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Phenomenology of transverse momentum dependent distribution and fragmentation functions

Phenomenology of transverse momentum dependent distribution and fragmentation functions . M. Boglione. In collaboration with M. Anselmino , S. Melis , A. Prokudin , …. Leading twist T M D Correlator.

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Phenomenology of transverse momentum dependent distribution and fragmentation functions

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  1. Phenomenology of transverse momentum dependent distribution and fragmentation functions M. Boglione In collaboration with M. Anselmino, S. Melis, A. Prokudin, …

  2. Leading twist TMD Correlator Mulders and Tangermann, NP B461 (1996) 197, Boer and Mulders, PR D57 (1998) 5780 M. Boglione

  3. TransverseMometum Dependent Distribution Functions Correlationsbetweenspin and transversemomentum Courtesy of Aram Kotzinian M. Boglione

  4. General Formalism with Helicity Amplitudes M. Anselmino, M. Boglione, U. D-Alesio, E. Leader, S. Melis, F. Murgia, PR D71, 014002 (2005), PR D73, 014020 (2006) M. Anselmino, M. Boglione, U. D-Alesio, S. Melis, F. Murgia, A. Prokudin (2010) in preparation The distribution function fa/A is the number density of partons of type a inside hadronA a A X M. Boglione

  5. General Formalism with Helicity Amplitudes M. Boglione

  6. TransverseMometum Dependent Distribution Functions ΔNfq/p↑(x,k) Sivers function Δfsz/p↑(x,k) Δfsy/p(x,k) Boer-Mulders function fq/p(x,k) Δfsz/p+(x,k) Helicity fn. Δfsx/p↑(x,k) Transversity function Δfsx/p+(x,k) Δfsy/p↑(x,k) Transversity function Correlationsbetweenspin and transversemomentum M. Boglione

  7. General Formalism with Helicity Amplitudes M. Boglione

  8. UnpolarizedSIDIS Cross Section M. Boglione

  9. TMD’s in SIDIS Trento conventions SIDIS in partonmodelwithintrinsick┴ Factorizationholds at largeQ2, and (Ji, Ma, Yuan) Unpolarized Cross Section M. Boglione

  10. TMD in unpolarized SIDIS → Cahn Effect Azimuthal dependence induced by quark intrinsic motion EMC data,µp and µd, E between 100 and 280 GeV W. Käfer, COMPASS collaboration, talk at Transversity 2008, Ferrara F. Giordano and R. Lamb, arXiv:0901.2438 [hep-ex] CLAS data, arXiv:0809.1153 [hep-ex] M. Boglione

  11. Cahn Effect → Parametrization of Unpolarized TMD’s • Assume a simple, factorized form for the TMD distribution and fragmentation • functions, with a gaussian dependence on the intrinsic transverse momentum Normalized Gaussian (two free parameters) x and z dependence from world data fits From fit <k2>=0.25 (GeV/c)2 <p2>=0.20 (GeV/c)2 M. Boglione

  12. General polarized SIDIS Cross Section M. Boglione

  13. Polarized SIDIS cross section Unpolarized Boer-Mulders Cahn Helicity Sivers Transversity Sivers M. Boglione

  14. Polarized SIDIS cross section Unpolarized proton and lepton The F structure functions contain all the TMD’s Longitudinally polarized proton, polarized lepton Transversely polarized proton, unpolarized lepton Transversely polarized proton, polarized lepton • Studying Sivers, Collins and other mechanisms is complicated by the fact that all these effects mix and overlap in the polarized SIDIS cross section and azimuthal asymmetries • Way out : appropriate azimuthal moments of the asymmetries ! Kotzinian, NP B441 (1995) 234, Muldersand Tangerman, NP B461 (1996) 197; Boer and Mulders, PR D57 (1998) 5780, Bacchettaet al., PL B595 (2004) 309, Bacchettaet al., JHEP 0702 (2007) 093, M. Anselmino, M. Boglione, U.D’Alesio, S. Melis, F. Murgia, A. Prokudin, (in preparation). M. Boglione

  15. TMD’s in polarized SIDIS chiral-even TMDs chiral-odd TMDs Cahn kinematical effects (Avakian, Efremov, Schweitzer, Metz, Teckentrup, arXiv:0902.0689) M. Boglione

  16. New fit of the Sivers distribution function (Preliminary results) M. Boglione

  17. X The SiversDistribution Function The Sivers function is related to the probability of finding an unpolarized quark inside a transversely polarized proton The Sivers function is T-odd The Sivers function inbeds the correlation between the proton spin and the quark transverse momentum M. Boglione

  18. Sivers effect in SIDIS single spin asymmetry Two soft mechanisms at work in SIDIS: • Distribution fn. → probability to find quark q carrying a light-cone fraction x of the parent proton momentum, an intrinsic transverse momentum k, at scale Q2. • Fragmentation fn.→ describes thehadronization of the struck quark into the final, detected hadron. Both mechanisms play an important role indetermining total cross section and spin asymmetries M. Boglione

  19. |Nq(x)| and |h(k)| are smaller than 1 for any x and for any k Positivity Bound automatically satisfied Parametrization of the Sivers distribution function M. Boglione

  20. Sivers Function Old fit - old data p+ production at HERMES K+ production at HERMES M.Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, S. Melis, F. Murgia, A. Prokudin, C. Türk, Eur.Phys.J.A39:89-100,2009. M. Boglione

  21. The SiversDistribution Function COMPASS deuteron data Until recently, Compass found Sivers = 0. Only HERMES data revealed Sivers effect. Need further check ! COMPASS Collaboration, Phys. Lett. B673: 127-135, 2009 M. Boglione

