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

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.

20 pages, 3 figures; typos corrected

References in corpus (8)

• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• Low temperature relaxational dynamics of the Ising chain in a transverse field
• Decay of particles above threshold in the Ising field theory with magnetic field
• Large-n excitations in the ferromagnetic Ising field theory in a small magnetic field: mass spectrum and decay widths
• Ward Identities and Integrable Differential Equations in the Ising Field Theory
• Formfactor perturbation expansions and confinement in the Ising field theory
• Study of the 2d Ising Model with mixed perturbation
• Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase

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