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Delia Hasch

Transversity & friends from HERMES. Delia Hasch. outline :. a very brief introduction. 1 and 2 hadron production: transversity + Sivers fct. theory meets experiments. International workshop on hadron and spectroscopy, Torino, Italy, 31. March – 02. April 2008.

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Delia Hasch

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  1. Transversity & friends from HERMES Delia Hasch outline: a very brief introduction 1 and 2 hadron production: transversity + Sivers fct. theory meets experiments International workshop on hadron and spectroscopy,Torino, Italy, 31. March – 02. April 2008

  2. quark structure of the nucleon transversely polarised quarks and nucleons unpolarised quarks and nucleons longitudinally polarised quarks and nucleons [also: h1q, DTq] dq:helicity-flip of both nucleon and quark dq is chiral-odd  needs a chiral odd partner: chiral-odd PDF chiral-odd FF chiral-odd fragmentation function acts as polarimeter of transverse quark polarisation chiral-even

  3. h q q h 1hadron production: “Collins-effect” CollinsFF H1(z,kT2)correlates transverse spin of fragmenting quark and transverse momentum Ph of produced hadron h  left-right(azimuthal) asymmetry in the direction of the outgoing hadron our observable: single-spin azimuthal asymmetry

  4. is this observable unique? “Sivers-effect ” another mechanism that produces single-spin azimuthal asymmetries: Sivers distribution function: distribution of unpolarised quarks in a transversely polarised nucleon  describes spin-orbit correlations [Matthias Burkardt] a non-zero Sivers fct. requires non-zero orbital angular momentum !

  5. sUU beam: target: lSL ,ST polarised DISh cross section q(x) Dq(x)

  6. SIDIS with transversely polarised targets but not only… polarised DISh cross section q(x) Dq(x) transversity (Collins effect)

  7. extraction of azimuthal amplitudes definition of angles + asymmetries acc. to “Trento convention” [PRD70(2004),117504] unbinned Maximum Likelihood fit to the log of the weighted PDF : fixed parameters for: …takes into account cross contamination of moments

  8. ep  pX Collins asymmetries first time: transversity & Collins FF are non-zero! p+ • p+ asymmetries positive – no surprise: u-quark dominance and expect dq>0 since Dq>0 • large negative p- asymmetries – ARE a surprise: suggests the disfavoured CollinsFF being large and with oposite sign: p-

  9. ep  KX Collins asymmetries first time: transversity & Collins FF are non-zero! K+ K+ amplitudes consistent with p+amplitudes as expected from u-quark dominance K- of opposite sign from p- (K- is all-sea object)

  10. more Collins asymmetries neutral pions:important ‘control’ asymmetry (isospin) holds for all tw-2 and tw-3 DF in LO and NLO in as

  11. more Collins asymmetries neutral pions:important ‘control’ asymmetry (isospin) neutral pions: results for the three pion charge states are consistent with isospin symmetry holds for all tw-2 and tw-3 DF in LO and NLO in as fulfilled!

  12. spin-dependent fragmentation function  e+e- e+ e- extracting transversity

  13. cQSM xdq(x) xdu(x) xdd(x) [Efremov,Goeke,Schweitzer PRD73(2006)] first glimpse of transversity global, simultaneous fit: compare to a model calculation: milestone! [Anselmino et al. PRD75(2007)]

  14. xdu(x) xdd(x) first glimpse of transversity global, simultaneous fit: compare to Dq: [Anselmino et al. PRD75(2007)]

  15. xdu(x) xdd(x) first glimpse of transversity global, simultaneous fit: looking forward: • include new high statistic data from BELLE and HERMES; identified hadrons from COMPASS • awaiting proton results from COMPASS  extending to lower x [Anselmino et al. PRD75(2007)]

  16. spin-orbit structure Sivers function: [Matthias Burkardt] a non-zero Sivers fct. requires non-zero orbital angular momentum !