  22. The SiversDistribution Function COMPASS deuteron data … But now COMPASS new data on proton target show a sizeable Sivers effect ! COMPASS proton data COMPASS Collaboration, Phys. Lett. B673: 127-135, 2009 M.G. Alekseev et al. , Phys.Lett.B692:240-246,2010 M. Boglione

  23. Sivers Function Old fit - New HERMES data New data (2009), old fit ! HERMES Collaboration, Phys.Rev.Lett.103:152002,2009. HERMES proton data are compared with the predictions from M. Anselmino et al. Eur.Phys.J.A39:89-100,2009. M. Boglione

  24. Sivers Function Old fit - NewCOMPASS data COMPASS proton data are compared with the predictions from M. Anselmino et al. Eur.Phys.J.A39:89-100,2009. M. Boglione

  25. COMPASS proton data – new re-analysis of Sivers asymmetry Compared with the predictions from M. Anselmino et al. Eur.Phys.J.A39:89-100,2009. Anna Martin for COMPASS Collaboration - DIS2010 Giulia Pesaro for COMPASS Collaboration – SPIN2010 M. Boglione

  26. Sivers Function New fit – valence only, no sea π+ → ud̄ π- → dū New fit – valence + sea π+ → ud̄ π- → dū M. Boglione

  27. Sivers Function New fit – Only valence, no sea π+ → ud̄ π- → dū New fit – valence + sea π+ → ud̄ π- → dū M. Boglione

  28. Sivers Function New fit – Only valence, no sea K+ → us̄ K- → sū New fit – valence + sea K- → sū K+ → us̄ M. Boglione

  29. Sivers Function New fit – Only valence, no sea K+ → us̄ K- → sū New fit – valence + sea K+ → us̄ K- → sū M. Boglione

  30. Sivers Function New fit Valence only Valence + sea M. Boglione

  31. Sivers Function New fit predictions for newCOMPASS proton data M. Boglione

  32. X The Boer-MuldersDistribution Function The Boer-Mulders function isrelated to the probability of finding a polarized quark inside an unpolarized proton The Boer-Mulders function is chirally odd and T-odd The Boer-Mulders function inbeds the correlation between the quark spin and its transverse momentum M. Boglione

  33. Role of the Boer-Mulders Function in the unpolarized cross section M. Boglione

  34. Extraction of the Boer-Mulders Function from the <cos 2φ>azimuthal moment V. Barone, S. Melis and A. Prokudin ArXiv:0912.5194 (to be published in Phys. Rev. D) • The angular distribution in the unpolarized SIDIS can be written as is the usual azimuthal-independent contribution subleading - Cahn + Boer-Mulderseffect +...other unknown twist-4 terms? M. Boglione

  35. Extraction of the Boer-Mulders Function • Simple parametrization of the Boer-Mulders functions: 2 parameters fit for valence quarks for sea quarks A. Prokudin, talk at Workshop on Transverse Spin Physics, Beijing (2008) Sivers function as determined by Anselmino et al,Eur.Phys.J.A39:89-100,2009. M. Boglione

  36. Extraction of the Boer-Mulders Function FIT I and both negative Bound saturated M. Boglione

  37. Extraction of the Boer-Mulders Function FIT I (C term) • GRV98 PDF • DSS FF • HERMES proton and deuteron • target (x,z,PT) charged hadrons • COMPASS deuteron target (x,z,PT) charged hadrons 2 • Gaussians: <k>=0.25 (GeV/c)2 <p>=0.20 (GeV/c)2 (from Cahn-cosφeffect) 2 Experimental data • Simulated evolution (unp.) Int. School Niccolo' Cabeo M. Boglione

  38. Extraction of the Boer-Mulders Function FIT I • Cahn effect (Twist-4)comparable to BM effect • Same sign of Cahn contribution for positive and negative pions FIT I • BM contribution opposite in sign for positive and negative pions M. Boglione

  39. Extraction of the Boer-Mulders Function COMPASS HERMES <k>=0.25 (GeV/c)2 <p>=0.20 (GeV/c)2 2 <k>=0.18 (GeV/c)2 <p>=0.20 (GeV/c)2 2 2 2 ~ EMC ~ HERMES MC FIT II Better description of HERMES but the BM is unchanged M. Boglione

  40. The Boer-MuldersDistribution Function V. Barone, S. Melis, A. ProkudinArXiv: 0912.5194 M. Boglione

  41. The Boer-MuldersDistribution contribution to <cosφ>azimuthal moment Anslemino, Boglione, Melis, Nocera, Prokudin, work in progress Francesca Giordano for the HERMES Collaboration – Spin 2010 GiulioSbrizzaifor the COMPASS Collaboration – Spin 2010 M. Boglione

  42. Conclusions • Boer-Mulders distribution function: new data → ?? • The Boer-Mulders function extracted from <cos 2φh>azimuthal moment gives a very tiny contribution to the <cosφh> moment. • Predictions of the <cosφh>azimuthal moment is not consistent with data. • More work to do ! • Use a better, more refined parametrization for a simultaneous fit of <cos 2φh> and <cosφh> • Estimate higher order contaminations to <cosφh> and <cos 2φh> → calculation of k2/ Q2kynematical corrections M. Boglione

  43. Conclusions • Sivers distribution function: new data → new fit • Pionazimuthal moments <sin(φS-φh)> can be fitted successfullly by considering only valence quark contributions, without any sea. • Kaon data seem to offer some constraint on the sea quark contribution to the Sivers function • Results of fit on HERMES proton data and COMPASS deuteron data are very satisfactory. • Predictions of COMPASS proton data predictions are in good agreement with experimental data. M. Boglione

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