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and the Spin of the Nucleon Selected Highlights

and the Spin of the Nucleon Selected Highlights . K. Rith. FAU Erlangen-Nürnberg. Frascati, 29.05.2007. s z = ½ = J q + J g = ½  + L q + ( G + L g ). Overview. Introduction. HERMES. Determination of . The quark helicity distributions q(x).

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and the Spin of the Nucleon Selected Highlights

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  1. and the Spin of the Nucleon Selected Highlights K. Rith FAU Erlangen-Nürnberg Frascati, 29.05.2007 sz=½= Jq + Jg = ½ + Lq + (G + Lg)

  2. Overview Introduction HERMES Determination of  The quark helicity distributions q(x) The gluon helicity distribution g(x) Transverse spin physics: transversity q(x), Collins FF, Sivers DF Quark orbital angular momenta Lq Summary and outlook

  3. Introduction and Motivation

  4. Spin-dependent DIS =E - E‘ Q2 = -q2 x=Q2/(2M) = fraction ofnucleon‘s momentum carried by struck quark ucleon Nucleon Nucleon     Quarks Quarks 1/2~q+(x)  3/2~q-(x)  Helicity DF: q(x):=q+(x)-q-(x) g1(x) := ½ q zq2q(x) 1/2- 3/2g1 Asymmetry: A1=  F1(x) := 1/2+ 3/2F1 ½ q zq2q(x)

  5. Integrals and sum rules 1 := g1(x)dx;  9 1p,(n)= 4(1)u +1(4)d +s SU(3): 2 relations a3= u -d=gA/gV=1,269Neutron decay a8= u +d-2s = 0,586 , decay a0== u +d+s = ? QCD MS scheme: =0 + 36 1p,(n)(Q2)= [ 3a3+a8] CNS(Q2) + 4CS(Q2) + 8nfGCG(Q2) - Bjorken sum rule: 6(1p -1n)  a3=gA/gV Ellis-Jaffe S.R.: s = 0  a8 = 1p =(1/12)[a3+ (5/3)a8]C(Q2) 0,175 (for Q2 10 GeV2)

  6. The EMC result for g1p(x) QPM: 4/3 -1/3 0 Consequence (1987): u 0,78 d  -0,47 s  -0,19 1) Quark-‘Sea‘ is negatively polarised 2)=u+d+s = 0,12 0,090,14 1 1p =0,126  0,010  0,015 Contribution of Quark Spins to Nucleon-Spin very small J. Ashman et al., PL B 206 (1988) 364 (1337 Cit.) J. Ashman et al. Nucl. Phys. B 328 (1989) 1 (1160 Cit.) Spin-‘crises‘

  7. HERMES

  8. HERMES history - I Idea: longitudinally polarisede- beam of HERA + internal polarised storage cell atomic gas target 12/87, 1/88: 2 Letters of intent 12/88: Formation of HERMES 1/90: HERMES proposal (11/91), 5/92: Experimental demonstration of e polarisation 6/92: LNF joins HERMES 10/92: Approval (subject to funding) 7/93: Final Approval - Technical Design Report 8/93 – 2/95: Detector construction and installation 10/5/95: Start data taking (3:40 hrs)

  9. HERMES history - II 1995-2000: Longitudinal target polarisation (1995: 3He, 1996-97 H, 1998-2000 D) + unpolarised targets (H2, D2, 4He, N2, Kr, Xe) 2002-2005: Transverse target polarisation (H ) + unpolarised targets 2006-2007: Recoil detector (H2, D2)– exclusive reactions 2/7/2007: End of HERA

  10. HERMES @ HERA Electron beam: E = 27,5 GeV, Ie < 50 mA

  11. hadron separation Aerogel n=1.03 C4F10 n=1.0014 RICH: Hadron:  ~ 98%, K ~ 88% , P ~ 85% HERMES spectrometer HERAe+/e- beam of 27.6 GeV Polarized internal gas target kinematics: 0.02<x<0.6, 1.0<Q2<15 GeV2 tracking: p/p~2%, <0.6 mrad, 40-220 mrad PID: Calorimeter, Preshower, TRD, RICH

  12. The polarised atomic gas target

  13. Data taking with polarised targets Longitudinal target polarisation (1995-2000) Transverse target polarisation (2002-2005) x106 Number of DIS events

  14. Determination of 

  15. The Asymmetry A1 g1/F1 P. R. D 75 (2007) 012007

  16. A1 g1/F1 P. R. D 75 (2007) 012007 A1 well known for x 10-3 Excellent agreement between all experiments A1 depends only weakly on Q2 <Q2> = f(x) Knowledge of A1d substantially improved by HERMES and COMPASS data ? A1p(x=1)  1 A1d(x=1) = ?

