Dressed scalar propagator in a non-abelian background from the worldline formalism

TL;DR

This paper develops a worldline formalism approach to compute the propagator of a colored scalar particle in a non-abelian gauge background, explicitly including multiple gluon interactions and arbitrary color charge configurations.

Contribution

It introduces a master formula for the scalar propagator with multiple gluons attached, extending previous loop-based results to open worldlines and arbitrary color tensors.

Findings

Derived a master formula for scalar propagator with gluons

Extended formalism to arbitrary color tensor products

Provided a new worldline approach for non-abelian backgrounds

Abstract

We study the propagator of a colored scalar particle in the background of a non-abelian gauge field using the worldline formalism. It is obtained by considering the open worldline of a scalar particle with extra degrees of freedom needed to take into account the color charge of the particle, which we choose to be in the fundamental representation of the gauge group. Specializing the external gauge field to be given by a sum of plane waves, i.e. a sum of external gluons, we produce a master formula for the scalar propagator with an arbitrary number of gluons directly attached to the scalar line, akin to similar formulas derived in the literature for the case of the scalar particle performing a loop. Our worldline description produces at the same time the situation in which the particle has a color charge given by an arbitrarily chosen symmetric or antisymmetric tensor product of the fundamental.