1 / 37

Polarized structure functions

‘Lepton scattering and the structure of nucleons and nuclei’ September 16-24, 2004. Polarized structure functions. Piet Mulders. pjg.mulders@few.vu.nl. Content. Spin structure & transversity Transverse momenta & azimuthal asymmetries T-odd phenomena & single spin asymmetries. DIS.

erin-scott
Download Presentation

Polarized structure functions

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. ‘Lepton scattering and the structure of nucleons and nuclei’ September 16-24, 2004 Polarized structure functions Piet Mulders pjg.mulders@few.vu.nl

  2. Content • Spin structure & transversity • Transverse momenta & azimuthal asymmetries • T-odd phenomena & single spin asymmetries

  3. DIS • Known leptonic part • Completeness allows reduction in hadronic tensor to commutator [Jm(x),Jn(0)] • Known structure of current in terms of quarks • OPE • ….

  4. Deep inelastic scattering (DIS)

  5. Lepton tensor • Lepton tensor can also be expanded using the spacelike and timelike vectors • Tensor encompasses many ‘polarization options’

  6. Polarized DIS

  7. Semi-inclusive deep inelastic scattering • Known lepton part with much flexibility (unused in DIS) • Involves two hadrons and hence a much more complex hadronic tensor

  8. SIDIS

  9. (calculation of) cross section in DIS Full calculation + + + … PARTON MODEL +

  10. Lightcone dominance in DIS

  11. A+ Ellis, Furmanski, Petronzio Efremov, Radyushkin A+ gluons  gauge link Leadingorder DIS • In limit of large Q2 the result of ‘handbag diagram’ survives • … + contributions from A+ gluons ensuring color gauge invariance

  12. leading part Parametrization of lightcone correlator • 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

  13. Basis of 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

  14. Bacchetta, Boglione, Henneman & Mulders PRL 85 (2000) 712 Matrix representationfor M = [F(x)g+]T Quark production matrix, directly 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

  15. Results for DIS • Structure functions in (sub)leading order in 1/Q • Two of three (Polarized) quark densities for each flavor: Not accessible in DIS

  16. (calculation of) cross section in SIDIS “Full” calculation + + PARTON MODEL + … +

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

  18. Leading order SIDIS • In limit of large Q2 only result of ‘handbag diagram’ survives • Isolating parts encoding soft physics ? ?

  19. Lightfront correlators 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

  20. Distribution including the gauge link (in SIDIS) A+ One needs also AT G+a = +ATa ATa(x)= ATa(∞) +  dh G+a Belitsky, Ji, Yuan, hep-ph/0208038 Boer, M, Pijlman, hep-ph/0303034 From <y(0)AT()y(x)> m.e.

  21. Parametrization of F(x,pT) • Link dependence allows also T-odd distribution functions since T U[0,] T = U[0,-] • Functions h1^ and f1T^ (Sivers) nonzero! • These functions (of course) exist as fragmentation functions (no T-symmetry) H1^ (Collins) and D1T^

  22. 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

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

  24. Wmn(q;P,S;Ph,Sh) = -Wnm(-q;P,S;Ph,Sh) • Wmn(q;P,S;Ph,Sh) = Wnm(q;P,S;Ph,Sh) • Wmn(q;P,S;Ph,Sh) = Wmn(q;P, -S;Ph, -Sh) • Wmn(q;P,S;Ph,Sh) = Wmn(q;P,S;Ph,Sh) _ _ _ _ _ _ _ _ _ _ _ _ T-oddsingle spin asymmetry symmetry structure hermiticity * * parity • with time reversal constraint only even-spin asymmetries • the time reversal constraint cannot be applied in DY or in  1-particle inclusive DIS or e+e- • In those cases single spin asymmetries can be used to select T-odd quantities time reversal * *

  25. Leptoproduction of pions H1 is T-odd and chiral-odd

  26. Acoll vs xBj COLLINS ASYMMETRYRESULTS OF COMPASS Acoll depends on phT, zh, xBj with more statistics, the full analysis is foreseen from 2002 data: Sign!

  27. COLLINS ASYMMETRYRESULTS OF COMPASS from 2002 data: AColl vs zh all the tests made are consistent with the fact that systematic effects, if present, are smaller than statistical errors Sign!

  28. Distribution including the gauge link (in SIDIS or DY) A+ SIDIS A+ DY SIDIS F[-] DY F[+]

  29. Difference between F[+] and F[-] upon integration Back to the lightcone (theoretically clean)  integrated quark distributions twist 2 transverse moments measured in azimuthal asymmetries twist 2 & 3 ±

  30. Difference between F[+] and F[-] upon integration In momentum space: gluonic pole m.e. (T-odd) Conclusion: T-odd parts are gluon-driven (QCD interactions)

  31. Time reversal constraints for distribution functions T-odd (imaginary) Time reversal: F[+](x,pT)  F[-](x,pT) pFG F[+] F T-even (real) Conclusion: T-odd effects in SIDIS and DY have opposite signs F[-]

  32. Time reversal constraints for fragmentation functions T-odd (imaginary) Time reversal: D[+]out(z,pT)  D[-]in(z,pT) pDG D[+] D T-even (real) D[-]

  33. Time reversal constraints for fragmentation functions T-odd (imaginary) Time reversal: D[+]out(z,pT)  D[-]in(z,pT) D[+]out pDG out D out T-even (real) D[-]out Conclusion: T-odd effects in SIDIS and e+e- are not related

  34. C. Bomhof, P.J. Mulders and F. Pijlman PLB 596 (2004) 277 other hard processes • qq-scattering as hard subprocess • insertions of gluons collinear with parton 1 are possible at many places • this leads for ‘external’ parton fields to gauge link to lightcone infinity e.g.

  35. other hard processes • qq-scattering as hard subprocess • insertions of gluons collinear with parton 1 are possible at many places • this leads for ‘external’ parton fields to gauge link to lightcone infinity • The correlator F(x,pT) enters for each contributing term in squared amplitude with specific link • The link may enhance the effect of the (T-odd) gluonic pole contribution involving also specific color factors • Finding the right observables, however is crucial

  36. Conclusions • Hard processes  quark and gluon structure of hadrons (quark distributions, their chirality and transverse polarization) • Many new observables accessible when going beyond collinearity, often in combination with (transverse) polarization (among others the simplest access to transverse quark polarization) • Going beyond collinearity gives access to gluon dynamics in hadrons, which can be done in a controlled way via weighted asymmetries (twist limited, t  3), use of chirality, and the specific time-reversal behavior of single spin asymmetries.

More Related