Hidden self-energy contributions of collinear functions in SCET

TL;DR

This paper investigates how self-energy contributions in soft-collinear effective theory (SCET) can be hidden within Wilson line diagrams, affecting the identification of these contributions in different operator bases.

Contribution

It introduces an analysis of self-energy contributions in SCET using different operator bases, revealing how some contributions are hidden in Wilson line diagrams.

Findings

Self-energy contributions can be identified from diagram topologies in a natural basis.

In an alternative basis, self-energy effects are hidden in Wilson line diagrams.

The choice of operator basis affects the transparency of self-energy contributions.

Abstract

Motivated by the requirement of the LSZ reduction formula to remove self-energy contributions on external legs, we examine quark self-energy contributions in soft-collinear effective (SCET) theory. We examine an operator basis that follows directly from full quantum chromodynamics (QCD) (upon application of the SCET equations of motion to express small Dirac components in terms of large Dirac components). We find that, for this basis, the self-energy contributions can be identified from their diagrammatic topologies, as in full QCD. However, for an alternative operator basis that is obtained from the direct-QCD basis by an application of Wilson-line identities, interactions are shifted from a covariant derivative to a Wilson line. Consequently, some self-energy contributions are hidden in diagrams involving Wilson lines, making their identification subtle.