The Two-Loop $\phi^4$ Kink Mass

TL;DR

This paper calculates the two-loop quantum correction to the mass of a scalar kink in $$ theory, including a vacuum energy counterterm, resulting in a finite and explicit mass contribution.

Contribution

It provides the first two-loop kink mass calculation with a vacuum energy counterterm, applicable to the $$ kink, yielding a concrete mass correction value.

Findings

Two-loop mass correction for the $$ kink is 0.0126λ/m.

Inclusion of a counterterm makes the kink mass finite with nonzero vacuum energy.

The result is expressed explicitly in terms of coupling λ and meson mass m.

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 $\phi^4$ 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.