Symmetries in collinear effective theory

TL;DR

This paper explores the symmetries in collinear effective theory, including gauge and reparameterization invariances, and discusses their implications for the transformation properties of fields and physical consequences.

Contribution

It systematically analyzes the gauge, reparameterization, and residual energy symmetries in collinear effective theory and their impact on field transformations and physical results.

Findings

Gauge invariance constrains transformation properties of fields.

Reparameterization invariance affects physical predictions.

Residual energy invariance has significant physical implications.

Abstract

We consider various symmetries present in the collinear effective theory and their implications. There are collinear, soft and ultrasoft gauge symmetries and we discuss transformation properties of a collinear quark and gauge fields under these gauge transformations. If we require the gauge invariance order by order, the gauge fields have definite transformation properties. We also probe reparameterization invariance and residual energy invariance in the collinear effective theory and discuss their physical consequences.