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

The two-dimensional scaling Ising model in a magnetic field at critical temperature is integrable and possesses eight stable particles Ai (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 t4/t5 is found to be 0.233; the particle A5 decays at 47% in the channel A1A1 and for the remaining fraction in the channel A1A2. 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. 1 Spectrum and analyticity in Ising field theory Quantum field theory in 1 + 1 dimensions allows for a subclass of integrable cases. While integrability is hardly detectable at the level of correlation functions, it has very visible implications at the scattering level. Indeed, the presence of infinitely many conserved quantities forces the Smatrix to be completely elastic and factorized [1]. These properties, in turn, allow for a feature of the particle spectrum which is peculiar to integrable quantum field theories: the existence of particles with mass higher than the lowest threshold which are stable even in the absence of an internal symmetry which would prevent them from decaying. Once integrability is broken by an arbitrarily small perturbation, the stability of these particles would contradict though the analyticity requirements on the S-matrix, so that they are forced to develop a finite lifetime. This phenomenon already appears in the field theory describing the simplest universality class of critical behavior, namely that of the Ising model in a magnetic field [2]. The quantitative study of the decay processes following the breaking of integrability in Ising field theory is the subject of this paper. The scaling Ising model in two dimensions is described by the action