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“ The 19 th International Spin Physics Symposium ”

A new twist-3 analysis of the single transverse-spin asymmetry for pion and kaon production at RHIC. Koichi Kanazawa , Yuji Koike (Niigata Univ ). PRD 82 : 034009 (2010). “ The 19 th International Spin Physics Symposium ”. Single transverse-Spin Asymmetry (SSA). ★ FNAL E704.

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“ The 19 th International Spin Physics Symposium ”

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  1. A new twist-3 analysis of the single transverse-spin asymmetry for pion and kaon production at RHIC Koichi Kanazawa , Yuji Koike (Niigata Univ) PRD 82 : 034009 (2010) “ The 19th International Spin Physics Symposium ”

  2. Single transverse-Spin Asymmetry (SSA) ★ FNAL E704 ★ P.L. B264 (’91) 462 P.L. B261 (’91) 201 ★ SIDIS : - HERMES, COMPASS ★ etc

  3. ★Twist-3 contribution to the spin-dependent cross-section : Qiu, Sterman (‘99) Kang, Yuan, Zhou (‘10) Kanazawa, Koike (‘00) -Graphical representation of the 1stand 2ndterms : -　　　　　　　　　⇒ The 3rd term can be ignored. This study

  4. Twist-3 quark-gluon correlation functions - Two independent quark-gluon correlation functions : - Symmetry property : 2-types of contribution : - Pole contribution to the spin-asymmetry : Soft-Gluon-Pole : ⇒ “SGP and SFP” Soft-Fermion-Pole :

  5. Cross-sections by SGP and SFP ・ Complete cross-section coming from the quark-gluon correlation functions : Kouvaris, Qiu, Vogelsang, Yuan (‘06) Newly derivedKoike, Tomita (‘09) ⇒Positive asymmtry for K- was not reproduced. ⇒ Large hard cross-sections compared to SGP. - Typically, or - Simple assumption for the SFP function: ⇒ Suggest the SFP effect may be important !

  6. The aim of this study ・ First phenomenological study including the SFP effect. ⇒See the importance of the SGP and SFP contributions by fittingthe RHIC data.

  7. Data included in the fitting 61 data points in total. ・RHIC-STAR - We include all data. ・RHIC-BRAHMS • useful to disentangle flavor structure of the asymmetry. • - AN data for and K with have been included. ・E704 • - NLO-QCD cannot reproduce the unpolarized cross-section. • PTvalues at each xFare unknown. ⇒ We did not include.

  8. Strategy of analysis ・Parametrization of the SGP and SFP functions - SGP : - SFP : - Scale dependence assumed to be same as unp.PDF. ・three types of fitting - FIT.1 : SGP + SFP with 13 free parameters : - FIT.2 : Only SGP contribution with 7 free parameters : ⇒ omission of the SFP in FIT.1 - FIT.3 : Only SGP contribution with 12 free parameters : ⇒ Maximal d.o.f to SGP

  9. Results for pion - Three fits well reproduce the SSA for pions.

  10. Results for kaon - FIT.2 (Omission of SFP) fail to reproduce the AN(K-) ← not good.

  11. PT dependence of SSA at RHIC ・ PT dependence is well reproduced in all cases. - Correct values of PT at each xF of the AN data have been used in the fitting. - E704 data was not used in the fitting.

  12. Comparison with the E704 data • Predictionstend toovershoot the experimental data. • FIT.3 shows deviation from the data at small xF.

  13. SGP functions in three fits and by KQVY06 - and in FIT.3 are extreme and physically unnatural. ⇒Difficult to explain the asymmetry by only the SGP contribution.

  14. SGP and SFP functions at each flavor in FIT.1 SGP SFP • The SGP functions spread more in the larger-x region • compared with the SFP functions. • ⇒ larger contribution to AN at large xF

  15. Decomposition of SGP and SFP in FIT 1 SGP SFP -The SGP effect is dominant.

  16. Flavor decomposition for charged pion in FIT.1 SGP SFP • - Valence components of the SGP effect are dominant for each hadron.

  17. Flavor decomposition for charged kaon in FIT.1 SGP SFP • The SFP contributions are small but non-negligible, especially for kaon.

  18. Conclusion ★ SSA at RHIC are better described for all kinds of pions and kaons by the SGP + SFP contributions !

  19. BACKUP

  20. Recent results on SSA at RHIC ★ BRAHMS (‘08) ★ STAR (‘08)

  21. Validity of the NLO-QCD at RHIC ★ RHIC-STAR (‘04) ★ RHIC-BRAHMS (‘07) ⇒ Justify to use the RHIC data. ⇔ in contrast to the case at E704.

  22. Comment on fragmentation function ・ DSS fragmentation function (PRD75) - Can describe greater variety of data compared with the older ones. • Large gluon fragmentation functions • ⇒ Sensitive to the SFP contributions ・ Kretzer fragmentation function - We could not get good fit by Kretzer’s fragmentation functions.

  23. Previous analysis based on SGP mechanism Kouvaris, Qiu, Vogelsang, Yuan (‘06) ( RHIC ) ⇒Positive asymmtry for K- was not reproduced.

  24. Parameters obtained by the fitting

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