Soft gluon corrections to double transverse-spin asymmetries for small-QTQT dilepton production at RHIC and J-PARC

We calculate the double transverse-spin asymmetries, ATT(QT)ATT(QT), in transversely polarized Drell–Yan process at the transverse-momentum QTQT of the produced lepton pair. We perform all-order resummation of the logarithmically enhanced contributions in the relevant Drell–Yan cross sections at small QTQT, which are due to multiple soft gluon emission in QCD, up to the next-to-leading logarithmic accuracy. The asymmetries ATT(QT)ATT(QT) to be observed in polarized experiments at RHIC and J-PARC are studied numerically as a function of QTQT. We show that the effects of the soft gluon resummation to the polarized and unpolarized cross sections largely cancel in ATT(QT)ATT(QT), but the significant corrections still remain and are crucial for making a reliable QCD prediction of ATT(QT)ATT(QT). In particular, the soft gluon corrections enhance ATT(QT)ATT(QT) considerably in the small QTQT region compared with the asymmetry in the fixed-order αsαs perturbation theory. We also derive a novel asymptotic formula which embodies those remarkable features of ATT(QT)ATT(QT) at small QTQT in a compact analytic form and is useful to extract the transversity δq(x)δq(x) from the experimental data.