1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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