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Selected Recent Results on Parton Distribution and Fragmentation Functions

Selected Recent Results on Parton Distribution and Fragmentation Functions. Klaus Rith University of Erlangen-Nürnberg & DESY. Main HERMES research topics:. Origin of nucleon spin. Details of nucleon structure.

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Selected Recent Results on Parton Distribution and Fragmentation Functions

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  1. Selected Recent Results on Parton Distribution and Fragmentation Functions Klaus Rith University of Erlangen-Nürnberg & DESY Main HERMES research topics: Origin of nucleonspin Details of nucleonstructure Klaus Rith Moriond QCD March 19, 2009

  2. RICH: Hadron:  ~ 98%, K ~ 88% , P ~ 85% HERMES Spectrometer e HERAlongitudinallypolarized 27.6 GeVe+/e- beam Polarized and unpolarized internal gas target (spin flip every 90 s) Kinematics: 0.02<x<0.7, 1.0 GeV2<Q2<15 GeV2 Data taking: summer 1995 – June 30, 2007 1995-2000: longitudinal target polarization, 2002-2005: transverse target pol. 2006-2007: unpolarized H, D targets + Recoil Detector 2

  3. Leading-twist Parton Distributions Complete description of nucleon by quark momentum and spin distri-butions at leading-twist: 3kT-integrateddistribution functions (DF) Transversity DF Unpolarised DF HelicityDF q(x)  h1q(x) q(x)  f1q(x) q(x)  g1q(x) known well known First glimpse HERMES 1995-2000 HERMES 2002-2005 3

  4. g1 h1 f1 Transverse Momentum Dependent DFs Quark distribution functions Boer-MuldersDF (chiral-odd) TransversityDF (chiral-odd) SiversDF (T-odd) Fragmentationfunctions (FF) D1 Dqh = ‚normal‘ FF, H1= spin-dependent Collins FF (chiral-odd) 4

  5. Quark Distributions from SIDIS Flavor tagging =E - E‘, Q2= -q2=-(l – l ‘)2 x=Q2/(2M) = fraction ofnucleon‘s longitudinal momentum carried by struck quark K- q(x) = quark number density K+ Leading hadronoriginates with large probability from struck quark Dqh(z):= Fragmentation function (FF) z = Eh/ zq2q(x)Dqh(z) ALL (x,z) zq2 q(x)Dqh(z) Measurehadronasymmetries Targets: H, D ; h = ±, K±, p (identified with RICH) 5

  6. Quark Helicity Distributions q(x) PRD 71 (2005) 012003 u quarks: large positive polarisation d quarks: negative polarisation d(x) -0.4u(x) Sea quarks (u, d, s): polarisation compatible with 0. HERMES x 6

  7. The Strange Sea: S(x), S(x) Inputs: Multiplicities for K+ and K- from unpolarized deuteron d2NDDIS/dxdQ2 = KU(x,Q2)[5 Q(x) + 2S(x)] where Q(x) = u(x)+u(x)+d(x)+d(x) and S(x) = s(x) + s(x) d2NDK/dxdQ2 = KU(x,Q2)[Q(x)DQK(z)dz + S(x) DSK(z)dz] where DQK(z) = 4DuK(z)+DdK(z) and DSK(z) = 2DsK(z) Inclusive and K+, K- asymmetries from polarized deuteron A1,Dd2NDIS/dxdQ2 = KLL(x,Q2)[5Q(x) + 2S(x)] A1,DKd2NK/dxdQ2 = KLL(x,Q2)[Q(x)DQK(z)dz + S(x) DSK(z)dz] 7

  8. S(x) from Kaon Multiplicities dNKQ(x)DQK(z)dz + S(x)DSK(z)dz DQK(z)dz x > 0.3 =  dNDIS5 Q(x) + 2 S(x) 5 P.L. B666 (2008) 466 S(x) from CTEQ6L with DQK(z)dz & DSK(z)dz as free parameters (dotted) does not fit the data S(x) much softer than assumed by current PDFs (mainly based on  NX) ( ) Take DSK(z)dz = 1.27  0.13 from de Florian et al. 8

  9. S(x) from Kaon Asymmetries P.L. B666 (2008) 466 S = 0.037  0.019(stat.)  0.027(syst.) compared to S = - 0.085  0.013(stat.)  0.012(syst.) from inclusive data and SU(3) Large negative contribution from low x? 9

