The Two-Loop ${\varphi }^4$ Kink Mass

Abstract

At one loop, quantum kinks are described by a free theory. The nonlinearity and so the interesting phenomenology arrives at two loops, where, for example, internal excitations couple to continuum excitations. We calculate the two-loop mass of a scalar kink. Unlike previous calculations, we include a counterterm which cancels the vacuum energy density at this order, so that our result for the kink mass is finite even when the vacuum energy density is nonzero. This allows us to apply our result to the ${\varphi }^4$ kink, for which we obtain a two-loop mass contribution of $0.0126\lambda /m$ in terms of the coupling $\lambda$ and the meson mass $m$ evaluated at the minimum of the potential.

arXiv comment11 pages, no figures

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Cited by in corpus (8)

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• Stable Kink-Kink and Metastable Kink-Antikink Solutions
• Leading Quantum Correction to the ${\Phi }^4$ Kink Form Factor
• Differential configurational entropy for multi-field of the ${\varphi }^6$ theory
• Removing Tadpoles in a Soliton Sector
• Examples for BPS solitons destabilized by quantum effects