Quark and Gluon Sivers Functions S. Brodsky D.S. Hwang J. Soffer Ivan Schmidt Como 2005

Sivers Function New distribution functions: Corrections to collinear approximation Possible explanation of Single Spin Asymmetries Among these: Sivers distribution function: Collins fragmentation function: Distr. of unpolarized quark in trans. polarized target Fragm. of trans. polarized quark into unpolarized hadron

Many times they appear together: transversity Sivers: T-odd correlation Azimuthal asymmetry with respect to (1993) Incorrect. Target rest frame Azimuthal asymmetry Transverse spin Helicity basis

Final state interactions Two spin amplitudes which couple to the same final state Helicity flip Helicity non-flip Interference (2) Non-trivial phase difference Conclusions SSA : QCD at amplitude level. SSA : understanding L. Similar to Need Im : cannot be tree level. Final state interactions

Sivers SSA shadowing Simple model Drell-Yan crossing Initial state interactions crossing Drell-Yan Final state interactions

How to obtain the Sivers function ? Drell-Yan: initial state interactions ( different gauge links ) How to obtain the Sivers function ? Weak interaction processes Produced quark left-handed Transversity cannot contribute In more detail (Boer, Mulders):

Parametrization which can be projected for the specific process. 1) Electromagnetic case : result: Drell-Yan crossing

2) Charged currents SSAs in get only Similar analysis for only Sivers 3) Neutral currents same SSA as in the em case factor with respect to em case

Some phenomenology Sivers Factorized form (Anselmino et al.) flavor separation

Only Sivers (photon does not fragment) Gluon Sivers function Gluon contribution to proton amm (J. Soffer, I. S.) Photon production Jet correlations D meson production (Boer, Vogelsang) Proposals (Anselmino et al.) Only Sivers (photon does not fragment) Unpolarized Gluon distribution Hard process dominant t-channel

SSA for Sivers functions quark Sivers function gluon Sivers function dominates gluons cannot have transverse spin Sivers functions quark Sivers function gluon Sivers function

Identify kinematic region where gluon Sivers function dominates : Take GeV for integrated low values contribute

Other possibilities: no integration more difficult experimentally quark annihilation dominates Prompt photon production at high is a good probe for extracting the gluon Sivers function. Conclusion: The Sivers function has interesting physics information