Factorization theorem for quasi-TMD distributions with kinematic power corrections

TL;DR

This paper derives a comprehensive factorization theorem for quasi-TMD distributions, including all-order kinematic power corrections, improving the accuracy of lattice and phenomenological comparisons.

Contribution

It provides the first all-orders derivation of the factorization theorem for quasi-TMDs with kinematic power corrections, maintaining frame invariance and clarifying the structure of evolution factors.

Findings

The derived expression differs from leading-power approximation by tens of percent in current lattice simulations.

Including power corrections enhances agreement between phenomenological and lattice results for the Collins-Soper kernel.

The TMD evolution factor enters as a convolution, not a simple multiplicative factor, in the corrected expression.

Abstract

We derive the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) correlator, including kinematic power corrections to all orders. The resulting expression involves only twist-two TMD distributions and is frame invariant. As in the leading-power approximation, the reduced soft factor factorizes multiplicatively; however, in contrast, the TMD evolution factor is not multiplicative but enters as a convolution with the nonperturbative TMD distribution. We present a numerical estimate of the difference between the derived expression and the leading-power approximation, finding it to be of the order of tens of percent for current lattice simulations. We also demonstrate that the inclusion of these corrections improves the agreement between phenomenological extractions of the Collins-Soper kernel and lattice results.