Outline

2. Outline • The HERMES Experiment at DESY Hamburg • Short introduction to Spin Physics • Transversity • What is transversity ? • Characteristics of transversity • How to measure transversity at HERMES • The results from 2002/2003 running • Interpretation of results • Summary and Outlook

3. HERA with polarised beam • HERA at DESY Hamburg • spin of electrons are transverse polarised • spin is rotated to longitudinal in experimental regions • HERMES is internal gas target experiment

4. The HERMES Spectrometer HERA Measurement of Spin: deep inelastic scattering of polarised electrons from polarised nucleon (fixed) gas targets • forward open geometry spectrometer capable of detecting and identifying electrons, hadrons, and photons • large solid angle acceptance: |qx|<170 mrad, 40<|qy|<140 mrad • good PID for pions, kaons and protons

5. H,D target filled atomic beam source • r = 7.6x1013 atoms/cm2 • polarisation: • additionally: unpol targets: H2, D2, He, N2, Ne,Kr The Polarised Internal Gas Target • years 1995-2000 longitudinally polarised • since 2002 transversely polarised • gas target within Hera vacuum

6. Naive quark parton model: quarks should carry largest part (58%) • EMC 1988: longitudinal quark contribution only llllllll • compatible with zero SPIN CRISIS • transverse quark contribution is unknown Where is the Spin of the Nucleon hidden? • Nucleons consist of quarks and gluons • Spin of the nucleon: known to be 1/2 • How contribute the different constituents to the spin? • From then until today a lot of work was done and we have a completely different picture by now

7. γ* • infinite momentum frame: • nucleon target is moving contrary to the photon with “infinite” momentum • transverse momenta of partons unchanged • kinematic variables: initial ( ) and final ( ) transverse momentum, Bjorken x and the fractional energy of the produced hadron (z) Deep Inelastic Scattering • absorption by a quark of a spacelike vitual photon with large squared four-momentum q2=-Q2 • after averaging over this intrinsic transverse momentum pT, three fundamental distributions in longitudinal quark momentum can be interpreted as probability densities

8. q:parton distribution Dq: helicity difference unknown dq: transversity well known known vector charge axial charge tensor charge HERMES 1996-2000 HERMES >2000 What is Transversity ? • q, Dq and dq provide a complete leading twist description of the nucleon at quark level

9. Bounds: • due to positivity of matrix in helicity space • Soffer bound: • Non-relativistic case and without spin-orbit effects: • difference connected to relativistic effects since boost and rotation do not commute • q and q contribute with opposite sign to tensor charge • tensor charge is a valence-only object Characteristics of Transversity • Angular momentum conservation • gluons have no transversity, play no role • dq has different Q2 evolution than Dq • Nomenclature: dq is also called h1q

10. Transversity in hard interactions • dq associated with a helicity flip • chirality is conserved in QCD and electroweak processes • impossible to measure transversity in • transversity is a chiral odd object • no access in fully inclusive DIS • a second chiral odd object is necessary to regain helicity conservation • a 2nd chiral odd distribution function or • a chiral odd fragmentation function • generates a single spin asymmetry (SSA)

11. Collins fragmentation function describing this spin-momentum correlation is chiral-odd • the transverse spin of quarks can be “transformed” into orbital angular momentum during the fragmentation process Collins Fragmentation Function • single spin asymmetry arises when transversely polarized quark fragments into p+ • single spin asymmetries involving long. target polarisation have been observed in pion electroproduction (Hermes) • theoretical interpretations and calculations suggest that the Collins function has a substantial magnitude • measurements with transverse target polarisation can constrain transversity

12. Sivers Distribution Function • alternatively a chiral even distribution function can generate a single spin asymmetry : Sivers function • asymmetry of p+ due to asymmetry in transverse momentum distribution of quarks (kT) in target • a vestige of the quark transverse momentum can survive the photo-absorption and the fragmentation process • be inherited in the transverse momentum component • influence azimuthal distribution

13. How to measure transverse spin effects? • single spin azimuthal asymmetries with a transverse polarised target • study count rate asymmetries arising from target spin flips • more specifically: • study azimuthal distribution of the produced p: fh: azimuthal angle of scattered hadron around the virtual photon g* direction llllllwith respect to the lepton scattering plane fs: azimuthal angle of target spin vector around g* with respect to the lepton llllllscattering plane

14. convolution integral over initial ( ) and final ( ) quark transverse momenta Distinction between Collins and Sivers • longitudinal target polarisation: Collins and Sivers have a common sinf behaviour • transverse target polarisation: distinctive signatures • weighting the asymmetries by certain kinematic factors leads to a transparent representation of the distribution and fragmentation function

15. information about fragmentation functions • for some hadrons h sufficiently known • Sivers function extraction possible • basic expectation of QCD: sign opposite in Drell-Yan • results of different asymmetries from other experiments, for example e+e- annihilation: BABAR, BELLE will make transversity extraction possible Extraction of the Distribution Functions • measure in many (x,z) bins • large statistics necessary

