Gauge-invariant TMD factorization for Drell-Yan hadronic tensor at small x

Abstract

The Drell-Yan hadronic tensor for electromagnetic (EM) current is calculated in the Sudakov region $s\gg Q^2\gg q_{\perp }^2$ with $\frac{1}{Q^2}$ accuracy, first at the tree level and then with the double-log accuracy. It is demonstrated that in the leading order in $N_c$ the higher-twist quark-quark-gluon TMDs reduce to leading-twist TMDs due to QCD equation of motion. The resulting tensor for unpolarized hadrons is EM gauge-invariant and depends on two leading-twist TMDs: $f_1$ responsible for total DY cross section, and Boer-Mulders function $h_1^{\perp }$. The order-of-magnitude estimates of angular distributions for DY process seem to agree with LHC results at corresponding kinematics.

Comments: Typos corrected, references added, and Fig. 3 replaced