ssas at small x and the the anomalous magnetic moment jian zhou regensburg university based on:...
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SSAs at small x and the the anomalous magnetic moment
Jian Zhou Regensburg University
Based on: Phys.Rev. D89 (2014) 074050. ZJ arXiV:1308.4961 A. Schafer and ZJ
ECT, Trento, 2014
Outline:
Tri-gluon correlations and their asymptotic behavior
Polarized odderon & the anomalous magnetic moment
Summary
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
TMD factorization V.S. Collinear twist-3 approach
Operator defination for tri-gluon correlations
Ji 1992
Kang & Qiu 2008
Beppu, Koike, Tanaka & Yoshida 2010
Receive contributions from:
Differ from the existing results Kang & Qiu 2008
Use the different paramertization for tri-gluon correlations Braun, Manashov & Pirnay 2009
Diagram b
Diagrams c, d, e
More work will be needed to settle this issue !
Diagram a
Within the leading logarithm lnx accuracy, we made approximations
Symmetry relations Beppu, Koike, Tanaka & Yoshida 2010
Schafer, ZJ 2013
The asymptotic behavior at small x
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 ?
The odderon origin of SSAs at small x
Ahmedov, Akushevich, Kuraev & Ratcliffe 1999
Ahmedov, Antonov, Bartos, Kuraev & Zemlyanaya 2003
kovchegov & Sievert 2012
Heavy fermion model
CGC calculation
Spin independent odderon !
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
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
cbaabc AAAd
BKP equation Bartels 1980, Kwiecinski & Praszalowicz 1980
BLV Solution: high energy intercept is exactly 1 Bartels, Lipatov & Vacca 2000
Formulation in the CGCHatta, Iancu, Itakura & McLerran 2005
Formulation in Mueller’s dipole model
Kovchegov, Szymanowski & Wallon 2004
Wilson line
The odderon origin of SSAs
kovchegov & Sievert 2012CGC calculation
The interaction between Spin depenent LC wave function & the odderon from unpolarized
nucleon/nucleus
Odderon in the MV model
Mclerran, Venugopalan 1994 Jeon, Venugopalan 2004
Valence quark distribution
The expectation value of the odderon operator
Jeon,Venugopalan 2005
Odderon in the MV model
M. Burkardt 2000, 2003
M. Burkardt 2003, and also see Alessandro’s talk
ZJ 2013
Impact parameter dependent valence quark distribution
An earlier attempt to connect SSA phenomena to GPD E has been made.
Remark: The application of the MV model to proton may not be well justified.
SSA in jet production in the backward region of pp collisions
Unpolarized gluon distribution
Polarized odderon
LO Dumitru & J. Marian 2002
NLO Chirilli, Xiao & Yuan 2012
SSA for open charm production in SIDIS
Collinear twist-3 approach Kang, Qiu 2008
Beppu, Koike, Tanaka & Yoshida 2010
Hard part ( transversely polarized photon)
LO Mueller 1999; Mclerran & Venugopalan 1999 NLO Balitsky & Chirilli 2011; Beuf 2012
SSA in open charm production and DY/direct photon
KT moment of the odderon & C-odd tri-gluon correlation
Kang, Qiu, Vogelsang & Yuan 2008
Koike & Yoshida 2011, 2012
Twist-3 approach
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,
OutlookThe CGC formalism the twist-3 apporach in the dilute limit ?