Stability of Q-balls and Catastrophe

TL;DR

This paper introduces a practical method using catastrophe theory to analyze the stability of Q-balls across their entire parameter space, including various limits and false vacuum states, applied to two specific models.

Contribution

It develops a comprehensive stability analysis method for Q-balls applicable to different regimes, revealing distinct catastrophe types and stability structures in two models.

Findings

V_3 model exhibits fold catastrophe stability structure.

V_4 model exhibits cusp catastrophe stability structure.

Stability structures differ significantly between the two models.

Abstract

We propose a practical method for analyzing stability of Q-balls for the whole parameter space, which includes the intermediate region between the thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false vacuum), using the catastrophe theory. We apply our method to the two concrete models, $V_3=m^2\phi^2/2-\mu\phi^3+\lambda\phi^4$ and $V_4=m^2\phi^2/2-\lambda\phi^4+\phi^6/M^2$. We find that $V_3$ and $V_4$ Models fall into {\it fold catastrophe} and {\it cusp catastrophe}, respectively, and their stability structures are quite different from each other.