1 / 67

The QCD structure of the nucleon

Frascati May 2003. The QCD structure of the nucleon. Universality of T-odd effects in single spin and azimuthal asymmetries, D. Boer, PJM and F. Pijlman, hep-ph/0303034. P.J. Mulders Vrije Universiteit Amsterdam mulders@nat.vu.nl. Content. Introduction: From global view to quarks

hayes
Download Presentation

The QCD structure of the nucleon

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Frascati May 2003 The QCD structure of the nucleon Universality of T-odd effects in single spin and azimuthal asymmetries, D. Boer, PJM and F. Pijlman, hep-ph/0303034 P.J. Mulders Vrije Universiteit Amsterdam mulders@nat.vu.nl

  2. Content • Introduction: From global view to quarks • Observables in (SI)DIS in field theory language  lightcone/lightfront correlations • Single-spin asymmetries in hard reactions T-odd correlations • T-odd observables in final (fragmentation) and initial state (distribution) correlations • Structure functions and parton densities • Universality of T-odd phenomena Frascati p j mulders

  3. Introducing the nucleon: from global view to quarks Frascati p j mulders

  4. Global properties of nucleons • mass • charge • spin • magnetic moment • isospin, strangeness • baryon number • Mp Mn 940 MeV • Qp = 1, Qn = 0 • s = ½ • gp 5.59, gn -3.83 • I = ½: (p,n) S = 0 • B = 1 Frascati p j mulders

  5. A real look at the proton g + N  …. Nucleon excitation spectrum E ~ 1/R ~ 200 MeV R ~ 1 fm Frascati p j mulders

  6. A virtual look at the proton _ g* + N  N g* N N Frascati p j mulders

  7. Spacelike form factor global density charge current Frascati p j mulders

  8. Nucleon e.m. form factors GEp GMp/mp  GMn/mn  Gdipole Gdipole = (1+Q2/L2)-2 L2 = 0.71 GeV2 Frascati p j mulders

  9. Nucleon form factors Present-day status (TJNAF) Frascati p j mulders

  10. Nucleon densities neutron proton • charge density  0 • u more central than d? • role of antiquarks? • n = n0 + pp- + … ? Frascati p j mulders

  11. Another (weak) look at the nucleon n  p + e- + n • = 900 s  Axial charge GA(0) = 1.26 Different weights depending on processes Frascati p j mulders

  12. Information on substructure quark number anom.mag.mom axial charge Frascati p j mulders

  13. A hard look at the proton • For hard momenta, it is improbable that system survives. One needs additional hard interactions • Best deal is hitting elementary or pointlike objects G(Q2) ~ (Q2R2)-(n-1) Frascati p j mulders

  14. A hard look at the proton • Hard virtual momenta ( q2 = Q2 ~ many GeV2) can couple to (two) soft momenta Frascati p j mulders g* + N  jet g* jet + jet

  15. DIS event ZEUS@DESY Hitting quarks in the proton Frascati p j mulders

  16. Soft physics in inclusive deep inelastic leptoproduction Frascati p j mulders

  17. (calculation of) cross sectionDIS Full calculation + + + … PARTON MODEL +

  18. Lightcone dominance in DIS

  19. Leadingorder DIS • In limit of large Q2 the result of ‘handbag diagram’ survives • … + contributions from A+ gluons A+ Ellis, Furmanski, Petronzio Efremov, Radyushkin A+ gluons  gauge link Frascati p j mulders

  20. Matrix elements <yA+y> produce the gauge link U(0,x) in leading quark lightcone correlator Color gauge link in correlator A+

  21. Distribution functions Soper Jaffe & Ji NP B 375 (1992) 527 Parametrization consistent with: Hermiticity, Parity & Time-reversal

  22. Distribution functions • M/P+ parts appear as M/Q terms in s • T-odd part vanishes for distributions but is important for fragmentation Jaffe & Ji NP B 375 (1992) 527 Jaffe & Ji PRL 71 (1993) 2547 leading part

  23. Distribution functions Selection via specific probing operators (e.g. appearing in leading order DIS, SIDIS or DY) Jaffe & Ji NP B 375 (1992) 527

  24. Lightcone correlatormomentum density y+ = ½ g-g+ y Sum over lightcone wf squared

  25. Basis for partons • ‘Good part’ of Dirac space is 2-dimensional • Interpretation of DF’s unpolarized quark distribution helicity or chirality distribution transverse spin distr. or transversity

  26. Bacchetta, Boglione, Henneman & Mulders PRL 85 (2000) 712 Matrix representation Related to the helicity formalism Anselmino et al. • Off-diagonal elements (RL or LR) are chiral-odd functions • Chiral-odd soft parts must appear with partner in e.g. SIDIS, DY

