Testing the Time-Reversal Modified Universality of the Sivers Function

We derive the time-reversal modified universality for both quark and gluon Sivers functions 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 the Brookhaven National Laboratory Relativistic Heavy Ion Collider (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.