On the gauge-invariance of SCET beyond leading power

TL;DR

This paper investigates the complex realization of gauge invariance in soft-collinear effective theory beyond leading power, highlighting the role of momentum conservation and implications for defining gauge-invariant jet functions.

Contribution

It reveals how gauge invariance is maintained through momentum-conservation violating terms and discusses the impact on gauge-invariant definitions of radiative jet functions.

Findings

Gauge invariance is preserved via momentum-conservation violating contributions.

Individual gauge-invariant terms can produce gauge-dependent matrix elements at subleading order.

Implications for defining gauge-invariant radiative jet functions are explored.

Abstract

We point out that the gauge-invariance of the subleading Lagrangian of soft-collinear effective theory is realised in an intricate way through momentum-conservation violating contributions. Although these terms are disregarded in diagrammatic calculations, the gauge invariance of any physical transition amplitude is preserved due to the soft equations of motion. When not working with gauge-invariant building blocks, individual manifestly gauge-invariant constituent terms in the Lagrangian may give rise to gauge-dependent matrix elements starting at $\mathcal{O}(\lambda^2)$. Implications for a gauge-invariant definition of radiative jet functions are discussed.