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

We calculate the double transverse-spin asymmetries, A(TT)(Q(T)), in transversely polarized Drell-Yan process at the transverse-momentum Q(T) of the produced lepton pair. We perform all-order resummation of the logarithmically enhanced contributions in the relevant Drell-Yan cross sections at small Q(T), which are due to multiple soft gluon emission in QCD, up to the next-to-leading logarithmic accuracy. The asymmetries A(TT)(Q(T)) to be observed in polarized experiments at RHIC and J-PARC are studied numerically as a function of Q(T). We show that the effects of the soft gluon resummation to the polarized and unpolarized cross sections largely cancel in A(TT)(Q(T)), but the significant corrections still remain and are crucial for making a reliable QCD prediction of A(TT)(Q(T)). In particular, the soft gluon corrections enhance A(TT)(Q(T)) considerably in the small Q(T) region compared with the asymmetry in the fixed-order alpha(s) perturbation theory. We also derive a novel asymptotic formula which embodies those remarkable features of A(TT)(Q(T)) at small Q(T) in a compact analytic form and is useful to extract the transversity delta q(x) from the experimental data. (C) 2007 Elsevier B.V. All rights reserved.