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  1. Recent results of the AAC analysis Masanori Hirai TUS, Noda (Asymmetry Analysis collaboration) Collaborators: S. Kumano and N. Saito arXiv:0808.0413 [hep-ph] 2009 1 10,KEK

  2. Contents • Introduction • AAC08 analysis • Global analysis of the polarized PDFs • Data sets • Assumptions: positivity condition, antiquark SU(3)f symmetry • Impact of RHIC p0 data • Discussion about a functional form of Dg(x) • Impact of E07-011 data • Relative errors dDG/DG ? • 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 • Unknown orbital angular moments Lq,g • Quantitative value from sum rule of GPDFs • Qualitative understanding ? • DG is an important piece of the spin puzzle ! • Undetermined DG = 0.49 1.27 (AAC03) • Experimental data from RHIC-Spin • p0 production [RUN05, PRD76, 051106 (2007)] • AAC analysis • AAC00 [PRD62, 0304017 (2000)]: DIS • AAC04 [PRD69, 054021 (2004)]: DIS, uncertainty estimation • AAC06 [PRD74, 014015 (2006)]:DIS+p0, uncertainty, DG • AAC08 [arXiv:0808.0413 [hep-ph]]: DIS+p0, uncertainty, E07-011(J-Lab)

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

  5. Spin asymmetry A1(x,Q2) • Polarized DIS experiments • Proton : E130, E143, EMC, SMC, HERMES, E155,CLAS • Deuteron: E143, E155, SMC, HERMES, COMPASS, CLAS • Neutron : E142, E154, HERMES, J-Lab (Hall-A) • Q2 dependence is obtained by the DGLAP equation • L. W. Whitlow et al., • Phys. Lett. B 250 (1990) 193 Total data 441 points (Q2>1GeV2)

  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) • Sing problem • gg process dominates at low pT • ALLp0  [Dg(x)]2, negative or positive ? PRD76, 051106 (2007)

  7. AAC analysis and uncertainty estimation • Initial distribution of polarized PDF • Constraint condition • Positivity condition: • Imposing on positive Dg(x), but not impose on node type • Antiquark SU(3)f symmetry: • Fixed 1st moments: Duv=0.926, Ddv= 0.341 • Fixed mq=1.0: undetermined small-x behavior • PDF uncertainty by Hessian method • Unpol PDF:GRV98 • Q02 = 1 GeV2

  8. Value of Dc2 • Hessian method • [K(N,s): c2 distribution ] • D2 ~ N (N: number of parameters) • 1s error of normal distribution in multi-parameterspace • Not 1s error for PDF uncertainties • Correspondence between uncertainties and variations of experimental data • Dc2=1 : statistically correct • 1s error for 1 degree of freedom • Asymmetry A1 • X-sections Data-theory

  9. AAC08 analysis • Added new data • DIS: CLAS(p,d), COMPASS(d, renewal data) • p0production: RHIC Run 5 final data (10 points) • Data sets • Set-A : DIS data only • Set-B : DIS + p0 data • Set-C : DIS + fake data of the E07-011 experiment • Impact on the determination of Dg(x) • Set-A vs. Set-B: effect on the functional form, node or positive • Set-B vs. Set-C: an impact on determination of the gluon spin contribution DG

  10. Fake data of the E07-011 experiment • Update experiment of the J-Lab • Expected errors for g1(x) • Converted to asymmetry errors • Expected asymmetry error

  11. Results • Minimal c2 • 1st moments:

  12. Impact of RHIC p0 data • Insensitive to Duv(x) and Ddv (x) • Same center values and uncertainties between Set-A and –B • gg process dominates • Dg(x) becomes small • Gluon uncertainty is reduced by RHIC data • RHIC data is sensitive to Dg(x) • Node type (DIS+p0) • Less c2 : 12.43(DG>0) , 11.32 (DG<0) • Changing sign at x=0.1 • Large uncertainty in small-x region • No data to constraint the behavior

  13. Impact of E07-011 data • Converged determination of the valence quark distributions • No changed these uncertainties • Assuming SUf(3) symmetry • Fixed 1st moments for uv and dv • Significant reducing the uncertainty of Dg(x) • Error correlation with antiquark distribution via Q2 evolution • Constraint via NLO gluon term • Low Q2 data • Higher twist term ?

  14. Impact of RHIC p0 and E07-011 data • Positive type • DIS: large distribution • p0: small distribution • Node type • DIS: small negative below x=0.02 • p0 : large negative at small-x • Large uncertainty in small-x • Positive distribution at high-x • Relative error dDG/DG (x>0.1) • Same impact as RHIC Run5 data

  15. Summary • Polarized PDF from polarized DIS data • Well determined valence quark distributions • Undetermined anti-quark and gluon distributions • Rather large uncertainties of these distributions • Reduction gluon uncertainty due to error correlation with antiquark distribution • NLO gluon term < statistical errors • Positive distribution of Dg(x) at medium and large-x region • E07-011 experiment (precise measurement ) • Constraint on Dg(x) via NLO gluon term • NLO gluon term > statistical errors • Same impact as RHIC run5 p0 data • Dg(x) from p0 production data • Node type, changing sign around x=0.1 • RHIC data: covering narrow x-region • Undetermined small-x behavior • No data in the small-x region • AAC08 numerical library: http://spin.riken.bnl.gov/aac/

  16. 1st moments of Dg(x) • Full range x=0~1 • 0.1< X <1 • CLAS data (x=0.175 ~0.55) • p0 data (s=200 GeV, pT= 1.29 ~ 7.79 GeV)

  17. Comparison of FF for p0 production • Model dependence of the FF global analysis ? • Kretzer’s FFs within LO uncertainty • KKP’s FFs without the uncertainty at large-pT • Cut of z for 2nd moments of FFs (z>0.05) • Heavy quark mass threshold • Uncertainty from NLO FFs becomes 1/3

  18. Positive Dg(x)/g(x) at large-x HERMES A1d 0.03 < xBj < 0.07, 1.2 < Q2 < 1.7 COMPASS-d: 4.5 < Q2 < 8.6 NLO gluon term Positive contribution Relative increasing for g1D euv2 : 4/9(P) → 2.5/9(D) Positive Dg(x) at large-x Other DOF for HERMES-d ? Higher Twist effects LSS, PRD73(2006)034023 Antiquark SUf(3) aymmetry D. de Florian, et al., PRD71(2005)094018 Constraint on large-x behavior of Dg(x)