.

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Transversity and Transverse-Momentum-Dependent Partonic Functions

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  1. Transversity andTransverse-Momentum-Dependent Partonic Functions Alessandro Bacchetta

  2. Outline • Theoretical framework • Transversity • Sivers function • Boer-Mulders function Alessandro Bacchetta - Transverse-momentum-dependent functions

  3. Theoretical framework

  4. Semi-inclusive Deep Inelastic Scattering proton lepton pion Alessandro Bacchetta - Transverse-momentum-dependent functions

  5. Partonic scattering amplitude Fragmentation amplitude Distribution amplitude Feynman diagrams & Factorization lepton lepton proton pion SIDIS Alessandro Bacchetta - Transverse-momentum-dependent functions

  6. proton lepton proton antilepton Drell-Yan electron pion Partonic scattering amplitude Fragmentation amplitude positron pion Distribution amplitude e–e+ to pions Feynman diagrams & Factorization lepton lepton proton pion SIDIS Alessandro Bacchetta - Transverse-momentum-dependent functions

  7. proton lepton proton antilepton Drell-Yan electron pion positron pion e–e+ to pions Feynman diagrams & Factorization lepton lepton proton pion SIDIS proton pion proton pion p-p to pions Alessandro Bacchetta - Transverse-momentum-dependent functions

  8. Factorization proofs Factorization proofs for involving TMD functions LEADING TWIST (1/Q0), NOT for pp to pions • Collins, Soper, NPB 193 (81) • Ji, Ma, Yuan, PRD 71 (04) • Ji, Ma, Yuan, PLB 597 (04) • Collins, Metz, PRL 93 (04) See talk by A. Metz Alessandro Bacchetta - Transverse-momentum-dependent functions

  9. = Nonperturbative elements 2 Alessandro Bacchetta - Transverse-momentum-dependent functions

  10. ... ... Origin of the gauge link Alessandro Bacchetta - Transverse-momentum-dependent functions

  11. Drell-Yan pp to hadrons Bacchetta, Bomhof, Mulders, Pijlman, hep-ph/0505268 Different processes SIDIS See talk by C. Bomhof Alessandro Bacchetta - Transverse-momentum-dependent functions

  12. The correlation functionintegrated over kT x- axis 0 a SIDIS Alessandro Bacchetta - Transverse-momentum-dependent functions

  13. The correlation functionintegrated over kT 0 a x- axis Drell-Yan Alessandro Bacchetta - Transverse-momentum-dependent functions

  14. The correlation functionUNintegrated over kT a xT 0 x- axis SIDIS Belitsky, Ji, Yuan, NPB656 (03) Alessandro Bacchetta - Transverse-momentum-dependent functions

  15. xT x- axis The correlation functionUNintegrated over kT a 0 Drell-Yan Ji, Yuan, PLB 543 (02); Belitsky, Ji, Yuan, NPB656 (03) Alessandro Bacchetta - Transverse-momentum-dependent functions

  16. Practical consequences • Some TMD functions will not be sensitive to the differences in the structure of the gauge link (i.e. they will be connected to standard partonic cross-sections) • Some TMD functions will be sensitive to it and will be multiplied by prefactors to be computed for each partonic subprocess (i.e. they will be connected to gluonic-pole cross-sections) See talk by C. Bomhof Alessandro Bacchetta - Transverse-momentum-dependent functions

  17. Decomposition of the correlation function integrated over kT Leading twist only Unpolarized distr. func. Helicity distr. func. Transversity distr. func. Alessandro Bacchetta - Transverse-momentum-dependent functions

  18. Sivers Boer-Mulders Decomposition of the correlation function UNintegrated over kT Mulders, Tangerman, NPB 461 (96) Goeke, Metz, Schlegel, PLB 618 (05) Sivers, PRD 43 (91) Boer, Mulders, PRD 57 (98) Alessandro Bacchetta - Transverse-momentum-dependent functions

  19. - Sivers Boer-Mulders - - Transversity Parton distribution functions with transverse spin Photon moves into the screen/ proton moves out of the screen Alessandro Bacchetta - Transverse-momentum-dependent functions

  20. Transversity

  21. Notation of Anselmino et al. - Definition of transversity distribution function Probability to find a quark with momentum xP+ and transverse spin sqin a proton with transverse spin S NOTE: transverse momentum is integrated over! Alessandro Bacchetta - Transverse-momentum-dependent functions

  22. Transversity: birth and growth Ralston, Soper, NPB 152 (79) Alessandro Bacchetta - Transverse-momentum-dependent functions

  23. Helicity and transversity         Alessandro Bacchetta - Transverse-momentum-dependent functions

  24. Transversity vs helicity • Different evolution g1 h1@ 0.079 GeV2 g1 h1@ 0.75 GeV2 S. Scopetta, V. Vento,PLB 424 (1997) Alessandro Bacchetta - Transverse-momentum-dependent functions

  25. Transversity vs helicity • Different evolution • Different integrals (axial and tensor charge of the nucleon). E.g. from lattice QCD: S. Aoki et al., PRD 56 (1997) M. Göckeler et al. [QCDSF/UKQCD], PLB (05) Alessandro Bacchetta - Transverse-momentum-dependent functions

  26. Transversity vs helicity • Different evolution • Different integrals (axial and tensor charge of the nucleon). E.g. from lattice QCD: • Different sum-rules Bakker, Leader, Trueman, PRD 70 (04) S. Aoki et al., PRD 56 (1997) M. Göckeler et al. [QCDSF/UKQCD], PLB (05) Alessandro Bacchetta - Transverse-momentum-dependent functions

