Stability of Q-balls and Catastrophe

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, $V_3=m^2{\varphi }^2\mathrm{/}2-\mu {\varphi }^3+\lambda {\varphi }^4$ and $V_4=m^2{\varphi }^2\mathrm{/}2-\lambda {\varphi }^4+{\varphi }^6\mathrm{/}{M}^2$. 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.