Soft gluon corrections to double transverse-spin asymmetries for small- [formula omitted] dilepton production at RHIC and J-PARC

Abstract

We calculate the double transverse-spin asymmetries, A T T ( 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 T T ( 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 T T ( Q T ) , but the significant corrections still remain and are crucial for making a reliable QCD prediction of A T T ( Q T ) . In particular, the soft gluon corrections enhance A T T ( Q T ) considerably in the small Q T region compared with the asymmetry in the fixed-order α s perturbation theory. We also derive a novel asymptotic formula which embodies those remarkable features of A T T ( Q T ) at small Q T in a compact analytic form and is useful to extract the transversity δ q ( x ) from the experimental data.