16. Transverse asymmetry for p+, p-, p0 Collins Asymmetries • a positive p+ asymmetry slightly rising with x as is expected when approaching the valence region • the x behaviour of the p- asymmetries negative and with higher magnitude than p+ • magnitude of p- larger than p+ => surprising! data sample:750k DIS events

17. Transverse asymmetry for p+, p-, p0 Sivers Asymmetries • significantly positive for p+ and p0 • consistent with zero for p-

18. Interpretation in leading order QPM Assumptions: • at present experimental precision neglect strange sea • assume isospin symmetry among fragmentation functions • similar symmetry among Collins fragmentation functions:

19. transverse spin-dependent spin-independent D Leading order quark parton model • the weighted Collins asymmetries can be written as e.g. for p+: • define new, combined observables for distribution and fragmentation functions

20. K K is a common factor for all three asymmetries D • the three equations with three unknowns are not independent • can be combined to a relationship without any unknowns • * • where C(x,z) is constructed of known spin-independent quantities: r(x) from CTEQ6 and R1990 D(x)from Kretzer et al. Eur.Phys. J C 22(2001)269 D D Leading order QPM, rearranged • in terms of these flavour ratios, the p+ asymmetrie becomes:

21. Collins asymmetry (stat) with weighted asymmetries Sivers asymmetry (stat) with weighted asymmetries Consistency Check with Hermes data Complete consistency

22. Interpretation for Collins result • have two constraints in three unknows: dr, hH and K • visualising relationship by taking ratios of the equations for llllllllllllllllllllllllllllll and thereby eliminating K • * • compatible with hH about -1 is compatible with xQSM predictions (Wakamatsu and Kubota Phys.Rev. D60:034020,1999) • a hint to

23. Interpretation for Collins result Artru string fragmentation model • String break produces quark- antiquark pair • pair must preserve vacuum quantum numbers • angular momentum conservation gives the produced hadron transverse momentum

24. Interpretation of Sivers Effect Sivers Effect • q(x) is not flat! -> higher probability to find quarks on one side in impact parameter space • rescattering of hit quark by gluon • M.Burkardt (hep-ph/0309269) - impact parameter formalism • orbital angular momentum at finite impact parameter • observed and true xb differ g* by bx

25. Summary and Outlook • First measurement of asymmetries directly related to transversity • first Collins function measured • The flavour-disfavoured Collins function appears to be opposite in sign to the favoured one, and to have a substantial magnitude • Sivers function nonzero -> Orbital angular momentum ???? • Sivers and Transversity flavor separation Thank you to Ulrike Elschenbroich and Ralf Seidl for doing this analysis • More than twice this amount of additional data has been recorded • Running on the transversely polarised hydrogen target is expected to continue until mid-2005

26. the transverse polarisation of the struck quark can influence the transverse momentum component of the hadron orthogonal to the virtual photon direction Semi-inclusive DIS • if a hadron produced from a struck quark is detected in addition to the scattered lepton in semi-inclusive measurements • influences its distribution in the azimuthal angle f about the virtual photon direction relative to the lepton scattering plane

27. transverse spin distribution Introductory Word on Transversity Nucleon at leading twist level: gluon helicity distribution gluon density distribution quark density distribution quark helicity distribution

28. Distinction between Sivers and Collins

29. Weighted asymmetries • transverse cross section contains convolution integrals over intrinsic transverse momenta • unweighted asymmetries can only be decoupled by making assumptions about transverse momentum dependencies • weighting the asymmetries decouples the integrals

30. DIS and SIDIS Cross Section • at Hermes asymmetries are studied • minimise acceptance effects • eliminate unpolarised cross section contributions

31. Distribution and Fragmentation Functions

32. Collins function can experimentally be accessed through the sin(fh+fs) moment of the asymmetry: Collins Fragmentation Function • rough description: the transverse spin of quarks can be “transformed” into orbital angular momentum during the fragmentation process • this requires a non-zero chiral-odd fragmentation function (Collins function ) • can lead to single spin asymmetry (SSA)

33. Sivers DF Azimuthal Asymmetries • Measurement of cross section asymmetries depending on azimuthal angles f and fs Collins FF convolution integral over initial ( ) and final ( ) quark transverse momenta

34. Data sample • recorded during 2002-2003 using transversely polarised target and unpolarised positron beam • tracking corrections: for the deflections of the scattered particles caused by the vertical 0.3T target holding field (verified by MC) • for each produced hadron type h and for each bin in either x or z the cross section asymmetries depending onazimuthal angles f and fs were evaluated • effects of acceptance, smearing and QED radiation all found to be negligible in Monte Carlo studies

35. Interpretation in the leading order QPM Assumptions: • neglect strange sea • assume isospin symmetry among fragmentation functions • QPM expression for simplify • similar symmetry among Collins functions: with

36. Extraction • AUT asymmetries are small and statistics are still limited but .... • First observation of non-zero Sivers effect • LargeCollins asymmetry measured for p+ and p- • Tentative conclusion: disfavoured Collins fragmentation function of opposite sign and similar magnitude to favoured function • Contamination of asymmetries from diffractive vector meson production must be better constrained and understood • More data eagerly anticipated ... !