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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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a new twist 3 analysis of the single transverse spin asymmetry for pion and kaon production at rhic

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 ”

single transverse spin asymmetry ssa
Single transverse-Spin Asymmetry (SSA)

★ FNAL E704

P.L. B264 (’91) 462

P.L. B261 (’91) 201

★ SIDIS :

- HERMES, COMPASS

★ etc

slide3

★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

twist 3 quark gluon correlation functions
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 :

cross sections by sgp and sfp
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 !

the aim of this study
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.

data included in the fitting
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.

strategy of analysis
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

results for pion
Results for pion

- Three fits well reproduce the SSA for pions.

results for kaon
Results for kaon

- FIT.2 (Omission of SFP) fail to reproduce the AN(K-)

← not good.

p t dependence of ssa at rhic
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.

comparison with the e704 data
Comparison with the E704 data
  • Predictionstend toovershoot the experimental data.
  • FIT.3 shows deviation from the data at small xF.
sgp functions in three fits and by kqvy06
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.

sgp and sfp functions at each flavor in fit 1
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
d ecomposition of sgp and sfp in fit 1
Decomposition of SGP and SFP in FIT 1

SGP

SFP

-The SGP effect is dominant.

flavor decomposition for charged pion in fit 1
Flavor decomposition for charged pion in FIT.1

SGP

SFP

  • - Valence components of the SGP effect are dominant for each hadron.
flavor decomposition for charged kaon in fit 1
Flavor decomposition for charged kaon in FIT.1

SGP

SFP

  • The SFP contributions are small but non-negligible, especially for kaon.
conclusion
Conclusion

★ SSA at RHIC are better described

for all kinds of pions and kaons

by the SGP + SFP contributions !

recent results on ssa at rhic
Recent results on SSA at RHIC

★ BRAHMS (‘08)

★ STAR (‘08)

validity of the nlo qcd at rhic
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.

comment on f ragmentation function
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.

previous analysis based on sgp mechanism
Previous analysis based on SGP mechanism

Kouvaris, Qiu, Vogelsang, Yuan (‘06)

( RHIC )

⇒Positive asymmtry for K- was not reproduced.