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

Transverse single spin asymmetris

p p

πL

R

Xπpp )(

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

Spin dependent odderon (transversely polarized proton)

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

Remark 1

Remark 2

Remark 3

BLV solution

AnDY at RHIC, 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 ?