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

TL;DR

This paper derives a gauge-invariant TMD factorization for the Drell-Yan process at small x, demonstrating the reduction of higher-twist TMDs to leading-twist and comparing results with LHC data.

Contribution

It provides a gauge-invariant factorization framework for the Drell-Yan hadronic tensor at small x, including higher-twist reduction and phenomenological estimates.

Findings

Tensor depends on two leading-twist TMDs: $f_1$ and $h_1^ot$

Results are consistent with LHC angular distribution data

Higher-twist effects reduce to leading-twist in large $N_c$ limit

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 ${1\over Q^2}$ 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.