Evidence for the Unbinding of the ${\varphi }^4$ Kink's Shape Mode

Abstract

The ${\varphi }^4$ double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is $-0.115567\lambda /m$ in terms of the coupling $\lambda /4$ and the meson mass $m$ evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is $-0.433\lambda /m$. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of $\lambda /4\sim 0.106m^2$, where the ${\mathbb{Z}}_2$ symmetry is still broken.

arXiv comment8 pages, 1 figure, v2: Refs added