(Anti-)Stokes scattering on kinks

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 ϕ4 double-well model.

Form factors for meson-kink scattering

“…Next an exhaustive treatment of scattering processes with probabilities of order O(g 2 ) was performed. There are only three processes, meson multiplication [23], in which the final state consists of two mesons and a kink, and (anti)-Stokes scattering [24], in which the final state consists of a single meson and a kink but an internal kink excitation is toggled. Meson multiplication was treated by evolving an incoming wave packet in Ref.…”

“…The results here justify some assumptions made in Refs. [23,25,24] regarding quantum corrections to the initial and final states in inelastic meson-kink scattering. In the short term, this was the last missing ingredient needed for the study of several problems.…”

“…Recently, we have begun a systematic treatment of such processes, as an expansion in the coupling g. The order O(g 0 ) scattering, corresponding to classical wave mechanics, was treated in Ref. [22].…”

“…Although the generalization is straightforward [22], in this paper we consider classically reflectionless kinks, such as those in the Sine-Gordon and φ 4 double-well models, for concreteness. For these, we fix the sign of k such that g * k (x) = g −k (x) and, for |x| 0, g k (x) is proportional to e −ikx .…”

“…We will treat this term in Ref. [21] where we will see that it exactly cancels a final state correction.…”