Measurement of TMDs in Semi-Inclusive DIS Rainer Joosten University of Bonn

1. Measurement of TMDs in Semi-Inclusive DIS Rainer JoostenUniversity of Bonn Charlottesville, VA, October 7, 2008

2. Content of the talk • SIDIS Experiments with transversely polarised targetHERMES 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. (E',k') (E,k) g*q=(n,q ) Perspective of the talk I will focus on SIDIS reactions in one photon exchange < Kinematical Variable: Q2 = -q2@4 E E' sin2θ/2 resolution n = (El – El') photon energy xBj= Q2/2Mn momentum of the struck quark z = Eh/n exclusivity lepton nucleon

4. 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. 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 m beam, energy 160 GeV

6. results are coming from COMPASS 2002-2004 transverse data HERMES CLAS Q2 – x range results are coming from given the different beam energies, the Q2 – x range is different complementary information, needed to study energy dependence and to disentangle higher order effects

7. = 7 GeV HERMES 27.5 GeV e+ Pure hydrogen gas target: flipped at high frequency (60- 90 s) 1H→ <|Pt|> ~ 85 ±3.8 % 2H→ <|Pt|> ~ 84 ±3.5 % 1H <|Pt|> ~ 74 ±4.2 % RICH PID:p, K, p ID

8. COMPASS • high energy beam • large angular acceptance • broad kinematical range • two stage spectrometer • Large Angle Spectrometer (SM1), • Small Angle Spectrometer (SM2) • PID • RICH in LAS Polarized Target: 6LiD (PT≈ 50%) or NH3 (PT≈ 85%) solid target cells Polarization reversal: once a week MuonWall SM2 E/HCAL E/HCAL SM1 MuonWall Polarised Target RICH • beam: • 160 GeV/c • longitudinal polarisation -76% • intensity 2·108 µ+/spill (4.8s/16.2s) mbeam

9. 11 days (19) 9 days (14) 14 days (24) running with transversely polarized target 2002-2004: 6LiD only 2007: NH3target (protons) Analyzed so far: 10·106 SIDIS events (~20% of data) proton only For latest HERMES results, see M. Contalbrigotalk in thissession For latest COMPASS protondata, see H. Wollny‘stalk in thissession SIDIS events (106)

10. q(x) = q+(x) + q-(x) How does transverse momentum enter? • collinear QPM f1(x) g1(x) Dq(x) = q+(x) – q-(x) Helicity Integrated over kT: three quark distribution functions contribute in leading order h1(x) DTq(x) = qT(x) – qT(x) Transversity

11. Transverse momentum in the QPM • collinear QPM • quarktransversemomentum kT Additional physics!

12. Transverse momentum • … can be the transverse momentum kTof the quarks in the struck nucleon. It enters the PDFs (e.g. the Sivers PDF) • … can be the transverse momentumof the fragmenting quark (and the produced hadron). It enters the PFF (e.g. the Collins FF) • … can create kinematical effects (Cahn effect)

13. Sivers Collins Full SIDIS cross-section in NLO A Bacchetta, M Diehl, K Goeke, A Metz, P Mulders, M Schlegel (06) General expression: also valid for exclusive reactions and for entire phase space of SIDIS 18 structure functions Unpolarizedtarget Cahn and Boer-Mulders longitudinallypolarizedtarget 8 modulations (4 LO) 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 “Pretzelosity” NLO transverselypolarizedtarget

14. Kinematical corrections: Cahn effect Leading order QED with kT 0 R.N. Cahn PL B78 (1978) 269-273 … After fragmentation: contributes to cosh and cos2hmoments Access to <kT>

15. SIDIS cross-section: PDFs and PFFs Boer Mulders Collins Sivers “Pretzelosity”

16. up down Boer Mulders effectRelation to transverse space Side view Front view A. Bacchetta quarks        proton Convolutedwith Collins function Contributes to cosh and cos2hmoments Quark spin can be unevenly distributed in transverse space A distortion in the distribution of quark spin in transverse space can give rise to a Boer-Mulders function Burkardt, hep-ph/0510408

17. Unpolarised Target SIDIS Cross-Section pQCD and beampolarisation Cahn effect, Boer-MuldersDF and pQCD Boer- MuldersCollins FF,Cahn effect and pQCD

