Elastic Kink-Meson Scattering in the $\Phi^4$ Double-Well Model

TL;DR

This paper computes the leading order elastic scattering amplitude between a meson and a kink in the $\

Contribution

It provides the first calculation of the one-loop elastic scattering amplitude in the $\

Findings

Identifies a resonance pole at twice the shape mode energy.

Shows classical reflectionless property of the kink.

Predicts the resonance width related to the shape mode lifetime.

Abstract

We calculate the leading order amplitude and probability for the elastic scattering of an elementary meson and a kink in the $\phi^4$ double-well model. Classically, the kink is reflectionless, and so the leading contribution arises at one loop. At this order, the scattering amplitude exhibits a pole when the incoming meson energy is twice the shape mode energy, corresponding to the excitation of an unstable resonance with the twice excited shape mode. We expect that higher order corrections will give this resonance a width equal to the inverse of the known lifetime of this unstable excitation.