Kink Form Factors

TL;DR

This paper develops a perturbation theory to calculate form factors for elastic meson-kink scattering, considering both localized wave packets and delocalized states, and compares quantum corrections across models.

Contribution

It introduces a linearized soliton perturbation framework to compute form factors for meson-kink scattering, including quantum corrections for localized wave packets.

Findings

Classical kink form factors match previous results by Goldstone and Jackiw.

Quantum corrections for delocalized kinks agree with earlier findings in the $$4 and Sine-Gordon models.

Localized wave packets exhibit corrections scaling with wave packet width, affecting coherent scattering.

Abstract

We use a recently constructed linearized soliton sector perturbation theory to calculate the form factors relevant to the elastic scattering of ultrarelativistic mesons off of nonrelativistic kinks. Both localized kink wave packets and also delocalized momentum eigenstate kinks are considered. In the delocalized case, the leading term is just the classical kink solution, as was found by Goldstone and Jackiw. The leading delocalized quantum correction agrees with that found by Gervais, Jevicki and Sakita in the $\phi^4$ model and Weisz in the Sine-Gordon model. In the case of localized kink wave packets, some corrections are found which scale with the wave packet width, and so will be relevant for the coherent scattering of mesons off of kink wave packets.