Factorization for quasi-TMD distributions of sub-leading power

TL;DR

This paper develops a next-leading power factorization theorem for quasi-TMD distributions in lattice QCD, including new nonperturbative functions and demonstrating boost invariance restoration at NLP.

Contribution

It derives the NLP factorization theorem for qTMD distributions, introduces a new nonperturbative function, and demonstrates boost invariance restoration at this order.

Findings

Derived NLP factorization theorem for qTMD distributions.

Presented NLO expressions for all factorization elements.

Showed boost invariance restoration at NLP.

Abstract

The quasi-transverse-momentum dependent (qTMD) distributions are equal-time correlators that can be computed within the lattice QCD approach. In the regime of large hadron's momentum, qTMD distributions are expressed in terms of standard TMD distributions via the factorization theorem. We derive the corresponding factorization theorem at the next-leading power (NLP), and, for the first time, we present the factorized expressions for a large class of qTMD distributions of sub-leading power. The NLP expression contains TMD distributions of twist-two, twist-three, and a new lattice-specific nonperturbative function. We point out that some of the qTMD distributions considered in this work can be employed to extract the Collins-Soper kernel using the standard techniques of different-momenta-ratio. We provide NLO expressions for all the elements of the factorization theorem. Also, for the first time, we explicitly demonstrate the restoration of boost invariance in NLP TMD factorization.