Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>Tc. Perturbative analysis

Two-particle scattering in Ising field theory in a weak magnetic field h is studied in the regime T>Tc, using perturbation theory in h². We calculate explicitly the cross-section of the process 2→3 to the order h². To this order, σ2→3 dominates σ_tot (the probability of all inelastic processes) at all energies E. We show that at high energy the h²-term in σ_tot grows as 16G3h²logE, where G3 is exactly the third moment of the Euclidean spin-spin correlation function. Going beyond the leading order, we argue that at small h2 the probability of the 2→2 process decays as E^-16G3h2 as E→infin;.