1. 1/8 Constraint on  g(x) from  0 production at RHIC Masanori Hirai Tokyo Tech (Asymmetry Analysis collaboration) With S. Kumano and N. Saito Phys.Rev.D74, 014015 (2006); hep-ph/0603217 2006, Oct 05 @Kyoto

2. 2/8 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 = 1/2  +L q : Generalized PDF from DVCS  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

3. 3/8 Spin asymmetry of  production Cross section –gg  gg, gg  qq,qg  qg –qq  qq, qq’  qq’ –qq  qq, qq  gg, gg  qq Consistent with unpolarized data –Fragmentation functions (FFs) Determined by e + e - data Ambiguity of D g  (z) PRL91, 241803 (2003)

4. 4/8 Initial distributions of polarized PDFs Initial distribution at Q 0 2 – –Chose of the functional form is arbitrary –Source of model dependence Constraint condition: –Positivity condition: Constraint of  f(x) at large x Avoiding unphysical behavior for the asymmetry: A 1 (x) >1 (x  1) –Antiquark SU F (3) symmetry:  0 asymmetry in low p T : gg process dominates –Insensitive to flavor dependence of  f(x) Fixed 1 st moments:  u v =0.926,  d v =  0.341 Fixed  q =1.0: undetermined small-x behavior

5. 5/8 AAC global analysis Added new data –DIS A 1 [=g 1 *2x(1+R)/F 2 ] COMPASS(d), HERMES(p,d), J-Lab(n) –  0 data PHENIX RUN05 preliminary data Total # of data: 421 –DIS: 413 (Q 2  1GeV 2 ) –  0 : 8 (1<p T <10 GeV,  R,F =p T ) NLO analysis –DIS:MS scheme –  0 : K factor: =1, =1.6 B. Jager, et al, PRD67,054005 (2000) –  2 (/d.o.f.) = 370.47 (0.90) DIS:359.29  0 : 11.18 Q 2 dependence of pol-PDFs –DGLAP eq –Q 0 2 = 1GeV 2 Minimizing  2 –Scaling error of  0 data is not included Error estimation –Hessian method –  2 (N=11) = 12.64

6. 6/8  g from DIS and  0 data 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) 40% scaling error is not include

7. 7/8 Small-x behavior of  g(x) 1st moment –  g>0: 0.31  0.32 –  g<0:  0.56  2.16 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 Huge uncertainty of  g<0 –Ambiguity of small-x behavior –No constraint on the behavior  g(x) is positive at large x

8. 8/8 Summary Gluon spin component  g –DIS only:  g = 0.47  1.08 Small contribution through Q 2 evolution (1<Q 2 <80 GeV 2 ) and higher order correction –DIS+  0 :  g = 0.31  0.32 Direct contribution to  0 cross section in low and medium p T Significant reduction of its uncertainty Assuming  g > 0 Sign problem:positive or negative  g ? –  g =  0.56  2.16 (DIS+  0 ) gg process dominates in low p T :  g(x)   Ambiguity of the small-x behavior of  g(x) Need constraint on the behavior

9. 9/8

10. 10/8 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) asymmetry D. de Florian, et al, PRD71(2005)094018

11. 11/8 Polarized PDFs by AAC analysis Improvements –  d v (x): J-Lab(n) data –  q(x): COMPASS and HERMES data –  g(x): PHENIX RUN05 data