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

2. Alessandro Bacchetta A sideways look at the proton2/60 Outline Introduction Transverse spin Transverse momentum Transverse spin and transverse momentum Factorization and hadron collisions Conclusions

3. Introduction

4. Alessandro Bacchetta A sideways look at the proton4/60 Deep Inelastic Scattering - DIS target proton electron

5. Alessandro Bacchetta A sideways look at the proton5/60 Inclusive DIS proton lepton transverse longitudinal 

6. Alessandro Bacchetta A sideways look at the proton6/60 Semi-inclusive DIS ( SIDIS ) proton pion lepton

7. Alessandro Bacchetta A sideways look at the proton7/60 Vectors and angles involved DIS

8. Alessandro Bacchetta A sideways look at the proton8/60 Vectors and angles involved SIDIS

9. Alessandro Bacchetta A sideways look at the proton9/60 Transverse momentum effects SIDIS Drell-Yan e - e + to pions 3-D p-p to pions Whenever we measure transverse-momentum effects, we need k T -factorization and we need transverse momentum dependent (or unintegrated) parton distributions Collins, Soper, NPB 193 (81)

10. Alessandro Bacchetta A sideways look at the proton10/60 Feynman diagrams & Factorization proton lepton pion SIDIS Partonic scattering amplitude Fragmentation amplitude Distribution amplitude

11. Alessandro Bacchetta A sideways look at the proton11/60 Feynman diagrams & Factorization Partonic scattering amplitude Fragmentation amplitude Distribution amplitude proton lepton pion SIDIS electron positron pion e – e + to pions proton lepton antilepton Drell-Yan

12. Alessandro Bacchetta A sideways look at the proton12/60 Feynman diagrams & Factorization proton lepton pion SIDIS proton lepton antilepton Drell-Yan proton pion p-p to pions electron positron pion e – e + to pions ?

13. Alessandro Bacchetta A sideways look at the proton13/60 Nonperturbative elements 2 =

14. Alessandro Bacchetta A sideways look at the proton14/60 Decomposition of the correlation function Unpolarized distr. func. Helicity distr. func. Transversity distr. func.

15. Alessandro Bacchetta A sideways look at the proton15/60 Longitudinal vs transverse momentum target parton photon Long. view  photon Trans. view Photon moves into the screen/ proton moves out of the screen

16. Alessandro Bacchetta A sideways look at the proton16/60 Longitudinal vs transverse momentum photon Long. view  photon Trans. view Photon moves into the screen/ proton moves out of the screen target parton

17. Alessandro Bacchetta A sideways look at the proton17/60 Probabilistic interpretation _ _     Photon moves into the screen/ proton moves out of the screen

18. Alessandro Bacchetta A sideways look at the proton18/60 Decomposition of the correlation function UN integrated over k T Boer-Mulders Sivers Sivers, PRD 43 (91) Boer, Mulders, PRD 57 (98) Mulders, Tangerman, NPB 461 (96) Goeke, Metz, Schlegel, PLB 618 (05)

19. Alessandro Bacchetta A sideways look at the proton19/60 Probabilistic interpretation - Sivers - Boer-Mulders Photon moves into the screen/ proton moves out of the screen

20. Alessandro Bacchetta A sideways look at the proton20/60 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)

21. Alessandro Bacchetta A sideways look at the proton21/60 Helicity distribution function  q(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)

22. Alessandro Bacchetta A sideways look at the proton22/60 What about the transverse spin distribution h 1 ( x ) ? What about the transverse momentum dependence, e.g. f 1 ( x,k T 2 )?

23. Transverse spin

24. Alessandro Bacchetta A sideways look at the proton24/60 Transversity in SIDIS see e.g. A.B., Diehl, Goeke, Metz, Mulders, Schlegel, JHEP 0702,093

25. Alessandro Bacchetta A sideways look at the proton25/60 Data from Hermes and Compass HERMES, hep-ex/0507013 HERMES, PRL 94 (05) COMPASS, NPB 765 (07) COMPASS, PRL 94 (05) PROTON DEUTERON

26. Alessandro Bacchetta A sideways look at the proton26/60 Data from BELLE BELLE, PRL 96 (06)

27. Alessandro Bacchetta A sideways look at the proton27/60 First extraction of transversity Anselmino et al., PRD 75, 054032 (07)

28. Alessandro Bacchetta A sideways look at the proton28/60 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)

29. Alessandro Bacchetta A sideways look at the proton29/60 Tensor charge from Lattice QCD S. Aoki et al., PRD 56 (1997) M. Göckeler et al. [QCDSF/UKQCD], PLB (05) Compared to axial charge

30. Alessandro Bacchetta A sideways look at the proton30/60 Comparison of tensor charges Barone, Drago, Ratcliffe, PR 359 (2002) lattice  quark soliton 1 spectator bag  quark soliton 2  quark non-relativistic 2.4 GeV 2 0.3 GeV 2 Wakamatsu, 0705.2917[hep-ph]

31. Alessandro Bacchetta A sideways look at the proton31/60 Evolution equations Barone, Drago, Ratcliffe, PR 359 (2002) Hayashigaki, Kanazawa, Koike, PRD56 (97)