  27. Summarizing DIS • Structure functions (observables) are identified with distribution functions (lightcone quark-quark correlators) • DF’s are quark densities that are directly linked to lightcone wave functions squared • There are three DF’s f1q(x) = q(x), g1q(x) =Dq(x), h1q(x) =dq(x) • Longitudinal gluons (A+, not seen in LC gauge) are absorbed in DF’s • Transverse gluons appear at 1/Q and are contained in (higher twist) qqG-correlators • Perturbative QCD  evolution Frascati p j mulders

  28. Soft physics in semi-inclusive (1-particle incl) leptoproduction Frascati p j mulders

  29. SIDIS cross section • variables • hadron tensor

  30. (calculation of) cross sectionSIDIS Full calculation + + PARTON MODEL + … +

  31. Lightfront dominance in SIDIS

  32. Lightfront dominance in SIDIS Three external momenta P Ph q transverse directions relevant qT = q + xB P – Ph/zh or qT = -Ph^/zh

  33. Leading order SIDIS • In limit of large Q2 only result of ‘handbag diagram’ survives • Isolating parts encoding soft physics ? ? Frascati p j mulders

  34. Lightfront correlator(distribution) + Lightfront correlator (fragmentation) Collins & Soper NP B 194 (1982) 445 no T-constraint T|Ph,X>out =|Ph,X>in Jaffe & Ji, PRL 71 (1993) 2547; PRD 57 (1998) 3057

  35. Distribution A+ including the gauge link (in SIDIS) One needs also AT G+a = +ATa ATa(x)= ATa(J) +dh G+a Ji, Yuan, PLB 543 (2002) 66 Belitsky, Ji, Yuan, hep-ph/0208038 From <y(0)AT(J)y(x)> m.e.

  36. Distribution A+ including the gauge link (in SIDIS or DY) SIDIS A+ DY SIDIS F[-] DY F[+] hep-ph/0303034

  37. Distribution • for plane waves T|P> = |P> • But... T U[0, J]T = U[0,- J] • this does affect F[](x,pT) • it does not affect F(x) • appearance of T-odd functions in F[](x,pT) including the gauge link (in SIDIS or DY)

  38. Ralston & Soper NP B 152 (1979) 109 Parameterizations including pT Tangerman & Mulders PR D 51 (1995) 3357 Constraints from Hermiticity & Parity • Dependence on …(x, pT2) • Without T: • h1^ and f1T^ • nonzero! • T-odd functions • Fragmentation f  D g  G h  H • No T-constraint: H1^ and D1T^ nonzero!

  39. Integrated distributions T-odd functions only for fragmentation

  40. Weighted distributions Appear in azimuthal asymmetries in SIDIS or DY

  41. T-odd  single spin asymmetry example:sOTO in ep epX • example of a leading azimuthal asymmetry • T-odd fragmentation function (Collins function) • T-odd  single spin asymmetry • involves two chiral-odd functions • Best way to get transverse spin polarization h1q(x) Collins NP B 396 (1993) 161 Tangerman & Mulders PL B 352 (1995) 129

  42. Single spin asymmetriessOTO • T-odd fragmentation function (Collins function) or • T-odd distribution function (Sivers function) • Both of the above can explain SSA in pppX • Different asymmetries in leptoproduction! Collins NP B 396 (1993) 161 Sivers PRD 1990/91 Boer & Mulders PR D 57 (1998) 5780 Boglione & Mulders PR D 60 (1999) 054007

  43. Summarizing SIDIS • Beyond just extending DIS by tagging quarks … • Transverse momenta of partons become relevant, effects appearing in azimuthal asymmetries • DF’s and FF’s depend on two variables, F[](x,pT) and D[](z,kT) • Gauge link structure is process dependent ([]) • pT-dependent distribution functions and (in general) fragmentation functions are not constrained by time-reversal invariance • This allows T-odd functions h1^ and f1T^ (H1^ and D1T^) appearing in single spin asymmetries Frascati p j mulders

  44. Structure functions are parton densities Frascati p j mulders

  45. Ralston & Soper NP B 152 (1979) 109 Distribution functions with pT Tangerman & Mulders PR D 51 (1995) 3357 Selection via specific probing operators (e.g. appearing in leading order SIDIS or DY)

  46. Bacchetta, Boglione, Henneman & Mulders PRL 85 (2000) 712 Lightcone correlatormomentum density Remains valid for F(x,pT) … and also after inclusion of links forF[](x,pT) Sum over lightcone wf squared Brodsky, Hoyer, Marchal, Peigne, Sannino PR D 65 (2002) 114025

  47. Interpretation unpolarized quark distribution need pT T-odd helicity or chirality distribution need pT T-odd need pT transverse spin distr. or transversity need pT need pT

  48. Matrix representationfor M = [F(x)g+]T Collinear structure of the nucleon!

  49. pT-dependent functions Matrix representationfor M = [F(x,pT)g+]T T-odd: g1T g1T – i f1T^ and h1L^  h1L^ + i h1^ Bacchetta, Boglione, Henneman & Mulders PRL 85 (2000) 712

  50. Positivity and bounds

More Related