1. AAC Global Analysis Naohito Saito (KEK) for Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) shunzo.kumano@kek.jphttp://research.kek.jp/people/kumanos/ AAC: http://spin.riken.bnl.gov/aac/

2. Contents  Introduction to polarized PDFs Global analysis of longitudinally polarized PDFs  Polarized PDFs of AAC  AAC (Asymmetry Analysis Collaboration)

3. Papers on polarized PDFs T. Gehrmann and W. J. Stirling, Z. Phys. C65 (1995) 461; Phys. Rev. D53 (1996) 6100. D. de Florian, L. N. Epele, H. Fanchiotti, C. A. Garcia Canal, and R. Sassot (+G. A. Navarro), Phys. Rev. D51 (1995) 37; D57 (1998) 5803; D62 (2000) 094025; D71 (2005) 094018. M. Glück, E. Reya, M. Stratmann, and W. Vogelsang, Phys. Lett. B359 (1995) 201; Phys. Rev. D53 (1996) 4775; D63 (2001) 094005. D. de Florian, R. Sassot, M. Stratmann, and W. Vogelsang, arXiv:0804.0422 [hep-ph]. G. Altarelli, R. D. Ball, S. Forte, and G. Ridolfi, Nucl. Phys. B496 (1997) 337; Acta Phys. Pol. B29 (1998) 1145. C. Bourrely, F. Buccella, O. Pisanti, P. Santorelli, and J. Soffer, Prog. Theor. Phys. 99 (1998) 1017; Eur. Phys. J. C23 (2002) 487; C41 (2005) 327; Phys. Lett. B648 (2007) 39. L. E. Gordon, M. Goshtasbpour, and G. P. Ramsey, Phys. Rev. D58 (1998) 094017. SMC (B. Adeva et al.), Phys. Rev. D58 (1998) 112002. E. Leader, A. V. Sidrov, and D. B. Stamenov, Phys. Rev. D58 (1998) 114028; Eur. Phys. J. C23 (2002) 479; PRD67 (2003) 074017; JHEP 0506 (2005) 033; PRD73 (2006) 034023; D75 (2007) 074027. AAC (Y. Goto et al., M. Hirai et al.), PRD62 (2000) 034017; D69 (2004) 054021; D74 (2006) 014015. J. Bartelski and S. Tatur, Phys. Rev. D65 (2002) 034002. J. Blümlein and H. Böttcher, Nucl. Phys. B636 (2002) 225. It is likely that I miss some papers! (Analyses of experimental groups)

4. Situation of data for polarized PDFs Neutrino factory: ~10 years later Small-x: EIC (eRHIC, ELIC) ? Charm: EIC (eRHIC, ELIC) ? RHIC pp: RHIC RHIC-Spin program should play an important role in determining polarized PDFs. J-PARC GSI-FAIR (MRST, hep/ph-9803445)

5. (from H1 and ZEUS, hep-ex/0502008) F 2 data for the proton [AAC, PRD74 (2006) 014015] It may be possible to remove small Q 2 data in an analysis of unpolarized PDFs, whereas it is difficult to remove them in g 1 (or A 1 ).

6. Comments on the previous figure

7. Three publications: (AAC00) Y. Goto et al., Phys. Rev. D62 (2000) 034017. (AAC03) M. Hirai, S. Kumano, N. Saito, Phys. Rev. D69 (2004) 054021; (AAC06) D74 (2006) 014015. Original Members: Y. Goto, N. Hayashi, M. Hirai, H. Horikawa, S. Kumano, M. Miyama, T. Morii, N. Saito, S. Kumano, M. Miyama, T. Morii, N. Saito, T.-A. Shibata, E. Taniguchi, T. Yamanishi T.-A. Shibata, E. Taniguchi, T. Yamanishi (Theorist, Experimentalist) http://spin.riken.bnl.gov/aac/ Asymmetry Analysis Collaboration (AAC) Active members now

8.  2000 version (AAC00) - Q 2 dependence of A 1, positivity -  q at small and large x   issue  2004 version (AAC03) - uncertainty estimation (very large  g uncertainty, impact of accurate g 1 p (E155)) - error correlation between  g and  q  2006 version (AAC06) - include RHIC-Spin  0 (  g uncertainty is significantly reduced) -  g at large x ? (Q 2 difference between HERMES and COMPASS) -  g < 0 solution at x < 0.1  2008 ? - effects of future JLab data (g 1 d ) on  g

9. General strategies for determining polarized PDFs Leading Order (LO)Next to Leading Order (NLO) Unpolarized PDFs

10. Initial distributions   fit to the data [p, n ( 3 He), d] We analyzed the data with the following conditions. unpolarized PDF GRV98 initial Q 2 Q 0 2 = 1 GeV 2 number of flavor N f = 3

11. Analysis procedure

12. AAC00 (Some Highlights)

13. Actual fit to A 1 data (AAC00) “neutron” proton deuteron * Used data set as raw as Possible

14. Q 2 dependence of A 1 Q 2 independence assumption was sometimes used for getting g 1 from A 1 data. 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.5110100 A 1 p Q 2 (GeV 2 ) LO NLO E143 SMC HERMES x = 0.117 A 1 is Q 2 dependent especially at small Q 2 (< 2 GeV 2 ). The lack of accurate Q 2 dependent data at small x makes the determination of  g very difficult. Figure from AAC00 analysis

15. “Spin content”   (from AAC00)

