Integrable scattering theories with unstable particles

TL;DR

This paper introduces a bootstrap principle for constructing scattering theories with both unstable and stable particles, revealing new Lie algebraic structures and decoupling rules validated through models and renormalization group analysis.

Contribution

It presents a novel bootstrap framework for theories with unstable particles, including new scattering matrices and a Lie algebraic decoupling rule for RG flow prediction.

Findings

New bootstrap principle for unstable particles

Proposed Lie algebraic decoupling rule

Validated predictions with TBA analysis

Abstract

We formulate a new bootstrap principle which allows for the construction of particle spectra involving unstable as well as stable particles. We comment on the general Lie algebraic structure which underlies theories with unstable particles and propose several new scattering matrices. We find a new Lie algebraic decoupling rule, which predicts the renormalization group flow in dependence of the relative ordering of the resonance parameters. The proposals are exemplified for some concrete theories which involve unstable particles, such as the homogeneous sine-Gordon models and their generalizations. The new decoupling rule can be validated by means of our new bootstrap principle and also via the renormalization group flow, which we obtain from a thermodynamic Bethe ansatz analysis.