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We derive the time-reversal modified universality for both quark and gluonSivers function from the parity and time-reversal invariance of QCD. Wecalculate the single transverse-spin asymmetry of inclusive lepton from thedecay of $W$ bosons in polarized proton-proton collision at RHIC, in terms ofthe 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 ismeasurable for a good range of lepton rapidity at RHIC. We argue that thismeasurable lepton asymmetry at RHIC is an excellent observable for testing thetime-reversal modified universality of the Sivers function.

Test the time-reversal modified universality of the Sivers function