Unstable-particle effective field theory

TL;DR

This paper develops an effective field theory framework for unstable particles, enabling systematic and gauge-invariant calculations of resonant processes by expanding in the coupling constant and width-to-mass ratio.

Contribution

It introduces a novel EFT approach for unstable particles that handles resonant processes systematically and gauge-invariantly at various orders.

Findings

Derived NLO line-shape of a scalar resonance.

Calculated NLO and NNLO corrections for W-boson and top quark pair production.

Provided a gauge-invariant expansion method for unstable particle processes.

Abstract

Unstable particles are notorious in perturbative quantum field theory for producing singular propagators in scattering amplitudes that require regularization by the finite width. In this review I discuss the construction of an effective field theory for unstable particles, based on the hierarchy of scales between the mass, M, and the width,Gamma, of the unstable particle that allows resonant processes to be systematically expanded in powers of the coupling alpha and Gamma/M, thereby providing gauge-invariant approximations at every order. I illustrate the method with the next-to-leading order line-shape of a scalar resonance in an abelian gauge-Yukawa model, and results on NLO and dominant NNLO corrections to (resonant and non-resonant) pair production of W-bosons and top quarks.