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

Abstract

We calculate the double transverse-spin asymmetries, $\text{aqt}$, 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 $\text{aqt}$ 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 $\text{aqt}$, but the significant corrections still remain and are crucial for making a reliable QCD prediction of $\text{aqt}$. In particular, the soft gluon corrections enhance $\text{aqt}$ 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 $\text{aqt}$ at small $Q_T$ in a compact analytic form and is useful to extract the transversity $\delta q(x)$ from the experimental data.

Comments: 26 pages, 12 figures, typos corrected, references added, version to appear in Nucl. Phys. B