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SSAs at small x and the the anomalous magnetic moment

SSAs at small x and the the anomalous magnetic moment. Jian Zhou Regensburg University. ECT, Trento, 2014. Based on: Phys.Rev. D89 (2014) 074050. ZJ arXiV:1308.4961 A. Schafer and ZJ. Outline:. Tri-gluon correlations and their asymptotic behavior

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SSAs at small x and the the anomalous magnetic moment

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  1. SSAs at small x and the the anomalous magnetic moment Jian Zhou Regensburg University ECT, Trento, 2014 Based on: Phys.Rev. D89 (2014) 074050. ZJ arXiV:1308.4961 A. Schafer and ZJ

  2. Outline: • Tri-gluon correlations and their asymptotic behavior • Polarized odderon & the anomalous magnetic moment  • Summary

  3. L π p p R Transverse single spin asymmetris

  4. TMD factorization V.S. Collinear twist-3 approach TMD factorization approach: quark Siverse distribution gluon Siverse distribution Collinear twist-3 approach:quark-gluon correlation (ETQS function) tri-gluon correlations We focuse on tri-gluon correlations, in particular, its asymptotic behavior at small x

  5. Operator defination for tri-gluon correlations Ji 1992 Kang & Qiu 2008 Receive contributions from: Beppu, Koike, Tanaka & Yoshida 2010

  6. Diagram a Diagram b Diagrams c, d, e Differ from the existing resultsKang & Qiu 2008 Use the different paramertization for tri-gluon correlations Braun, Manashov & Pirnay 2009 More work will be needed to settle this issue !

  7. The asymptotic behavior at small x Within the leading logarithm lnx accuracy, we made approximations Symmetry relations Beppu, Koike, Tanaka & Yoshida 2010 Schafer, ZJ 2013

  8. Phenomenological implications I. Gluon Sivers function could change sign at small x II. Gluon Sivers function dies out quickly with decreasing x III. C-odd tri-gluon correlation dominates SSA at small x AUT→ Constant, when x →0 ?

  9. The odderon origin of SSAs at small x Heavy fermion model Ahmedov, Akushevich, Kuraev & Ratcliffe 1999 Ahmedov, Antonov, Bartos, Kuraev & Zemlyanaya 2003 CGC calculation kovchegov & Sievert 2012 Spin independent odderon !

  10. Elastic hadron-hadron scattering In Regge theory, an object exchanged called pomeron, C=+1 In QCD, pomeron modeled as two gluon exchange(Low-Nussinov Pomeron) BFKL pomeron, resuming leading higher order corrections log(s) Leading to the growth of cross section with energy

  11. Odderon Regge exchange with vacuum quantum numbers except for C=-1 Lukaszuk & Niolescu,1974 Responsible for the difference between proton-proton and proton-antiproton scatterings. In PQCD, exchange of three gluon in a colorless C=-1 state BKP equationBartels1980, Kwiecinski & Praszalowicz 1980 BLV Solution:high energy intercept is exactly 1Bartels, Lipatov & Vacca 2000

  12. Formulation in the CGC Formulation in Mueller’s dipole model Kovchegov, Szymanowski & Wallon 2004 Hatta, Iancu, Itakura & McLerran 2005 Wilson line

  13. The odderon origin of SSAs CGC calculation kovchegov & Sievert 2012 The interaction between Spin depenent LC wave function & the odderon from unpolarized nucleon/nucleus

  14. Spin dependent odderon (transversely polarized proton)

  15. Odderon in the MV model Mclerran, Venugopalan 1994 Jeon, Venugopalan 2004 The expectation value of the odderon operator Jeon,Venugopalan 2005 Valence quark distribution

  16. Odderon in the MV model Impact parameter dependent valence quark distribution M. Burkardt 2000, 2003 ZJ 2013 • An earlier attempt to connect SSA phenomena to GPD E has been made. M. Burkardt 2003, and also see Alessandro’s talk Remark:The application of the MV model to proton may not be well justified.

  17. SSA in jet production in the backward region of pp collisions LODumitru & J. Marian 2002 NLOChirilli, Xiao & Yuan 2012 Unpolarized gluon distribution Polarized odderon

  18. Remark 1 Remark 2 Remark 3 BLV solution

  19. AnDY at RHIC, 2012

  20. SSA for open charm production in SIDIS LOMueller 1999; Mclerran & Venugopalan 1999 NLOBalitsky & Chirilli 2011; Beuf 2012 Hard part ( transversely polarized photon) • Collinear twist-3 approach Kang, Qiu 2008 Beppu, Koike, Tanaka & Yoshida 2010

  21. KT moment of the odderon & C-odd tri-gluon correlation • SSA in open charm production and DY/direct photon Twist-3 approach Kang, Qiu, Vogelsang & Yuan 2008 Koike & Yoshida 2011, 2012

  22. Summary The C-odd tri-gluon correlation dominates SSA at small x The gluon Sivers distribution is irrelevant to SSA phenomenology at small x Identify a spin dependent odderon, propotional to the anomalous magnetic moment  the moment of polarized odderon related to the C-odd tri-gluon correlation according to the BLV solution, Outlook The CGC formalism the twist-3 apporach in the dilute limit ?

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