  17. Sivers asymmetries p+ p+are subtantial and positive: • first unambiguous evidence for a non-zeroT-odd distribution function in DIS • a signature for quark orbital angular momentum ! p-

  18. Sivers asymmetries • SURPRISE: • K+ amplitude 2.3±0.3 times larger than for p+ p+  conflicts with usual expectations based on u-quark dominance  suggests substantial magnitude of the Sivers fct. for sea quarks p-

  19. kaon data suggest that sea quark contribution may be significant comparison to models [Anselmino et al. PRD72(2005)] excellent description of pion data but: cannot constrain sea predictions for kaons:  see talk from D’Alesio about choice of fragmentation functions

  20. kaon data suggest that sea quark contribution may be significant comparison to models [Anselmino et al. PRD72(2005)] excellent description of pion data but: cannot constrain sea predictions for kaons: [M. Anselmino @PACSPIN07] FF from [deFlorian, Sassot, Stratmann, arXiv:0703.242]  see talk from D’Alesio about choice of fragmentation functions

  21. crucial test of pQCD: extracting the Sivers function usual unpolarised fragmentation function ToDo: @FAIR (GSI)

  22. semi-inclusive 2-hadron production

  23. 2-hadron asymmetries interference fragmentation function between pions in s-wave and p-wave • only relative momentum of hadron pair relevant  integration over transverse momentum of hadron pair simplifies factorisation (collinear!) and Q2 evolution • however cross section becomes very complicated (depends on 9! variables)

  24. [Bacchetta, Radici PRD74(2006)] Mpp (GeV) model for H1<|q (Mhh) combined with various models for dq(x) models for 2-hadron asymmetries pythia: [Jaffe et all, PRL80(1998)] r0 due to r0-s interference r0 w

  25. 2-hadron asymmetries • BOTH: transversity and interference fragmention function are non-zero ! [arXiv:0803.2367]

  26. [Bacchetta, Radici PRD74(2006)] Mpp (GeV) shape compares well ruled out models for 2-hadron asymmetries pythia: • model calculation for H1<|q (z) combined with various models for dq(x) [Jaffe et all, PRL80(1998)] r0

  27. 2-hadron asymmetries first evidence for non-zero interference FF • BELLE plans to measure it ! • this kind of interference effect is a very promising way to access dq @RHIC dq(x) from SIDIS + pp + e+e-

  28. where do we stand ? precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct

  29. where do we stand ? precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct more to come: 1/7/07@ 1:09:56 am T

  30. where do we stand ? precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct more to come: PT-weighted Collins and Sivers asymmetries  model-independent interpretation of asymmetries  requires control of acceptance effects (more @transversity08) Boer-Mulders fct. via <cos(2f)>, <kT> via Cahn-effect <cosf>  requires control of acceptance effects (more @transversity08) <cos(f-fS)>LT : access to tw-2 fct. g1T ; other AUT moments T inclusive pion photoproduction AUT (“E704 effect”) stay tuned !

  31. BACKUP SLIDES [courtesy of A. Bacchetta]

  32. Sivers asymmetries neutral pions: results for the three pion charge states are consistent with isospin symmetry

  33. contributions from VM AUT of VM prod.n and decay distributions not yet available for a correction …

  34. resolving the convolution integral  pT weighted asymmetries:

  35. what about the PT weighted asymmetries? MC study of acceptance effects: gmc_trans: generator for transversity + TMDs Collins asymmetries unweighted [L. Pappalardo, PhD Thesis University Ferrara]

  36. what about the PT weighted asymmetries? MC study of acceptance effects: gmc_trans: generator for transversity + TMDs Collins asymmetries weighted [L. Pappalardo, PhD Thesis University Ferrara]

  37. what about the PT weighted asymmetries? acceptance depends strongly on PT: <pT>=<kT>=0.38, constant

  38. what about the PT weighted asymmetries? very promising  more details @transversity08, Ferrara, May 28-31 solutions under study:

  39. multiplicities compared to theory new FF from combined NLO analysis of single-inclusive hadron production in e+e-, pp and DIS [deFlorian,Sassot,Stratmann arXiv:0708.0769]

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