A sideways look into the proton Transverse momentum and transverse spin in QCD

1. A sideways look into the protonTransverse momentum and transverse spin in QCD Alessandro Bacchetta

2. Outline • Introduction • Transverse spin • Transverse momentum • Transverse spin and transverse momentum • Factorization and hadron collisions • Conclusions Alessandro Bacchetta A sideways look at the proton

3. Introduction

4. Deep Inelastic Scattering - DIS electron target proton Alessandro Bacchetta A sideways look at the proton

5. transverse  longitudinal Inclusive DIS proton lepton Alessandro Bacchetta A sideways look at the proton

6. Semi-inclusive DIS (SIDIS) proton lepton pion Alessandro Bacchetta A sideways look at the proton

7. Vectors and angles involved DIS Alessandro Bacchetta A sideways look at the proton

8. Vectors and angles involved SIDIS Alessandro Bacchetta A sideways look at the proton

9. Drell-Yan p-p to pions 3-D e-e+ to pions Transverse momentum effects SIDIS Whenever we measure transverse-momentum effects, we need kT-factorization and we need transverse momentum dependent (or unintegrated) parton distributions Collins, Soper, NPB 193 (81) Alessandro Bacchetta A sideways look at the proton

10. Partonic scattering amplitude Fragmentation amplitude Distribution amplitude Feynman diagrams & Factorization lepton lepton proton pion SIDIS Alessandro Bacchetta A sideways look at the proton

11. 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 A sideways look at the proton

12. 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 A sideways look at the proton

13. = Nonperturbative elements 2 Alessandro Bacchetta A sideways look at the proton

14. Decomposition of the correlation function Unpolarized distr. func. Helicity distr. func. Transversity distr. func. Alessandro Bacchetta A sideways look at the proton

15. Trans. view Photon moves into the screen/ proton moves out of the screen  photon Longitudinal vs transverse momentum Long. view photon parton target Alessandro Bacchetta A sideways look at the proton

16. Trans. view Photon moves into the screen/ proton moves out of the screen  photon Longitudinal vs transverse momentum Long. view photon parton target Alessandro Bacchetta A sideways look at the proton

17. _     _ Probabilistic interpretation Photon moves into the screen/ proton moves out of the screen Alessandro Bacchetta A sideways look at the proton

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 A sideways look at the proton

19. Probabilistic interpretation Photon moves into the screen/ proton moves out of the screen - Sivers Boer-Mulders - Alessandro Bacchetta A sideways look at the proton

20. Unpolarized distribution functions q(x) ZEUS Coll, EPJ C42 (05) 7 groups are working on the extraction of these PDFs (see www-spires.dur.ac.uk/hepdata/pdf.html) Alessandro Bacchetta A sideways look at the proton

21. Helicity distribution function Dq(x) AAC, Hirai et al. PRD69 (04) 6 groups are working on the extraction of these PDFs (see www-spires.dur.ac.uk/hepdata/pdf.html) Alessandro Bacchetta A sideways look at the proton

22. What about the transverse spin distribution h1(x)? • What about the transverse momentum dependence, e.g. f1(x,kT2)? Alessandro Bacchetta A sideways look at the proton

23. Transverse spin

24. Transversity in SIDIS see e.g. A.B., Diehl, Goeke, Metz, Mulders, Schlegel, JHEP 0702,093 Alessandro Bacchetta A sideways look at the proton

25. Data from Hermes and Compass DEUTERON PROTON HERMES, hep-ex/0507013 HERMES, PRL 94 (05) COMPASS, NPB 765 (07) COMPASS, PRL 94 (05) Alessandro Bacchetta A sideways look at the proton

26. Data from BELLE BELLE, PRL 96 (06) Alessandro Bacchetta A sideways look at the proton

27. First extraction of transversity Anselmino et al., PRD 75, 054032 (07) Alessandro Bacchetta A sideways look at the proton

28. 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) Alessandro Bacchetta A sideways look at the proton

29. Tensor charge from Lattice QCD Compared to axial charge S. Aoki et al., PRD 56 (1997) M. Göckeler et al. [QCDSF/UKQCD], PLB (05) Alessandro Bacchetta A sideways look at the proton

30. 2.4 GeV2 0.3 GeV2 Wakamatsu, 0705.2917[hep-ph] 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 A sideways look at the proton

31. Evolution equations Barone, Drago, Ratcliffe, PR 359 (2002) Hayashigaki, Kanazawa, Koike, PRD56 (97) Alessandro Bacchetta A sideways look at the proton

32. Dihadron fragmentation Efremov, Mankiewicz, Tornquist, PLB 284 (92) Collins, Heppelmann, Ladinsky, NPB 420 (94) Jaffe, Jin, Tang, PRL 80 (98) Doubly polarized Drell-Yan Ralston, Soper, NPB 152 (79) Other observables Alessandro Bacchetta A sideways look at the proton

33. Transverse momentum

34. Semi-inclusive DIS proton lepton pion Alessandro Bacchetta A sideways look at the proton

35. Example of model calculation quark diquark Jakob, Mulders, Rodrigues, NPA 626 (1997) proton Alessandro Bacchetta A sideways look at the proton

36. Example of a measurement H1 Coll, NPB485(97) Alessandro Bacchetta A sideways look at the proton

37. Transverse momentum distribution h fragmentation q pQCD q intrinsic Koike, Nagashima, Vogelsang, NPB744 (06) Alessandro Bacchetta A sideways look at the proton

38. Differences between flavors? u d ud diquark uu diquark proton proton Up and down quark can have different transverse momentum distributions Alessandro Bacchetta A sideways look at the proton

39. Transverse momentum and transverse spin

40. left lepton right Semi-inclusive Deep Inelastic Scattering proton  pion Alessandro Bacchetta A sideways look at the proton

41. Measured asymmetries in DIS HERMES Coll, hep-ex/0507013 Alessandro Bacchetta A sideways look at the proton

42. - Transversity Parton distribution functions with transverse spin Photon moves into the screen/ proton moves out of the screen - Sivers Boer-Mulders - Alessandro Bacchetta A sideways look at the proton

43. left right Chromodynamic lensing Burkardt, PRD 66 (02) Long. view Trans. view quarks proton Alessandro Bacchetta A sideways look at the proton

44. left right Chromodynamic lensing Long. view Trans. view photon NOTE: QCD tells us that the FSI has to be attractive, since quark and remnants form a color antisymmetric state Alessandro Bacchetta A sideways look at the proton

45. left right Chromodynamic lensing Long. view Trans. view photon Alessandro Bacchetta A sideways look at the proton

46. left right Distortions in transverse space Long. view Trans. view quarks proton Alessandro Bacchetta A sideways look at the proton

47. left right Distortions in transverse space Long. view Trans. view quarks  proton The presence of spin can distort the distribution of quarks in transverse space (orbital angular momentum of quarks is required) Spin-orbit correlations A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers function Alessandro Bacchetta A sideways look at the proton

48. Results from Lattice QCD • Sivers function expected to be: • NEGATIVE for up quarks • POSITIVE for down quarks QCDSF/UKQCD Collab. (see e.g. hep-ph/05110032) Alessandro Bacchetta A sideways look at the proton

49. Data from Hermes and Compass PROTON HERMES, hep-ex/0507013 HERMES, PRL 94 (05) DEUTERON COMPASS, PRL 94 (05) Alessandro Bacchetta A sideways look at the proton

50. 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 A sideways look at the proton