Single transverse spin asymmetry of dilepton production near Z⁰ pole

Using the latest quark Sivers functions extracted from the global analysis of available data on single transverse spin asymmetry (SSA), we calculate the SSA of Drell-Yan inclusive production of lepton pairs of invariant mass $Q$ at both $4<Q<9$ GeV and $Q\sim M_Z$ in $p^\uparrow p$ collisions at RHIC energies. We find that the features of the asymmetry $A_N$ for $Q\sim M_Z$ are significantly different from that when $4<Q<9$ GeV. The $A_N$ near $Z^0$ pole is positive and sizable in the central rapidity region while the $A_N$ at low $Q$ is negative and only sizable in the forward rapidity region. We show that the size of $A_N$ is sufficiently large for a wide range of $Q$ around the $Z^0$ pole, and even with the lepton pair's invariant mass integrated from Q=70 GeV to 110 GeV, the $A_N$ is still close to 10 percent for the central and near forward rapidity region. We argue that the SSAs of Drell-Yan inclusive dilepton production at low $Q$ and that near the $Z^0$ pole provide complementary information for testing the time-reversal modified universality (the sign change) of the Sivers functions.