1. R. Joosten, Oct. 7, 2008 Measurement of TMDs in Semi-Inclusive DIS in Semi-Inclusive DIS Rainer Joosten University of Bonn Charlottesville, VA, October 7, 2008

2. R. Joosten, Oct. 7, 2008 Content of the talk SIDIS Experiments with transversely polarised target HERMES and COMPASS Transverse momentum in SIDIS Results Unpolarized cross section (Cahn effect, Boer-Mulders) Sivers Distribution Function Transversity Distribution Function, Collins Function Other TMD Distribution Functions Conclusions

3. R. Joosten, Oct. 7, 2008 Perspective of the talk I will focus on SIDIS reactions in one photon exchange Kinematical Variable: Q 2 = -q 2  4 E E' sin 2 θ/2 resolution   = (E l – E l' ) photon energy x Bj = Q 2 /2M momentum of the struck quark z = E h / e xclusivity (E,k) (E',k')  * q=(,q ) lepton nucleon <

4. R. Joosten, Oct. 7, 2008 Perspective of the talk Also I will focus on 1 hadron production up to NLO using different targets (p, d, n) and identifying the final hadron one can perform flavour separation unique feature of SIDIS

5. R. Joosten, Oct. 7, 2008 SIDIS Experiments transverse spin effects are an important part of the program of the experiments JLAB experiments electron beam, energy 6 GeV to be upgraded to 12 GeV HERMES at DESY electron beam, energy 27.5 GeV COMPASS at CERN long pol  beam, energy 160 GeV

6. R. Joosten, Oct. 7, 2008 results are coming from Q 2 – x range COMPASS 2002-2004 transverse data CLAS HERMES results are coming from given the different beam energies, the Q 2 – x range is different  complementary information, needed to study energy dependence and to disentangle higher order effects

7. R. Joosten, Oct. 7, 2008 HERMES RICH PID: , K, p ID 27.5 GeV e  = 7 GeV Pure hydrogen gas target: flipped at high frequency (60- 90 s) 1 H → ~ 85 ±3.8 % 2 H → ~ 84 ±3.5 % 1 H ~ 74 ±4.2 %

8. R. Joosten, Oct. 7, 2008 SM1 SM2  beam MuonWall E/HCAL RICH Polarised Target COMPASS two stage spectrometer Large Angle Spectrometer (SM1), Small Angle Spectrometer (SM2) PID RICH in LAS high energy beam large angular acceptance broad kinematical range beam: 160 GeV/c longitudinal polarisation -76% intensity 2·10 8 µ + /spill (4.8s/16.2s) Polarized Target: 6 LiD (P T ≈ 50%) or NH 3 (P T ≈ 85%) solid target cells Polarization reversal: once a week

9. R. Joosten, Oct. 7, 2008 running with transversely polarized target 2002-2004: 6 LiD only 11 days (19) 9 days (14) 14 days (24) proton only SIDIS events (10 6 ) 2007: NH 3 target (protons) Analyzed so far: 10 · 10 6 SIDIS events (~20% of data) For latest HERMES results, see M. Contalbrigo talk in this session For latest COMPASS proton data, see H. Wollny‘s talk in this session

10. R. Joosten, Oct. 7, 2008 How does transverse momentum enter? - collinear QPM  T q(x) = q T  (x) – q T  (x) Transversity Integrated over k T : three quark distribution functions contribute in leading order  q(x) = q + (x) – q - (x) Helicity q(x) = q + (x) + q - (x) f 1 (x) g 1 (x) h 1 (x)

11. R. Joosten, Oct. 7, 2008 Transverse momentum in the QPM - collinear QPM- quark transverse momentum k T Additional physics!

