Decay of particles above threshold in the Ising field theory with magnetic field

TL;DR

This paper investigates the decay properties of particles above threshold in the two-dimensional Ising model with a magnetic field, using form factor perturbation theory to analyze how small deviations from criticality affect particle stability.

Contribution

It introduces a method to compute decay widths of particles above threshold in the Ising model when integrability is slightly broken, providing quantitative lifetime ratios.

Findings

The lifetime ratio t_4/t_5 is approximately 0.233.

Particle A_5 decays predominantly into A_1A_1 and A_1A_2 channels.

Decay lifetimes increase with particle mass, enhanced by model dynamics.

Abstract

The two-dimensional scaling Ising model in a magnetic field at critical temperature is integrable and possesses eight stable particles A_i (i=1,...,8) with different masses. The heaviest five lie above threshold and owe their stability to integrability. We use form factor perturbation theory to compute the decay widths of the first two particles above threshold when integrability is broken by a small deviation from the critical temperature. The lifetime ratio t_4/t_5 is found to be 0.233; the particle A_5 decays at 47% in the channel A_1A_1 and for the remaining fraction in the channel A_1A_2. The increase of the lifetime with the mass, a feature which can be expected in two dimensions from phase space considerations, is in this model further enhanced by the dynamics.