Evidence for the Unbinding of the $\phi^4$ Kink's Shape Mode

Jarah Evslin

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arXiv · 2104.14387

Evidence for the Unbinding of the $\phi^4$ Kink's Shape Mode

Jarah Evslin

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Abstract

The $\phi^4$ 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 $\lambda/4\sim 0.106 m^2$, where the $\mathbb{Z}_2$ symmetry is still broken.

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Jarah Evslin. 2021-04-29. Evidence for the Unbinding of the $\phi^4$ Kink's Shape Mode. https://arxiv.org/abs/2104.14387

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