  10. Transverse Azimuthal Angular Asymmetries Amplitude has 2 components: TransversityDF 2sin( + S)hUT ~ h1q(x)H1q(z) CollinsFF U: unpol. e-beam T: transv. pol. Target Unpolarised FF z = Eh/ 2sin( - S)hUT~ f1Tq(x) D1q(z) (Requires non-vanishing orbital angular momentaLq of quarks) SiversDF 10

  11. Collins Amplitudes TransversityDF  2sin( + S)hUT~ h1q(x)  H1q(z)    CollinsFF First measurement of non-zero Collins effect Both Collinsfragmentation function and transversity distribution function are sizeable Surprisingly large - asymmetry Possible source: large contribution (with opposite sign) from unfavored fragmentation, i.e. u - H1 ,disf - H1 ,fav 11

  12. Sivers Amplitudes SiversDF  2sin( - S)hUT ~ f1Tq(x) D1q(z)    First observationof non-zeroSiversdistribution functioninDIS Experimental evidence for orbital angular momentum Lqofquarks But: Quantitative contributionofLqtonucleonspinstillunclear 12

  13. Transverse SSA for + - - access to Siversvalence distribution 13

  14. sT kT kT sT Azimuthal Asymmetries in Unpolarised SIDIS Boer-Mulders DF     transversely polarised quarks in unpolarised nucleon 2cos(2h) 14

  15. kT kT Azimuthal Asymmetries in Unpolarised SIDIS Cahn effect     Intrinsic transverse quark momentum 2cos(h) 15

  16. Transverse Azimuthal Asymmetry in DIS 1-photon exchange approximation: TAA forbidden (Spin-flip every 90 s) AN 0: Signature of 2-photon exchange Compatible with zero ! AN = O(10-3) 16

  17. Conclusions HERMES provides new constraints for S(x) at low Q2 HERMES made a first glimpse at various Transverse Momentum dependent parton Distribution functions TMDs offer a large amount of new information on the nucleon structure They need to be explored in detail by the next generation of experiments at future high-luminosity e-N facilities 17

  18. Backups

  19. I[h1H1┴] Transversity & Collins d TMDs in SIDIS le ST  I[f1TD1] Sivers le  SL le    

  20. I[h1TH1┴] ┴ I[h1LH1┴] I[g1TD1] ┴ ┴ d TMDs in SIDIS le ST le  le SL    

  21. kT kT sT kT kT sT Cahn and Boer-Mulders effect Boer-Mulderseffect Cahneffect

  22. Transverse SSA for pion pairs JHEP 06 (2008) 017 First evidence for (transversity and) chiral-odd, naive-T-odd spin-dependent di-hadron fragmentation function

  23. Transverse SSA for pion pairs h1,q h1,q Trans. component of relative momentum survives integration over the Ph┴of pair Collinear kinematics (factorization, evolution) Simple product of unknown functions Limited statistical power Explicit dependence on transverse momentum of hadron Ph┴ Convolution of two unknown functions High statistical power

  24. h q q h Azimuthal angular asymmetries Transverse quark spin + spin-dependentfragmentation Azimuthal asymmetry ~ sin( +  S)h COLLINS Left-right distribution asymmetry (due to orbitalangular momentum) + final state interaction Azimuthal asymmetry ~ sin( -  S)h SIVERS green quark anti-green remnant

  25. ? + - + - chiral-odd chiral odd fragmentation function + h1 H1 - + - chiral even! + Transversity Sq(pqxPh) - SIDIS: How to measure Transversity Need another chiral-odd object!

  26. Sivers Amplitudes SiversDF large! T  2sin( - S)hUT ~ f1Tq(x) D1q(z)    First observationof non-zeroSiversdistribution functioninDIS Experimental evidence for orbital angular momentum Lqofquarks But: Quantitative contributionofLqtonucleonspinstillunclear Final result: K+ enhancement will be smaller, Q2 dependent? 12

  27. ┴ ┴ x vs z z vs Ph x vs Ph 2-D Collins Moments for ±

  28. ┴ ┴ x vs z z vs Ph x vs Ph 2-D Sivers Moments for ±

  29. A. Prokudin at Transversity 2008 Consistent picture Also with new proton data from COMPASS Extraction of Transversity • Global fit • HERMES, COMPASS, BELLE (ed->ehX) (ee->hhX) (ep->ehX) First extraction of transversity distribution

  30. E. Boglione at Transversity 2008 Sivers Extraction xf1T(x)

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