# Interacting kinks and meson mixing

## TL;DR

This paper uses a perturbation scheme to analyze weakly interacting kinks from two scalar fields, revealing condensate behaviors, mass effects, bound states, and meson flavor mixing with implications for kink interactions.

## Contribution

It introduces a novel perturbation approach to study kink interactions, condensate formation, and meson mixing effects in a two-field scalar model.

## Key findings

- Condensates inhabit the other kink, affecting system mass.
- Mass defect allows for loosely bound states at small distances.
- Interaction induces meson flavor mixing and oscillations.

## Abstract

A Rayleigh-Schr\"{o}dinger type of perturbation scheme is employed to study weakly interacting kinks and domain walls formed from two different real scalar fields $\chi$ and $\varphi$. An interaction potential $% V_{1}(\chi,\varphi)$ is chosen which vanishes in a vacuum state of either field. Approximate first order corrections for the fields are found, which are associated with scalar field condensates inhabiting the zeroth order topological solitons. The model considered here presents several new and interesting features. These include (1) a condensate of \textit{each} kink field inhabits the \textit{other} kink, (2) the condensates contribute an associated mass to the system which vanishes when the kinks overlap, (3) a resulting mass defect of the system for small interkink distances allows the existence of a loosely bound state when the interkink force is repulsive. An identification of the interaction potential energy and forces allows a qualitative description of the classical motion of the system, with bound states, along with scattering states, possible when the interkink force is attractive. (4) Finally, the interaction potential introduces a mixing and oscillation of the perturbative $\chi$ and $\varphi$ meson flavor states, which has effects upon meson-kink interactions.