  17. g1 P. R. D 75 (2007) 012007

  18. [Q2>1 GeV2 data only] x MS a0= DS (exp) (theory) (evol) = 0,330 ± 0,025 ± 0,011 ± 0,028 Integrals,  measured a8=0,586 QCD QCD ωD=0,05±0.05 Assumption:1dsaturates forx<0.05 1d= 0,042  0,001(stat)  0,003(sys) SMC:  = 0,12 0,090,14

  19. Quark helicity distributions q(x)

  20. q(x) from SIDIS Leading hadron originates with large probability from struck quark Dqh(z):= Fragmentation function (FF) z = Eh/ zq2q(x)Dqh(z) A1h(x,z) = zq2 q(x)Dqh(z) Measurehadronasymmetries Measure hadron asymmetries Targets: H, D ; h=±, K±, p(identified with RICH)

  21. Quark helicity distributions PRL 92 (2004) 012005, 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. u > d ? In measured range (0,023 – 0.6): • u(x) dx = +0.601  0.063 • d(x) dx = -0.226  0.063 • u(x) dx = -0.002  0.043 • d(x) dx = -0.054  0.035 • s(x) dx = +0.028  0.034 s < 0 ? x

  22. Gluon helicity distribution g(x)

  23. uvanddv(rather)well determined q and g from (N)NLO-QCD Fits gandqvery badly determinedg  0,5  1,1 Note: From g1d (0,01<x<1)exp  0,330,03 From NLO fits (0<x<0.01)fit  -0,13 0,11

  24. Direct determination of g/g Method: Photon-Gluon-Fusion q q t  h/2mq  Charm-production (Hard scale: mass of c-Quarks) e+, + e-, - D J/ * * c pt c c c g c g c D  (Pairs) of hadrons with high transverse momenta (Hard scale: pt ) h2 * g () h1

  25. Direct determination of g/g Data: Deuteron target Singlehadron with high transverse momentum No scattered electron in acceptance MC: PYTHIA 6.2 Simulation of total ep cross section Determination of relative contributions R of sub-processes - Vector mesons - anomalous (*  qq ) processes - direct photon processes (PGF, QCDC) - LO DIS (* q q ) and their asymmetries

  26. Measured asymmetries Comparison of measured asymmetries with those from MC for: g/g = 0 (middle curve) (contribution of quarks) g/g = -1 (upper curve) g/g = +1 (lower curve) Determination of g/g:

  27. g/g x Direct determination of g/g HERMES, PRL 84 (2000) 2584 <m2>=1.35 GeV2 +0.127 g/g(x,2) = 0.071 ± 0.034(stat) ± 0.010 (sys-exp)(sys-model) -0.105

  28. Transverse spin physics

  29. The 3 leading twist distribution functions All equally important for a complete description of momentum and spin distribution of the nucleon at leading-twist. Transversity DF Unpolarised DF Helicity DF q(x), f1q(x) q(x), g1q (x) q(x), h1q (x) ‚unknown‘ well known known HERMES 1995-2000 HERMES 2002-2005

  30. The transversity distribution q(x,Q2) Helicity basis: |+, |- q(x,Q2) Transverse Spin basis: | , |  q is chiral-odd associated with helicity flip of struck quark q in helicity basis: | ,  Hard EM and strong interactions cannot flip the chirality of the probed quark qis not accessible in inclusive DIS

  31. How can one measure transversity? Need another chiral-odd object!  Semi-Inclusive DIS one hadron in the initial state and at least one in the final state (semi-inclusive leptoproduction) chiral – odd DF chiral – odd FF How to measure transversity q FF q h FF chiral-odd FF chiral-odd DF

  32. h q q h The Collins fragmentation function Collins FF H1(z,kT2) correlates transverse spin of fragmenting quark and transverse momentum Ph of produced hadronh Chiral – odd & naïve T – odd produces left-right asymmetry in the direction of the outgoing hadron

