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

TL;DR

This paper investigates two-particle scattering in Ising field theory under a weak magnetic field at temperatures above the critical point, using perturbation theory to analyze inelastic processes and their energy dependence.

Contribution

It provides explicit calculations of the 2->3 scattering cross-section to order h^2 and explores the energy growth of the total cross-section in this regime.

Findings

The 2->3 cross-section dominates the total inelastic scattering probability at all energies.

The high-energy total cross-section grows as 16 G_3 h^2 log(E).

The 2->2 process probability decays as E^(-16G_3 h^2) at high energies.

Abstract

Two-particle scattering in Ising field theory in a weak magnetic field h is studied in the regime T>T_c, using perturbation theory in h^2. We calculate explicitly the cross-section of the process 2->3 to the order h^2. 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 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 correlation function. Going beyond the leading order, we argue that at small h^2 the probability of the 2->2 process decays as E^(-16G_3 h^2) as E->infinity.