Test the time-reversal modified universality of the Sivers function

TL;DR

This paper derives the modified universality of the Sivers function due to time-reversal symmetry in QCD and proposes measuring lepton asymmetry from W decay at RHIC to test this property.

Contribution

It provides a theoretical derivation of time-reversal modified universality for quark and gluon Sivers functions and suggests an experimental test at RHIC.

Findings

Lepton asymmetry from W decay is several percent and measurable.

The asymmetry can test the modified universality of the Sivers function.

Theoretical derivation based on QCD symmetries.

Abstract

We derive the time-reversal modified universality for both quark and gluon Sivers function from the parity and time-reversal invariance of QCD. We calculate the single transverse-spin asymmetry of inclusive lepton from the decay of $W$ bosons in polarized proton-proton collision at RHIC, in terms of the Sivers function. We find that although the asymmetry is diluted from the $W$ decay, the lepton asymmetry is at the level of several percent and is measurable for a good range of lepton rapidity at RHIC. We argue that this measurable lepton asymmetry at RHIC is an excellent observable for testing the time-reversal modified universality of the Sivers function.