UV stability of 1-loop radiative corrections in higher-derivative scalar field theory

Abstract

We consider the theory of a higher-derivative (HD) real scalar field $\varphi$ coupled to a complex scalar $\sigma$, the coupling of the $\varphi$ and $\sigma$ being given by two types, ${\lambda }_{\sigma \varphi }{\sigma }^{†}\sigma {\varphi }^2$ and ${\xi }_{\sigma \varphi }{\sigma }^{†}\sigma {\left({\partial }_{\mu }\varphi \right)}^2$. We evaluate $\varphi$ one-loop corrections $\delta V(\sigma )$ to the effective potential of $\sigma$, both the contribution from the positive norm part of $\varphi$ and that from the {\it negative norm part} (ghost). We show that $\delta V({\sigma }_{\mathrm{cl}})$ at ${\sigma }_{\mathrm{cl}}\to \infty$, where ${\sigma }_{\mathrm{cl}}$ is a classical value of $\sigma$, is positive, implying the stability of $\delta V({\sigma }_{\mathrm{cl}})$ by the HD 1-loop radiative corrections at high energy.

20 pages