  33. requires a quark rescattering via soft gluon exchange (gauge link) (Brodsky, Hwang, Schmidt) The Sivers distribution function f1T Describes correlation between intrinsic quark pT and transverse nucleon spin f1Tq(pT2) describes probability to find an unpolarised quark with transverse momentum in a transversely polarised nucleon Chiral – even & naïve T – odd Non-zero Sivers DF requires non-vanishing orbital angular momentum in the nucleon wave function

  34. The Sivers effect Attractive FSI deflects quark inwards Left-right distribution asymmetry is converted into right-left momentum asymmetry Impact parameter formalism (M. Burkardt hep-ph/030926) Orbital angular momentum of quarks Virtual photon sees different x for different b Quark distributions depend on b green quark anti-green remnant

  35. Angular distributions in SIDIS : angle between lepton scattering plane and hadron production plane S: angle between lepton scattering plane and transverse spin component S of target nucleon

  36. Azimuthal angular asymmetries in SIDIS U: unpol. e-beam T: transv. pol. Target Collins Sivers

  37. Extraction of SSA amplitudes Maximum likelihood fits of SSA amplitudes for pions and charged kaons: F( 2sin( + S)hUT, 2sin( - S)hUT, 2sin(2 - S)hUT, 2sin(3 - S)hUT, 2sin(S)hUT)

  38. Collins amplitudes for +/- (2002-05) 2sin( + S)hUT ~q(x)H1q(z) also: A. Airapetian et al, P. R. L. 94 (2005) 012002 Non-zero Collins effect Both Collins FF and transversity DF sizeable Surprisingly large - asymmetry Possible source: large contribution (with opposite sign) from unfavored fragmentation, i.e. u - H1,disf - H1,fav

  39. Collins amplitudes for +/-und K+/- 2sin( + S)hUT ~q(x)H1q(z) also: A. Airapetian et al, P. R. L. 94 (2005) 012002

  40. Collins amplitudes for +/-und K+/-

  41. Sivers amplitudes for +/- (2002-05) 2sin(-S)hUT~f1Tq(x)D1q(z) +asymmetry significantly different from zero and positive First hint of naive T-odd DF from DIS also: A. Airapetian et al, P. R. L. 94 (2005) 012002 orbital angular momentum Lzq But: Contributionof Lzqto nucleon spin unclear -asymmetryconsistent with zero FF D1known  Sivers DF can be extracted from HERMES data

  42. Sivers amplitudes for +/- and K+/- large! 2sin(-S)hUT~f1Tq(x)D1q(z) also: A. Airapetian et al, P. R. L. 94 (2005) 012002 K+ amplitudes larger than + amplitudes Possibly substantial contribution of sea quarks to Sivers DF

  43. SSA amplitudes for neutral pions Isospin symmetry of -mesons is fullfilled within the statistical uncertainties

  44. Quark orbital angular momentum Lq

  45. Q2 t Determination of Lq Ji sum rule: Jq=1/2 + Lq= lim dx x [H(x,,t) + E(x,,t)] H(x,,t), E(x,,t): Generalised Parton Distributions (GPDs) t  0 Access: exclusive processes Final state sensitive to different GPDs Vector mesons (, , ) H, E Pseudoscalar mesons(,) H, E DVCS () H, E, H, E    

  46. e+/- p→ e+/- p g (MX<1.7 GeV) (in HERMES acceptance) Regge, D-term Regge, no D-term fac., D-term fac., no D-term Determination of Lq DVCS: Beam charge asymmetry DVCS: Transv. target spin asymmetry (SA) DVCS: Long. target SA 0: Transv. target SA

  47. Q2 t Determination of Lq Program until July 3rd 2007: Detailed study of exclusive processes with Recoil-Detector:

  48. Nucleon Spin Structure & HERMES Unpolarised DIS SLAC, BCDMS, NMC, HERA… g/g = 0.071 ±0.035(exp) a0 =0.330±0.025(exp)  Signals for GPDs  Ju+Jd Lq 0 individual quark helicity distributions q(x)  0 After Delia Hasch, Spin06, Kyoto

  49. Further results - Outlook Many more results on various subjects: at present 40 publications with in average 62 citations each hadronisation in nuclei  quark hadron duality in A1p  Q2 dependence of GDH-integral SSAfor inclusiveand exclusive production DIS on nuclear targets DSAfor exclusive VM production Nuclear attenuation of coherent and incoherent ‘s (coherence length, colour transparency) pion multiplicities and fragmentation functions longitudinal and transverse  polarisation vector meson production   LNF HERMES is a big success !!

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