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

2. longitudinally polarised quarks and nucleons transversely polarised quarks and nucleons unpolarised quarks and nucleons quark structure of the nucleon  q: helicity-flip of both nucleon and quark  needs a chiral odd partner:  q is chiral-odd [also: h 1 q,  T q] chiral-odd PDF chiral-odd FF chiral-even chiral-odd fragmentation function acts as polarimeter of transverse quark polarisation

3. h h qq Collins FF H 1  (z,k T 2 ) correlates transverse spin of fragmenting quark and transverse momentum P h  of produced hadron h  left-right (azimuthal) asymmetry in the direction of the outgoing hadron 1hadron production: “Collins-effect” our observable: single-spin azimuthal asymmetry

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

5. polarised DIS h cross section UUUU beam: target:   S L,S T q(x)  q(x)

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

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

8. Collins asymmetries   first time: transversity & Collins FF are non-zero!   asymmetries positive – no surprise: u-quark dominance and expect  q>0 since  q>0 large negative   asymmetries – ARE a surprise: suggests the disfavoured CollinsFF being large and with oposite sign: ep    X

9. Collins asymmetries KK first time: transversity & Collins FF are non-zero! ep  K  X K + amplitudes consistent with   amplitudes as expected from u- quark dominance K  of opposite sign from   (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  s

11. more Collins asymmetries 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  s fulfilled! neutral pions: important ‘control’ asymmetry (isospin)

12. extracting transversity extracting transversity e-e- e+e+

13. first glimpse of transversity x  d(x) x  u(x) [Anselmino et al. PRD75(2007)] x  q(x)  QSM [Efremov,Goeke,Schweitzer PRD73(2006)] compare to a model calculation: global, simultaneous fit:

14. first glimpse of transversity x  d(x) x  u(x) [Anselmino et al. PRD75(2007)] global, simultaneous fit: compare to  q:

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

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

17. Sivers asymmetries    are subtantial and positive:   first unambiguous evidence for a non-zero T-odd distribution function in DIS a signature for quark orbital angular momentum !

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

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

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

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

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 Q 2 evolution however cross section becomes very complicated (depends on 9! variables)

24. models for 2-hadron asymmetries M  (GeV) [Bacchetta, Radici PRD74(2006)] pythia: [Jaffe et all, PRL80(1998)] 00 due to    interference 00  model for H 1 <|q (M hh ) combined with various models for  q(x)

25. 2-hadron asymmetries interference fragmentation function between pions in s-wave and p-wave more than 2 hadrons  all combinations exclusive  0 excluded missing energy of the event

26. 2-hadron asymmetries BOTH: transversity and interference fragmention function are non-zero ! [arXiv:0803.2367]

27. models for 2-hadron asymmetries M  (GeV) [Bacchetta, Radici PRD74(2006)]  model calculation for H 1 <|q (z) combined with various models for  q(x) pythia: [Jaffe et all, PRL80(1998)] ruled out shape compares well 00

28. 2-hadron asymmetries first evidence for non-zero interference FF first evidence for non-zero interference FF this kind of interference effect is a very promising way to access  q @RHIC this kind of interference effect is a very promising way to access  q @RHIC  q(x) from SIDIS  pp  e  e - BELLE plans to measure it ! BELLE plans to measure it !

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

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

31. where do we stand ? where do we stand ? more to come: more to come: precision of data for identified hadrons adequate for quantitative extraction of flavour dependence of both transversity and Sivers fct P T -weighted Collins and Sivers asymmetries  model-independent interpretation of asymmetries  requires control of acceptance effects (more @transversity08) Boer-Mulders fct. via, via Cahn-effect  requires control of acceptance effects (more @transversity08) LT : access to tw-2 fct. g 1T ; other A UT moments T inclusive pion photoproduction A UT (“E704 effect”) stay tuned !

32. BACKUP SLIDES [courtesy of A. Bacchetta]

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

34. contributions from VM A UT of VM prod. n and decay distributions not yet available for a correction …

36. resolving the convolution integral resolving the convolution integral  pT weighted asymmetries:

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

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

39. what about the P T weighted asymmetries? what about the P T weighted asymmetries? acceptance depends strongly on P T : = =0.38, constant

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

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