Pinched Gluon Vertex Operator in Super-Worldline Formalism

TL;DR

This paper reformulates the pinched gluon vertex operator within super worldline formalism, revealing it as a product of two gluon operators with delta-function insertions, and applies this to two-loop QED corrections in gluon scattering.

Contribution

It introduces a super worldline formalism approach to the pinched gluon vertex operator, providing new formulae for pinched N-point functions in two-loop diagrams.

Findings

Pinched vertex operators are equivalent to delta-function insertions.

Derived explicit formulae for two-loop QED corrections to gluon scattering.

Unified the pinched vertex operator concept within super worldline formalism.

Abstract

We reformulate, using super worldline formalism, the pinched gluon vertex operator proposed by Strassler. The pinched vertex operator turns out to be the product of two gluon vertex operators with the insertion of $\delta$-function which makes the super distances between them zero. Thus the pinch procedures turn out to be nothing but the insertions of $\delta$-function. Applying our formulation to two-loop diagrams which are the QED correction to gluon scatterings via a single spinor loop, with the QED charge e being replaced by the strong coupling g, we show various formulae on pinched N-point functions.