12. R. Joosten, Oct. 7, 2008 Transverse momentum … can be the transverse momentum k T of the quarks in the struck nucleon. It enters the PDFs (e.g. the Sivers PDF) … can be the transverse momentum of the fragmenting quark (and the produced hadron). It enters the PFF (e.g. the Collins FF) … can create kinematical effects (Cahn effect)

13. R. Joosten, Oct. 7, 2008 Full SIDIS cross-section in NLO A Bacchetta, M Diehl, K Goeke, A Metz, P Mulders, M Schlegel (06) 8 modulations (4 LO) Sivers Collins “Pretzelosity” Cahn and Boer-Mulders Unpolarized target longitudinally polarized target transversely polarized target Kotzinian, NP B441 (1995) 234 Mulders and Tangermann, NP B461 (1996) 197 Boer and Mulders, PR D57 (1998) 5780 Bacchetta et al., PL B595 (2004) 309 Bacchetta et al., JHEP 0702 (2007) 093 NLO General expression: also valid for exclusive reactions and for entire phase space of SIDIS 18 structure functions

14. R. Joosten, Oct. 7, 2008 Kinematical corrections: Cahn effect Leading order QED with k T  0 After fragmentation: contributes to cos  h and cos 2  h moments Access to R.N. Cahn PL B78 (1978) 269-273 …

15. R. Joosten, Oct. 7, 2008 SIDIS cross-section: PDFs and PFFs “Pretzelosity” Boer Mulders SiversCollins

16. R. Joosten, Oct. 7, 2008 down up      Boer Mulders effect Relation to transverse space proton quarks Side viewFront view A distortion in the distribution of quark spin in transverse space can give rise to a Boer-Mulders function Burkardt, hep-ph/0510408 Quark spin can be unevenly distributed in transverse space   A. Bacchetta Convoluted with Collins function Contributes to cos  h and cos 2  h moments

17. R. Joosten, Oct. 7, 2008 Unpolarised Target SIDIS Cross-Section Cahn effect, Boer-Mulders DF and pQCD Boer- Mulders  Collins FF, Cahn effect and pQCD pQCD and beam polarisation

18. R. Joosten, Oct. 7, 2008 the azimuthal distributions have to be corrected by the apparatus acceptance  dedicated MC simulations for L and T target polarisation data acceptance final azimuthal distribution the corrected azimuthal distributions are fitted: Unpolarised Azimuthal Asymmetries data sample: -part of the 2004 data - L and T target polarisation -each with both target configurations to cancel possible polarisation effects

19. R. Joosten, Oct. 7, 2008 Deuteron target Unpolarised Azimuthal Asymmetries cos  modulation (Cahn + Boer-Mulders) error bars: statistical errors bands: systematical errors First determination of charge dependent cos moments First determination of charge dependent cos  moments

20. R. Joosten, Oct. 7, 2008 Unpolarised Azimuthal Asymmetries cos  modulation comparison with theory Effect up to 40% NOT in agreement with predictions

21. R. Joosten, Oct. 7, 2008 Unpolarised Azimuthal Asymmetries cos2  modulation (Cahn + Boer-Mulders) error bars: statistical errors bands: systematical errors First determination of charge dependent cos2 moments First determination of charge dependent cos2  moments Deuteron target

22. R. Joosten, Oct. 7, 2008 Unpolarised Azimuthal Asymmetries cos2  modulation comparison with theory pQCD charge independent Cahn charge independent (if k T u = k T d ) Boer–Mulders charge dependent Effect up to 10% Well in agreement with predictions Indication for non-vanishing Boer-Mulders function

23. R. Joosten, Oct. 7, 2008 HERMES results on Cahn and Boer Mulders Analysis is under way! See F. Giordano‘s talk later today!

