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

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 1 A 1 and for the remaining fraction in the channel A 1 A 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.