16. AAC03 (Some Highlights)

17. Error estimation Hessian method  2 (  ) is expanded around its minimum  0 (  =parameter) where the Hessian matrix is defined by In the  2 analysis, 1  standard error is The error of a distribution F(x) is given by

18. Polarized PDFs (AAC03) PDF uncertainties are reduced by including precise (E155-p) data Valence-quark distributions are well determined –Small uncertainties of  u v,  d v Antiquark uncertainty is significantly reduced – g 1 p  4  u v +  d v +12  q  g (x) is not determined –Large uncertainty –Indirect contribution to g 1 p –Correlation with antiquark AAC03 uncertainties AAC00 uncertainties AAC00  AAC03 (with E155-p) E155 data

19. (A 1 exp -A 1 theo )/A 1 theo at the same Q 2 point

20. Correlation between  q(x) and  g(x) analysis with  g(x)=0 at Q 2 =1 GeV 2  2 /d.o.f. = 0.915  q v (x) uncertainties are not affected antiquark uncertainties are reduced Strong correlation with  g(x) Note: correlation with  g(x) is almost terminated in the  g=0 analysis The error band shrinks due to the correlation with  g(x).  g=0 uncertainties AAC03 uncertainties

21. Trial Fit! Utilized NLO  0 calculation (thanks to Vogelsang and Stratmann) –to find “relevant-x” for each p T bin Trial Fit to –A*x (GRSV ~ 1*x) –A*x*x From PANIC05 talk

22. AAC06

23. Gluon polarization at large x AAC, PRD74 (2006) 014015: Analysis without higher-twist effects NLO  C G =0 This term is terminated. x=0.001 x=0.05 x=0.3

24. However, it may be a higher-twist effect. LSS, PRD73 (2006) 034023. LT fit LT+HT fit Leading Twist (LT) Higher Twist (HT) LT+HT fit, only LT term is shown At this stage, we cannot conclude that the difference between the HERMES and COMPASS data should be 100% HT or HT+  G(large x)>0, or 100%  G(large x)>0 effects.

25. Parton distribution functions Parton interactions Fragmentation functions Description of  0 production

26. Subprocesses The  0 production process is suitable for finding the gluon polarization  g. (from Torii’s talk at Pacific-Spin05)

27. Comparison of fragmentation functions in pion Gluon and light-quark fragmentation functions have large uncertainties, but they are within the uncertainty bands.  The functions of KKP, Kretzer, AKK, DSS, and HKNS are consistent with each other. All the parametrizations agree in charm and bottom functions. (KKP) Kniehl, Kramer, Pötter (AKK) Albino, Kniehl, Kramer (HKNS) Hirai, Kumano, Nagai, Sudoh (DSS) de Florian, Sassot, Stratmann M. Hirai, SK, T.-H. Nagai, K. Sudoh, PRD75 (2007) 094009. A code is available at http://research.kek.jp/people/kumanos/ffs.html

28. Analysis with RHIC pion data (AAC06) AAC03 AAC06 (with PHENIX π 0 )

29. Possibility of negative gluon polarization  g < 0  0 production data do not distinguish between  g 0 Possibility of a node-type ∆g(x) for explaining p T =2.38 GeV (Type 3).

30. Roles of RHIC-pion data Polarized PDFs, especially  g, are better determined by the additional RHIC-  0 data. (AAC06)

31. Gluon polarization from lepton scattering S. Koblitz@DIS07 (AAC06)

32. Situation of g 1 measurements and polarized PDF errors

33. Comparison with other parameterizations

34. 1st moments –GRSV01(Sta) [ Phys. Rev. D63 (2001) 094005 ] –LSS01 (MS) [ Eur.Phys.J. C23 (2002) 479 ] –BB02 (SET3) [ Nucl. Phys. B636 (2002) 225 ] –DNS05 (KKP) [ Phys. Rev. D71 (2005) 094018 ] (Q 2 =10 GeV 2 ) gg  AAC06 0.31  0.320.27  0.07 AAC03 0.50  1.270.21  0.14 GRSV010.4200.204 LSS0.6800.210 BB1.0260.138 DNS0.5740.311

35. AAC08 ?

36. Effects of expected JLab E07-011 data “Expected data” from Xiaodong Jiang AAC asymmetries Analyses with / without E07-011 data in comparison with effects of RHIC π 0 data Two initial functions for∆g(x) “positive” “node” x

37. Effects of expected JLab E07-011 data preliminary Positivity is not satisfied at this stage! preliminary

38. ∆g(x) with PHENIX run-5 or JLab E07-011 data preliminary Significant improvements Note: π 0 data are from run-5 although it may not be a good idea to compare future data with past ones. JLab-E07-011 is comparable to RHIC run-5 π 0 in determining ∆g(x). preliminary Positivity is not satisfied.

39. Summary of the AAC global analysis for polarized PDFs –  u v (x),  d v (x) are determined well –  = 0.27  0.07 (Q 2 = 1 GeV 2 ) –  g(x) could not be well constrained AAC-polarized-pdfs code could be obtained from http://spin.riken.bnl.gov/aac/ Uncertainties of polarized PDFs Effects of E155-proton data Global analysis also with  g=0 Error correlation between  g and  q Better  g determination by RHIC-pion  g determination at large x by scaling violation (HERMES, COMPASS) Possibility of a node-type  g (  g>0 at x>0.1,  g<0 at x<0.1) AAC03 AAC06 AAC08 ? in progress

40. The End