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1/9 Constraint on g(x) at large-x Bj Masanori Hirai Titech (Asymmetry Analysis collaboration) With S. Kumano and N. Saito hep-ph/0603213 2006 4 22,TUKUBA

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2/9 Contents Introduction AAC analysis with DIS and 0 production –Global analysis and PDF uncertainty estimation –Spin contents : , g ? –Comparison with experimental data and other PDFs set Large-x behavior from HERMES and COMPASS data –Positive g(x) at large-x Bj Summary

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3/9 Introduction Origin of the nucleon spin 1/2 –1/2 = 1/2 + g + L q,g –Quark spin component from polarize DIS: 0.1-0.3 Orbital angular momentum L q,g ? –J q = q+L q : Generalized PDF from DVCS –SSA: Sivers function ? g is an important piece of the spin puzzle ! –Undetermined g = 0.49 1.27 (AAC03) –Experimental data from RHIC-Spin Prompt photon, Jet, heavy quark production, et al. – 0 production PRL93, 202002 (2004) RUN05

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4/9 AAC analysis and uncertainty estimation Initial distribution of polarized PDF Constraint condition –Positivity condition: Constraint on the large-x behavior of f(x) –Antiquark SU(3) f symmetry: Fixed 1 st moments: u v =0.926, d v = 0.341 Fixed q =1.0: undetermined small-x behavior PDF uncertainty by Hessian method –N=11, 2 = 12.64: [K(N,s): 2 distribution ] Unpol PDF:GRV98 Q 0 2 = 1 GeV 2 QCD Nf=3 = 299 MeV

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5/9 g from DIS Added new data A 1 (=g 1 /F 1 ) –HERMES(p,d), J-Lab(n) COMPASS(d) –Total # of data: 413 (Q 2 1GeV 2 ) NLO analysis –MS scheme – 2 (/d.o.f.) = 358.05 (0.89) = 0.25 0.10 –Well determined quark and antiquark distributions –J-Lab: d v (x) at large-x –HERMES,COMPASS: q(x) g = 0.47 1.08 –Undetermined by only DIS

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6/9 Spin content , g –AAC06 (DIS only) –BB02 (ISET4) : Nucl. Phys. B636 (2002) 225 –GRSV01(Sta) : Phys. Rev. D63 (2001) 094005 –LSS05 (MS) : Phys. Rev. D73 (2006) 034023

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7/9 g from 0 production (RUN05) 1 st moment g –0.31 0.32 (DIS+ 0 ) –0.47 1.08 (DIS only) Significant reduction of the g uncertainty Sign problem –gg process dominates g(x) Positive or negative g? 2 0 : 11.18( g>0) vs. 11.05 ( g<0) (8 data points) Consistent results –1 st moment (0.1<x Bj <1) g>0: 0.30 0.30 g<0: 0.32 0.42 –DIS + 0 data covered –Large-x is positive

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8/9 Constraint on large-x behavior of g(x) Positive g(x)/g(x) at large-x –HERMES A 1 d 0.03 < x Bj < 0.07, 1.2 < Q 2 < 1.7 COMPASS-d: 4.5 < Q 2 < 8.6 – NLO gluon term Positive contribution Relative increasing for g 1 D –e uv 2 : 4/9(P) → 2.5/9(D) Positive g(x) at large-x Other DOF for HERMES-d ? –Higher Twist effects LSS, PRD73(2006)034023 –Antiquark SU f (3) aymmetry D. de Florian, et al., PRD71(2005)094018

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9/9 Summary Polarized PDF from polarized DIS data – Ave = 0.17 0.07 (Q 2 = 1 GeV 2 ) – g(x) could not be determined g Ave =0.29 0.75 –Positive g(x) at large-x HERMES-d (0.03 < x Bj < 0.07, 1.2 < Q 2 < 1.7 ) Positive NLO gluon term 0 production at RHIC-Spin –RUN05 0 : g = 0.31 0.32 (AAC06, Q 2 = 1 GeV 2 ) –positive or negative g ? – g <0 Ambiguity of small-x behavior of g(x) Need constraint on the behavior

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