  27. Comparison of tensor charges c quark spectator non-relativistic lattice bag c quark soliton 2 c quark soliton 1 Barone, Drago, Ratcliffe, PR 359 (2002) Alessandro Bacchetta - Transverse-momentum-dependent functions

  28. First data: Collins asymmetry Airapetian et al. [HERMES], PRL 94 (05) Alexakhin et al. [COMPASS], PRL 94 (05) hadron plane See talk by G. Schnell, A. Martin lepton plane Alessandro Bacchetta - Transverse-momentum-dependent functions

  29. First attempt to combine BELLE and HERMES data Efremov, Goeke, Schweitzer, PRD 73 (06) 1. Get Collins function from BELLE Talk by R. Seidl Talks by P. Schweitzer and M. Boglione Alessandro Bacchetta - Transverse-momentum-dependent functions

  30. First attempt to combine BELLE and HERMES data 2. Check size of transversity at HERMES See talk by P. Schweitzer Alessandro Bacchetta - Transverse-momentum-dependent functions

  31. Where to observe it Talks by Schnell,Martin, Avakian, Elschenbroich Martin, Radici, Giordano Heppelman, Dalpiaz Koch, Fischer Heppelman, Aidala Alessandro Bacchetta - Transverse-momentum-dependent functions

  32. The Sivers function

  33. T-odd - Introducing the Sivers function Probability to find a quark with momentum xP+ and kTin a proton with transverse spin S see e.g. Bacchetta, D’Alesio, Diehl, Miller, PRD 70 (04) Alessandro Bacchetta - Transverse-momentum-dependent functions

  34. Sivers function: birth and growth D. Sivers, PRD41 (90) Alessandro Bacchetta - Transverse-momentum-dependent functions

  35. Two ingredients • Final-state interactions (included in the gauge link) Ji, Yuan, PLB 543 (02); Belitsky, Ji, Yuan, NPB656 (03) • Transverse-spin dependent distribution of quarks in transverse space Burkardt, PRD 66 (02); Diehl, Hägler, EPJ C44 (05) Alessandro Bacchetta - Transverse-momentum-dependent functions

  36. up down Final-state interactions Side view Front view quarks proton Alessandro Bacchetta - Transverse-momentum-dependent functions

  37. up down Final-state interactions Side view Front view photon NOTE: QCD tells us that the FSI has to be attractive, since quark and remnants form a color antisymmetric state Alessandro Bacchetta - Transverse-momentum-dependent functions

  38. up down Chromodynamic lensing Burkardt, PRD 66 (02) Final-state interactions Side view Front view photon See talk by M. Burkardt Alessandro Bacchetta - Transverse-momentum-dependent functions

  39. up Clear-cut prediction of QCD down Collins, PLB 536 (02) Change of sign in Drell-Yan Side view Front view quarks antiquark proton photon Alessandro Bacchetta - Transverse-momentum-dependent functions

  40. up down Distortions in transverse space Side view Front view quarks proton Alessandro Bacchetta - Transverse-momentum-dependent functions

  41. up down Distortions in transverse space Side view Front view quarks  proton The presence of spin can distort the distribution of quarks in transverse space (orbital angular momentum of quarks is required) A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers function Alessandro Bacchetta - Transverse-momentum-dependent functions

  42. Relation to GPDs • The transverse-space deformation of unpolarized quarks in a transversely polarized nucleon is described by the generalized parton distribution function E Work of Burkardt Alessandro Bacchetta - Transverse-momentum-dependent functions

  43. Lattice-QCD studies up quarks Sivers function for up quarks expected to be NEGATIVE See talk by P. Hägler Preliminary results by QCDSF Collab. (see e.g. hep-ph/05110032) Alessandro Bacchetta - Transverse-momentum-dependent functions

  44. down up Bacchetta, Schäfer, Yang, PLB 578 (04) Model calculations See talk by L. Gamberg Brodsky, Hwang, Schmidt PLB530 (02) Gamberg, Goldstein, Oganessyan, PRD 67 (03) spectator proton Alessandro Bacchetta - Transverse-momentum-dependent functions

  45. Fits to HERMES and COMPASS data Airapetian et al. [HERMES], PRL 94 (05) Anselmino et al., PRD72 (05) Alessandro Bacchetta - Transverse-momentum-dependent functions

  46. Comparison with COMPASS data deuteron Alexakhin et al. [COMPASS], PRL94 (05), Anselmino et al., PRD72 (05) Alessandro Bacchetta - Transverse-momentum-dependent functions

  47. Different fits Anselmino et al., hep-ph/0511017 [20] Anselmino et al., PRD72 (05) [21] Vogelsang, Yuan, PRD72 (05) [23] Collins et al., hep-ph/0510342 Alessandro Bacchetta - Transverse-momentum-dependent functions

  48. New preliminary kaon data See talk by U. Elschenbroich Alessandro Bacchetta - Transverse-momentum-dependent functions

  49. Future experimental data See talk by U. D’Alesio • HERMES@DESY: p0 and weighted asymmetries (this year?) • COMPASS@CERN: proton data (this year?) • CLAS@Jlab • STAR,PHENIX@RHIC: jet-production in pp collisions • EIC (DIS with polarized protons) • FAIR@GSI (Drell-Yan with polarized protons) Alessandro Bacchetta - Transverse-momentum-dependent functions

  50. The Boer-Mulders function

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