(Anti-)Stokes Scattering on Kinks

TL;DR

This paper analyzes inelastic scattering processes involving quantum kinks and mesons, deriving analytic formulas for (anti-)Stokes scattering amplitudes and probabilities, with specific results for the $^4$ model.

Contribution

It provides the first analytic formulas for (anti-)Stokes scattering amplitudes on general scalar kinks, extending previous work on meson multiplication.

Findings

Derived formulas for forward and backward scattering amplitudes.

Specialized results to the $^4$ double-well kink.

Quantitative predictions for inelastic scattering probabilities.

Abstract

At leading order, there are three inelastic scattering processes beginning with a quantum kink and a fundamental meson. Meson multiplication, in which the final state is a kink and two mesons, was treated recently. In this note we treat the other two, (anti)-Stokes scattering, in which the kink's shape mode is (de-)excited and the final state contains one meson. In the case of a general scalar kink, we find analytic formulas for the forward and backward scattering amplitudes and probabilities as functions of the momentum of the incident meson. The general results are then specialized to the kink of the $\phi^4$ double-well model.