1. 1/10 Global analysis and the impact of eRHIC data Masanori Hirai TiTech (Asymmetry Analysis Collaboration) With S. Kumano and N. Saito 2006 7 19, BNL

2. 2/10 Contents Introduction AAC analysis with DIS and  0 production –Global analysis and PDF uncertainty estimation –Spin contents : ,  g ? Issues in the global analysis of polarized PDFs –Undetermined large-x and small-x behavior Summary

3. 3/10 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  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. 4/10 AAC analysis and uncertainty estimation Initial distribution of polarized PDF Constraint condition –Positivity condition: Constraint on the large-x behavior of  f(x) Avoiding unphysical behavior of the asymmetry: A 1 (x) >1 (x  1) –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 –  2 (N=11) = 12.64: [K(N,s):  2 distribution ] Unpol PDF:GRV98 Q 0 2 = 1 GeV 2  QCD Nf=3 = 299 MeV

5. 5/10 Polarized PDFs from DIS data Added new data A 1 –COMPASS(d), HERMES(p,d), J-Lab(n) 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 current DIS data

6. 6/10 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. 7/10  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  g uncertainty Sign problem –gg process dominates  g(x)   –Positive or negative  g?  g=  0.56  2.16  2  0 : 11.18(  g>0) vs. 11.05 (  g<0) Consistent results –1 st moment (0.1<x Bj <1)  g>0: 0.30  0.30  g<0:  0.32  0.42 –Covered by DIS +  0 data Ambiguity of the small-x behavior –No experimental data

8. 8/10 Issues of the global analysis Narrow Q 2 rage (1<Q 2 <80 GeV 2 ) –Extract  g(x) via Q 2 evolution –Need data covering wide rage of Q 2 eRHIC : Q 2 <10 4 GeV 2 Large uncertainty of asymmetry A 1 (x) at large x –Undetermined large-x behavior –Need precise measurements eRHIC: High luminosity Undetermined  q(x) at small x –Fixing one parameter:  q =1.0 –No data in the small-x region eRHIC : x>10 -4 (Q 2 >1 GeV 2 )

9. 9/10 Small-x behavior of  q(x) Small-x behavior of  q(x) affects value of  –Quark spin component :  =  u v +  d v +6  q –Well determined  u v (x) and  d v (x) –  depends on extrapolated behavior of  q(x) to the small-x region –Undetermined  q(x) in the small-x region No experimental data (x<0.004)

10. 10/10 Summary Polarized PDF from polarized DIS and  0 data –  = 0.27  0.07 (Q 2 = 1 GeV 2 ) Assuming flavor SU(3) symmetry for the antiquark distributions –  g = 0.31  0.32 (Q 2 = 1 GeV 2 ) Uncertainty reduction due to  0 data Sign problem: positive or negative  g? Ambiguity of the small-x behavior Issues of current global analysis –Narrow Q 2 range (1<Q 2 <80 GeV 2 ) eRHIC: Q 2 <10 4 GeV 2 –Large uncertainty at large x High luminosity, precise measurements –Undetermined small-x behavior of  q(x) eRHIC : x>10 -4 (Q 2 >1 GeV 2 )