An effective Lagrangian approach for unstable particles

TL;DR

This paper introduces a gauge-invariant effective Lagrangian method to accurately incorporate unstable particles' decay widths into theoretical calculations, ensuring consistent and reliable predictions in particle physics.

Contribution

It presents a new gauge-invariant resummation technique using effective Lagrangians to handle unstable particles in quantum field theory calculations.

Findings

Constructed gauge-invariant tree-level amplitudes with decay widths included

Derived modified Feynman rules for unstable particles

Applied method to particles like top-quark, W, Z, and Higgs bosons

Abstract

We propose a novel procedure for handling processes that involve unstable intermediate particles. By using gauge-invariant effective Lagrangians it is possible to perform a gauge-invariant resummation of (arbitrary) self-energy effects. For instance, gauge-invariant tree-level amplitudes can be constructed with the decay widths of the unstable particles properly included in the propagators. In these tree-level amplitudes modified vertices are used, which contain extra gauge-restoring terms prescribed by the effective Lagrangians. We discuss the treatment of the phenomenologically important unstable particles, like the top-quark, the $W$- and $Z$-bosons, and the Higgs-boson, and derive the relevant modified Feynman rules explicitly.