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

19. UnpolarisedAzimuthal Asymmetries cosmodulation (Cahn + Boer-Mulders) First determination of chargedependentcosmoments error bars: statistical errors bands: systematical errors Deuteron target

20. UnpolarisedAzimuthal Asymmetries cosmodulation comparison with theory Effect up to 40% NOT in agreementwithpredictions

21. UnpolarisedAzimuthal Asymmetries cos2modulation (Cahn + Boer-Mulders) First determination of chargedependent cos2moments error bars: statistical errors bands: systematical errors Deuteron target

22. UnpolarisedAzimuthal Asymmetries cos2modulation comparison with theory • pQCDcharge independent • Cahncharge independent • (ifkTu = kTd) • Boer–Mulderschargedependent Effect up to 10% Well in agreementwithpredictions Indicationfornon-vanishingBoer-Muldersfunction

23. HERMES results on Cahn and Boer Mulders Analysis isunder way! See F. Giordano‘stalklatertoday!

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

25. up down Sivers effectDistortions in transverse space Side view Front view A. Bacchetta quarks  proton The Sivers asymmetry: The presence of spin can distort the distribution of quarks in transverse space (needs orbital angular momentum of quarks) A distortion in the distribution of quarks in transverse space can give rise to a nonzero Sivers function

26. COMPASS Results: Sivers Effect preliminary K0 Deuteron target Data arecompatiblewith 0 ! Strongindication of cancelation of u and d quarkSiversFunctions in deuterontarget Constrains d quarkcontribution in global fit preliminary only statistical errors shown final results from 2002-2004 data[arXiv:0802.2160]

27. Siversasymmetries p+are substantial and positive: Evidence for a non-zero Sivers function p-,K-are compatible with 0 K+:2.3±0.3 times larger than p+ • Surprising for u-quark dominance expectations  large sea quark contribution? Proton target

28. extracting the Sivers function usual unpolarised fragmentation function new results using latest HERMES (p) and COMPASS (d) pion and kaon data

29. h q q h Collins-effect The CollinsFFcorrelatesthe transversespin of thefragmentingquarkand the transversemomentumPh of producedhadron h The measured asymmetry AColl gives access to the transversity distribution times the Collins fragmentation function:

30. Collins asymmetries • p+ asymmetries positive • – u-quark dominance • p-large negative asymmetries • – suggests • p0 fulfills isospin symmetry • K+: consistent with p+ • K-of opposite sign from p- • – all-sea object Proton target

31. COMPASS Results: Collins Effect preliminary K0 Deuteron target preliminary Asymmetriescompatiblewith 0 ! Againindication of cancelation of u and d Quark contributionfor a deuterontarget Access to d quarkcontribution in global fit only statistical errors shown final results from 2002-2004 data[arXiv:0802.2160]

32. extracting transversity spin-dependent fragmentation function See A. Vossen‘stalklatertoday! hep-ex 0805.2975

33. Fits to Data A. Prokudin: Transversity 08, Ferrara new results using latest HERMES (p) COMPASS (d) pion data, and BELLE data See A. Prokudin‘stalk on Thursday!

34. Transverse target spin asymmetries (4 LO) Sivers transversity ……. pretzelosity by now allmeasured by COMPASSon deuteron (and proton)

35. Target transverse spin results – (LO) “Pretzelosity” Estimate on thebasis of thepositivitylimit Avakian, Efremov, Schweitzer, Yuan, hep-ph/0808.3982

36. Target transverse spin results – (LO) g1Tis 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 ?

37. HERMES results on transversetargetspinasymmetries definition of angles + asymmetries acc. to “Trento convention” [PRD70(2004),117504] unbinned Maximum Likelihood fit to the log of the weighted PDF : Accessible in the HERMES data! fixed parameters for: …takes into account cross contamination of moments Talk by Delia Hasch @ IWHSS 2008

38. target transverse spin dependent asymmetries (NLO)

39. target transverse spin dependent asymmetries (NLO)

40. 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 <kT> First COMPASS (d) data on charge dependent cosand cos 2moments: Indication of non vanishing Boer-Mulders function HERMES data and COMPASS proton data underway • Transverse Target Spin asymmetries (Pretzelosity, g1T) 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. Outlook ThankYou !! See also A. Bacchetta’s talk on Thursday! • 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!