University of Erlangen-Nürnberg & DESY 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 Klaus Rith Moriond QCD March 19, 2009

HERMES Spectrometer e HERA longitudinally polarized 27.6 GeV e+/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 RICH: Hadron:  ~ 98%, K ~ 88% , P ~ 85% 1995-2000: longitudinal target polarization, 2002-2005: transverse target pol. 2006-2007: unpolarized H, D targets + Recoil Detector 2

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

Quark distribution functions Fragmentation functions (FF) Transverse Momentum Dependent DFs Quark distribution functions f1 Boer-Mulders DF g1 (chiral-odd) h1 Transversity DF (chiral-odd) Sivers DF (T-odd) Fragmentation functions (FF) D1  Dqh = ‚normal‘ FF, H1 = spin-dependent Collins FF (chiral-odd) 4

Quark Distributions from SIDIS Flavor tagging  = E - E‘, Q2 = -q2 = -(l – l ‘)2 x = Q2/(2M) = fraction of nucleon‘s longitudinal momentum carried by struck quark K- q(x) = quark number density K+ Leading hadron originates 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) Measure hadron asymmetries Targets: H, D ; h = ±, K±, p (identified with RICH) 5

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

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,D d2NDIS/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

S(x) from Kaon Multiplicities dNK Q(x)DQK(z)dz + S(x) DSK(z)dz DQK(z)dz x > 0.3 =  dNDIS 5 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

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

Transverse Azimuthal Angular Asymmetries Amplitude has 2 components: Transversity DF 2sin( + S)hUT ~ h1q(x)H1q(z) Collins FF 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 momenta Lq of quarks) Sivers DF 10

Collins Amplitudes Transversity DF Collins FF N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T 2sin( + S)hUT ~ h1q(x)  H1q(z)     Collins FF First measurement of non-zero Collins effect Both Collins fragmentation 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

Sivers Amplitudes 2sin( - S)hUT ~ f1Tq(x)  D1q(z) Sivers DF N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T 2sin( - S)hUT ~ f1Tq(x)  D1q(z)     First observation of non-zero Sivers distribution function in DIS Experimental evidence for orbital angular momentum Lq of quarks But: Quantitative contribution of Lq to nucleon spin still unclear 12

Transverse SSA for + - - access to Sivers valence distribution 13

Azimuthal Asymmetries in Unpolarised SIDIS Boer-Mulders DF N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T kT sT     transversely polarised quarks in unpolarised nucleon 2cos(2h) 14

Azimuthal Asymmetries in Unpolarised SIDIS Cahn effect N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T  kT    Intrinsic transverse quark momentum 2cos(h) 15

1-photon exchange approximation: TAA forbidden 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

HERMES provides new constraints for S(x) at low Q2 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

Backups

TMDs in SIDIS I[f1TD1] I[h1H1┴] le ST le SL le Sivers Transversity & Collins I[f1TD1]  Sivers d le N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T  SL le    

TMDs in SIDIS I[h1TH1┴] ┴ I[g1TD1] ┴ I[h1LH1┴] ┴ le ST le SL le d f1 N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T  I[h1LH1┴] ┴ SL le    

Cahn and Boer-Mulders effect kT sT Boer-Mulders effect Cahn effect kT

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

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

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

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

Sivers Amplitudes large! 2sin( - S)hUT ~ f1Tq(x)  D1q(z) Sivers DF N/q U L T f1 h1 g1 h1L f1T g1T h1 h1T large! 2sin( - S)hUT ~ f1Tq(x)  D1q(z) T     First observation of non-zero Sivers distribution function in DIS Experimental evidence for orbital angular momentum Lq of quarks But: Quantitative contribution of Lq to nucleon spin still unclear Final result: K+ enhancement will be smaller, Q2 dependent? 12

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

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

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

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