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Two-particle scattering in Ising field theory in a weak magnetic field h isstudied in the regime T>T_c, using perturbation theory in h^2. We calculateexplicitly the cross-section of the process 2->3 to the order h^2. To thisorder, the corresponding cross-section dominates the total cross-section (theprobability of all inelastic processes) at all energies E. We show that at highenergies the h^2 term in the total cross-section grows as 16 G_3 h^2 log(E)where G_3 is exactly the third moment of the Euclidean spin-spin correlationfunction. Going beyond the leading order, we argue that at small h^2 theprobability of the 2->2 process decays as E^(-16G_3 h^2) as E->infinity.

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