The heavy quark decomposition of the S-matrix and its relation to the pinch technique

TL;DR

This paper introduces a method to decompose the S-matrix into gauge-invariant parts by analyzing limits with heavy external particles, linking it to the pinch technique and ensuring physical consistency.

Contribution

It presents a novel decomposition of the S-matrix into gauge-invariant sub-amplitudes using mass limits, connecting to the pinch technique at one-loop level.

Findings

Effective gluon self-energy matches the gauge-independent pinch technique result.

Decomposition applies to arbitrary gluonic n-point functions.

Method ensures gauge invariance of sub-amplitudes.

Abstract

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.