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.

Typos corrected, references added, and Fig. 3 replaced

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• Factorization for Azimuthal Asymmetries in SIDIS at Next-to-Leading Power
• Definition and evolution of transverse momentum dependent distribution of twist-three
• Several Topics on Transverse Momentum-Dependent Fragmentation Functions
• Rapidity evolution of TMDs with running coupling
• The $q_{\mathrm{T}}$ and $\Delta {\varphi }_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities