Transverse momentum dependent operator expansion at next-to-leading power

TL;DR

This paper develops a systematic operator expansion method for transverse momentum dependent factorization, enabling separation of power corrections and deriving the factorization theorem at next-to-leading power for various processes.

Contribution

It introduces a TMD operator expansion ordered by TMD-twist, providing a systematic way to derive TMD factorization at next-to-leading power.

Findings

Derived TMD factorization at next-to-leading power for two-state processes.

Systematic separation of kinematic and genuine power corrections.

Process dependence incorporated via boundary conditions.

Abstract

We develop a method of transverse momentum dependent (TMD) operator expansion that yields the TMD factorization theorem on the operator level. The TMD operators are systematically ordered with respect to TMD-twist, which allows a certain separation of kinematic and genuine power corrections. The process dependence enters via the boundary conditions for the background fields. As a proof of principle, we derive the TMD factorization up to the next-to-leading power $(\sim q_T/Q)$ at the next-to-leading order for any process with two detected states.