32. Alessandro Bacchetta A sideways look at the proton32/60 Other observables Efremov, Mankiewicz, Tornquist, PLB 284 (92) Collins, Heppelmann, Ladinsky, NPB 420 (94) Jaffe, Jin, Tang, PRL 80 (98) Dihadron fragmentation Doubly polarized Drell-Yan Ralston, Soper, NPB 152 (79)

33. Transverse momentum

34. Alessandro Bacchetta A sideways look at the proton34/60 Semi-inclusive DIS proton pion lepton

35. Alessandro Bacchetta A sideways look at the proton35/60 Example of model calculation diquark proton quark Jakob, Mulders, Rodrigues, NPA 626 (1997)

36. Alessandro Bacchetta A sideways look at the proton36/60 Example of a measurement H1 Coll, NPB485(97)

37. Alessandro Bacchetta A sideways look at the proton37/60 Transverse momentum distribution q q h intrinsic pQCD Koike, Nagashima, Vogelsang, NPB744 (06) fragmentation

38. Alessandro Bacchetta A sideways look at the proton38/60 Differences between flavors ? ud diquark proton u uu diquark proton d Up and down quark can have different transverse momentum distributions

39. Transverse momentum and transverse spin

40. Alessandro Bacchetta A sideways look at the proton40/60 rightleft lepton Semi-inclusive Deep Inelastic Scattering proton pion 

41. Alessandro Bacchetta A sideways look at the proton41/60 Measured asymmetries in DIS HERMES Coll, hep-ex/0507013

42. Alessandro Bacchetta A sideways look at the proton42/60 Parton distribution functions with transverse spin - Sivers - Boer-Mulders - Transversity Photon moves into the screen/ proton moves out of the screen

43. Alessandro Bacchetta A sideways look at the proton43/60 right left Chromodynamic lensing proton quarks Long. viewTrans. view Burkardt, PRD 66 (02)

44. Alessandro Bacchetta A sideways look at the proton44/60 right left Chromodynamic lensing photon Long. viewTrans. view NOTE: QCD tells us that the FSI has to be attractive, since quark and remnants form a color antisymmetric state

45. Alessandro Bacchetta A sideways look at the proton45/60 right left Chromodynamic lensing photon Long. viewTrans. view

46. Alessandro Bacchetta A sideways look at the proton46/60 right left Distortions in transverse space proton quarks Long. viewTrans. view

47. Alessandro Bacchetta A sideways look at the proton47/60 right left Distortions in transverse space proton quarks Long. viewTrans. view  A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers function The presence of spin can distort the distribution of quarks in transverse space (orbital angular momentum of quarks is required) Spin-orbit correlations

48. Alessandro Bacchetta A sideways look at the proton48/60 Results from Lattice QCD QCDSF/UKQCD Collab. (see e.g. hep-ph/05110032) Sivers function expected to be: NEGATIVE for up quarks POSITIVE for down quarks

49. Alessandro Bacchetta A sideways look at the proton49/60 Data from Hermes and Compass HERMES, hep-ex/0507013 HERMES, PRL 94 (05) COMPASS, PRL 94 (05) PROTON DEUTERON

50. Alessandro Bacchetta A sideways look at the proton50/60 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

51. Factorization and hadron-hadron collisions

52. Alessandro Bacchetta A sideways look at the proton52/60 Feynman diagrams & Factorization proton lepton pion SIDIS proton lepton antilepton Drell-Yan proton pion p-p to pions electron positron pion e – e + to pions

53. Alessandro Bacchetta A sideways look at the proton53/60 right left Sivers effect in SIDIS proton quarks Long. viewTrans. view 

54. Alessandro Bacchetta A sideways look at the proton54/60 right left Sivers effect in Drell-Yan proton Long. viewTrans. view  photon antiquark The Sivers effect gets an extra minus sign due to the difference between initial and final state interactions. Impossible to predict it in parton model. Clear-cut prediction of QCD Collins, PLB 536 (02)

55. Alessandro Bacchetta A sideways look at the proton55/60 Final/initial state interactions SIDIS pp to hadrons A.B., Bomhof, Mulders, Pijlman, hep-ph/0505268 Drell-Yan

56. Alessandro Bacchetta A sideways look at the proton56/60 k T -factorization is broken My personal opinion: what is shown by Collins and Qiu is not sufficient to make such a statement. Maybe new concepts (i.e. “advanced” factorization and “generalized” universality) can work. Bomhof, Mulders, Pijlman, PLB596 A.B., Bomhof, Mulders, Pijlman, PRD72 Is k T -factorization broken ?

57. Alessandro Bacchetta A sideways look at the proton57/60 An example A.B., D’Alesio, Bomhof, Mulders, Murgia, hep-ph/0703153 “Standard” factorization & universality “Generalized” factorization & universality Broken factorization?

58. Alessandro Bacchetta A sideways look at the proton58/60 Conclusions Transverse spin and transverse momentum observables uncover a new dimension of the structure of the nucleon Intense progress is taking place both from the theoretical and experimental point of view Impact also on hadron colliders and unpolarized physics