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偏極パートン分布の現状

偏極パートン分布の現状. Masanori Hirai TUS, Noda 2011 1. 8@KEK. Contents. Introduction Global analysis of polarized PDFs DIS and p 0 production Initial distributions of pol-PDFs BB10, LSS10, AAC09, DSSV09 Current status of the polarized PDFs

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偏極パートン分布の現状

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  1. 偏極パートン分布の現状 Masanori Hirai TUS, Noda 2011 1. 8@KEK

  2. Contents • Introduction • Global analysis of polarized PDFs • DIS and p0 production • Initial distributions of pol-PDFs • BB10, LSS10, AAC09, DSSV09 • Current status of the polarized PDFs • Quark and gluon spin contribution and orbital angular momentum contributions • DS , DG and L • Summary

  3. Introduction • Origin of the nucleon spin 1/2 • 1/2 = 1/2 DS+ DG + Lq,g • Quark spin component from polarize DIS: DS =0.1-0.3 • Orbital angular momentum Lq,g ? • Jq=DQ+Lq:Generalized PDF from DVCS • DG is an important piece of the spin puzzle ! • Undetermined DG = 0.49 1.27 (AAC03) • Experimental data from RHIC-Spin • Prompt photon, Jet, heavy quark production, et al. • p0 production • PRD76, 051106 (2007), PRL103, 012003 (2009), PRD79, 012003 (2009) • Unknown flavor dependence of antiquark distributions

  4. Cross section Hadron tensor (asymmetric part) Structure function g1 Polarized deeply inelastic scattering

  5. Spin asymmetry A1(x,Q2) of DIS • Polarized DIS experiments • Proton : E130, E143, EMC, SMC, HERMES, E155,CLAS • Deuteron: E143, E155, SMC, HERMES, COMPASS, CLAS • Neutron : E142, E154, HERMES, Hall-A • Q2 dependence is obtained by DGLAP equation • L. W. Whitlow et al., • Phys. Lett. B 250 (1990) 193

  6. Spin asymmetry of p production • Cross section • gggg, ggqq,qgqg • qqqq, qq’qq’ • qqqq, qqgg, qqq’q’ • Consistent with unpolarized data • Fragmentation functions (FFs) • Determined by e+e- data • Ambiguity of Dgp(z) • No ambiguity of FF for jet production PRD76, 051106 (2007)

  7. Initial distributions of polarized PDF • BB10 • Unpol: NMC • Q02 = 4 GeV2 • LSS10 • Unpol: MRST02 • Q02 = 1 GeV2 • AAC • Unpol: GRV98 • Q02 = 1 GeV2 • DSSV09 • Unpol: MRST03 • Q02 = 1 GeV2 * http://hepdata.cedar.ac.uk/pdfs

  8. BB [NPB841,205(2010)] • DIS data only (# of data=1385) • New data sets: J-Lab(p,n,d), COMPASS(p,d), HERMES(p,d) • Data cut: Q2>1 GeV, W2>3.24 GeV • Higher twist • Including target mass correction • Higher twist term: g1(x) =g1,LT(x)+h(x)/Q2 • 5 data points for hp(x) and hn(x), respectively • Assuming the SU(3)F symmetry for antiquark distributions • Uncertainty estimation • Statistical error by the Hessian method • Systematic error from experimental data • Added in quadrature, uncertainties from NMC F2, R(x,Q2) • Theoretical systematic uncertainty • LQCD(4) (30 MeV), errors of the F and D, initial Q02(2-6 GeV)

  9. LSS [PRD82,114018 (2010)] • DIS and SI-DIS data (# of data=1043) • New data sets (DIS):CLAS(p,d), COMPAS(p,d), HERMES(p,d) (SI-DIS): SMC, HERMES, COMPASS • Data cut: Q2>1 GeV • Higher twist • Including target mass correction • Higher twist term: g1(x) =g1,LT(x)+h(x)/Q2 • 5 data points for hp(x) and hn(x), respectively • Flavor separation of the antiquark distributions by using SI-DIS data • Non target mass correction because of being less important due to the kinematic region and not enough precession of data • Estimating uncertainty by using the Hessian method

  10. AAC09 [NPB813,106 (2009)] • DIS and p0 production data (# of data=446) • New data set (DIS): COMPASS (p,d), CLAS(p,d) (p0 production): PHENIX(s=200 GeV) • Data cut: Q2>1 GeV, pT>1 GeV • Constraint condition: • Positivity condition: • Antiquark SUF(3)symmetry: • p0 asymmetry in low pT: gg process dominates • Insensitive to flavor dependence of Df(x) • Fixed 1st moments: Duv=0.926, Ddv= 0.341 • Not including the higher twist correction • Need to fit to the CLAS data ? • Estimation uncertainty by using the Hessian method