24. R. Joosten, Oct. 7, 2008 LO target transverse spin asymmetries Sivers Collins 8 Structure Functions for target transverse spin part, 4 LO Pretzelosity“Boostisity”

25. R. Joosten, Oct. 7, 2008 Sivers effect Distortions in transverse space 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 (needs orbital angular momentum of quarks) down up proton quarks Side viewFront view A. Bacchetta The Sivers asymmetry:

26. R. Joosten, Oct. 7, 2008 COMPASS Results: Sivers Effect only statistical errors shown Deuteron target preliminary final results from 2002-2004 data [arXiv:0802.2160] K0K0 Data are compatible with 0 ! Strong indication of cancelation of u and d quark Sivers Functions in deuteron target Constrains d quark contribution in global fit

27. R. Joosten, Oct. 7, 2008 Sivers asymmetries    are substantial and positive: Evidence for a non-zero Sivers function K  : 2.3±0.3 times larger than    Surprising for u-quark dominance expectations  large sea quark contribution? Proton target  , K   are compatible with 0

28. R. Joosten, Oct. 7, 2008 new results using latest HERMES (p) and COMPASS (d) pion and kaon data usual unpolarised fragmentation function extracting the Sivers function

29. R. Joosten, Oct. 7, 2008 h h qq The Collins FF correlates the transverse spin of the fragmenting quark and the transverse momentum P h  of produced hadron h Collins-effect The measured asymmetry A Coll gives access to the transversity distribution times the Collins fragmentation function:

30. R. Joosten, Oct. 7, 2008 Collins asymmetries   asymmetries positive – u-quark dominance   large negative asymmetries – suggests K + : consistent with   K  of opposite sign from   – all-sea object Proton target   fulfills isospin symmetry

31. R. Joosten, Oct. 7, 2008 preliminary COMPASS Results: Collins Effect only statistical errors shown Deuteron target preliminary final results from 2002-2004 data [arXiv:0802.2160] K0K0 Asymmetries compatible with 0 ! Again indication of cancelation of u and d Quark contribution for a deuteron target Access to d quark contribution in global fit

32. R. Joosten, Oct. 7, 2008 extracting transversity hep-ex 0805.2975 See A. Vossen‘s talk later today!

33. R. Joosten, Oct. 7, 2008 Fits to Data new results using latest HERMES (p) COMPASS (d) pion data, and BELLE data A. Prokudin: Transversity 08, Ferrara See A. Prokudin‘s talk on Thursday!

34. R. Joosten, Oct. 7, 2008 ……. Sivers transversity Transverse target spin asymmetries (4 LO) by now all measured by COMPASS on deuteron (and proton) pretzelosity

35. R. Joosten, Oct. 7, 2008 Target transverse spin results – (LO) “Pretzelosity” Avakian, Efremov, Schweitzer, Yuan, hep-ph/0808.3982 Estimate on the basis of the positivity limit

36. R. Joosten, Oct. 7, 2008 g 1T is the only parton DF which is chiral-even, T-even, leading twist function in addition to the unpolarised DF and to the helicity DF again cancellation between the u and d quarks in the deuteron ? Target transverse spin results – (LO)

37. R. Joosten, Oct. 7, 2008 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] HERMES results on transverse target spin asymmetries Accessible in the HERMES data! Talk by Delia Hasch @ IWHSS 2008

38. R. Joosten, Oct. 7, 2008 target transverse spin dependent asymmetries (NLO)

39. R. Joosten, Oct. 7, 2008 target transverse spin dependent asymmetries (NLO)

40. R. Joosten, Oct. 7, 2008 CONCLUSIONS Transversity, Collins Function and Sivers Function Great progress in determining transversity, Sivers and Collins function based on pion and kaon data by HERMES, Belle and COMPASS Boer Mulders Function and Cahn effect First COMPASS (d) data on charge dependent cos  and cos  moments: Indication of non vanishing Boer-Mulders function HERMES data and COMPASS proton data underway Transverse Target Spin asymmetries (Pretzelosity, g 1T ) COMPASS transverse target spin asymmetries on deuteron target available (LO and NLO): no significant asymmetries HERMES data on proton (LO) should be available soon COMPASS proton data (LO and NLO) underway

41. R. Joosten, Oct. 7, 2008 Outlook We have abundant and good data on tape! There is more to come from COMPASS and JLAB (SIDIS, Drell-Yan, DVCS) Now we have to analyze all data and learn as much as possible from it! See also A. Bacchetta’s talk on Thursday! Thank You !!