Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>Tc. Perturbative analysis
Abstract
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, the corresponding cross-section dominates the total cross-section (the probability of all inelastic processes) at all energies E. We show that at high energies the h2 term in the total cross-section grows as 16 G3 h2 log(E) 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(-16G3 h2) as E->infinity.
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