  11. DSSV09 [PRD80,034030 (2009)] • Data sets (# of data=467) • DIS • SI-DIS : SMC, HERMES, COMPSS • RHIC [p0(s=200,62 GeV), Jet (s=200 GeV)] • PEHNIX, STAR • Full NLO analysis • Double Melline method • Uncertainty by Lagrange multiplier and Hessian method • Flavor decomposition of Dq(x)

  12. Comparing pol-PDFs from DIS • Consistent with them in the uncertainty • Well determination of DS(x) • Showing the same behavior • Almost uncertainty comes from the antiquark distributions • Large uncertainty of the Dg(x) • Undetermined Dg(x) from the DIS data • Contribution to g1(x) via Q2 evolution • However, narrower range of Q2 • 1< Q2 < 70 GeV (pol-DIS) • Positive distribution at medium and large-x • Existing rather large uncertainty as a theoretical uncertainty • Rather large uncertainty from LQCD BB: NPB841,205(2010)

  13. Dg from DIS and p0 data • Positive Dg(x) from DIS data • Positive value in the medium and large-x region • Appearing node type function by including the RHIC data • Fitting to small negative asymmetry data • gg process dominates at low-pT • Ds Dg(x1) Dg(x2) • c2p0: 12.43(positive) vs. 11.32 (node) (10 data points) • Rather large FF dependence at rather large-pT (pT >4 GeV) • Large uncertainty from Dg(z)

  14. DSSV09 [DIS,SI-DIS,p0,Jet] • 1st moments & uncertainties • effective region • Covered by DIS data [0.001-1] • DgRHIC: [x:0.05-0.2] • Well determined Du, Dd • Small gluon contributions • Appearing node type function • Positive contribution from the large-x region • Rather large uncertainties of antiquark • Comparing between truncate and full range

  15. Flavor decomposition of Dq(x) by SI-DIS • Node type distribution Du(x) • Negative distribution Dd(x) • Determined by h, p  data • Node type distribution Ds(x) • Appearing the node type by including K data • Obtaining all negative distribution by using DIS data only • Depending on the Kaon FFs • Difference in the small-x region ? • Taking negative value at small-x, however different from DSSV • Using the same FFs (DSS) • Higher twist for neutron target ? LSS: PRD82,114018 (2010)

  16. Higher twist contribution • LSS (Dc2=1) • Negative hp(x) and positive hn(x) • Clearly evidence of higher twist tem • Consistent with the QCD sum rule, large Nc limit and instanton model • BB (Dc2=9.3) • Showing the same behavior as the LSS • 0 consistent results within the errors • Target mass correction • Collinear factorize, OPE BB: NPB841,205(2010) LSS: PRD82,114018 (2010)

  17. Antiquark distributions for polarized PDFs • SUf(3) symmetry • AAC, BB • Low accuracy of DIS data • SUf(3) symmetry braking • LSS (DIS,SI-SIS) • DSSV (DIS, SI-DIS, p0, Jet) • FF dependence • SI-DIS (h, p) • Useful to determined Du, Dd • Separation of FFs for charged hadron ? • Effect of uncertainty from FFs ? • FF independence • Drell-Yan (J-PARC) • Jet production (RHIC) • W production (RHIC)

  18. W production • Single spin asymmetry AL(W-) • q: polar angle of lepton in the partonic c.m.s • Large negative lept (~p, x1 << x2) • probe of Du/u(x1) at medium x1 • positive lept (~0, x1 >> x2) • probe of -Dd/d(x1) at high x1 • Dd/d(x11) : Positive or negative ? • Single spin asymmetry AL(W+) • Suppressed by angular factor • Competing the both terms

  19. DS, DG and L • DS & DG at Q2=4GeV2 • Still large uncertainty of the DG • Undetermined DG from DIS and SI-DIS data • Large uncertainty in the small-x region for node type • Due to no data in the region • Main uncertainty for spin sum rule • Reducing DS uncertainty by including SI-DIS • Reducing the uncertainty of the antiquark distributions • But not including uncertainty from FFs

  20. Summary • Polarized PDF from polarized DIS data • Well determined valence quark distributions • Undetermined anti-quark and gluon distributions • Rather large uncertainties of these distributions • Positive Dg(x) in the large-x region • Dg(x) from p0 production data • Significant reduction of DG uncertainty • Sign problem • Favored node type Dg(x) by including p0 data • Positive or negative DG ? • Needing well determination of the small-x behavior • Requiring the prompt photon, charged pion productions • Liner contribution of Dg(x) to the asymmetries • Flavor decomposition of antiquark distributions • SI-DIS data (dependence of FFs ?) • W production (RHIC-Spin), Drell-Yan (J-PARC) • Error correlation between the gluon and antiquark distributions

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