1 / 30

Selected Recent Results on Parton Distribution and Fragmentation Functions

This document presents recent findings on parton distribution and fragmentation functions from HERMES experiments at DESY. It discusses key topics such as the origin of nucleon spin and details of nucleon structure, highlighting the measurements of leading-twist parton distributions and various transverse momentum-dependent functions. Data taken from 1995 to 2007 contributes to resolving the structure of nucleons, providing insights into quark distributions, helicity, and related fragmentation functions. The results underscore the need for further exploration of these functions in upcoming high-luminosity e-N facilities.

rae
Download Presentation

Selected Recent Results on Parton Distribution and Fragmentation Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related