Transverse-momentum-dependent parton distribution function in soft-collinear effective theory

TL;DR

This paper analyzes transverse-momentum-dependent parton distribution functions within soft-collinear effective theory, clarifying their definition, radiative corrections, and scale evolution in semi-inclusive deep inelastic scattering at low transverse momentum.

Contribution

It introduces a new approach to defining TMD PDFs without extra Wilson lines and derives their renormalization group equations, highlighting their coupled scale dependence.

Findings

TMD PDFs are defined on the lightcone without extra Wilson lines.

Radiative corrections are computed with divergence cancellation.

The RG equation shows coupled dependence on longitudinal and transverse momenta.

Abstract

Transverse-momentum-dependent parton distribution functions are analyzed in semi-inclusive deep inelastic scattering at low transverse momentum using soft-collinear effective theory. The transverse-momentum-dependent parton distribution functions are defined on the lightcone without distorting the lightcone path nor adding additional soft Wilson lines. In this approach, the comparison between the integrated and unintegrated parton distribution functions becomes transparent. The procedure of computing radiative corrections in dimensional regularization is explained in detail, and the divergence, which is a product of infrared and ultraviolet divergence, is cancelled. The renormalization group equation for the transverse-momentum-dependent parton distribution functions is derived. It depends only on the relevant physical quantities and exhibits a nontrivial scaling behavior because the longitudinal momentum fraction and the transverse momentum are coupled in the renormalization group equation.