Singular and Regular Gauges in Soft Collinear Effective Theory: The Introduction of the New Wilson Line T

TL;DR

This paper addresses gauge invariance issues in soft-collinear effective theory (SCET) by introducing a new Wilson line T, which ensures gauge invariance of non-perturbative matrix elements involving transverse separations in both regular and singular gauges.

Contribution

It proposes a novel Wilson line T in SCET that depends on transverse gluon fields, extending the theory's gauge invariance to previously problematic non-perturbative matrix elements.

Findings

The existing SCET formalism cannot define certain gauge-invariant non-perturbative matrix elements.

Introducing the Wilson line T restores gauge invariance for these matrix elements.

The new Wilson line T depends solely on the transverse gluon component.

Abstract

Gauge invariance in soft-collinear effective theory (SCET) is discussed in regular (covariant) and singular (light-cone) gauges. It is argued that SCET, as it stands, is not capable to define in a gauge invariant way certain non-perturbative matrix elements that are an integral part of many factorization theorems. Those matrix elements involve two quark or gluon fields separated not only in light-cone direction but also in the transverse one. This observation limits the range of applicability of SCET. To remedy this we argue that one needs to introduce a new Wilson line as part of SCET formalism, that we call T. This Wilson line depends only on the transverse component of the gluon field. As such it is a new feature to the SCET formalism and it guarantees gauge invariance of the non-perturbative matrix elements in both classes of gauges.