Calculation of transverse momentum dependent distributions beyond the leading power

TL;DR

This paper advances the calculation of transverse momentum dependent distributions by including higher-twist contributions and target-mass corrections, providing new detailed expressions for quark distributions beyond leading power.

Contribution

It introduces a comprehensive twist-decomposition method for all eight quark TMDs and derives the first explicit expression for the pretzelosity distribution.

Findings

Derived all twist-2 and twist-3 contributions to TMD distributions.

Provided the first explicit expression for the pretzelosity distribution.

Included target-mass corrections in the small-$b$ expansion.

Abstract

We compute the contribution of twist-2 and twist-3 parton distribution functions to the small-$b$ expansion for transverse momentum dependent (TMD) distributions at all powers of $b$. The computation is done by the twist-decomposition method based on the spinor formalism for all eight quark TMD distributions. The newly computed terms are accompanied by the prefactor $(M^2b^2)^n$ and represent the target-mass corrections to the resummed cross-section. For the first time, a non-trivial expression for the pretzelosity distribution is derived.