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

TL;DR

The paper addresses the UV stability of one-loop corrections in a higher-derivative (HD) scalar theory containing a ghost by analyzing a minimal model where a HD real field φ couples to a complex scalar σ. The authors compute the φ-loop contribution to the σ effective potential via a path-integral determinant of the quadratic fluctuation operator, carefully handling the UV-divergent structure and renormalization. The main result is that the leading high-energy finite part of the HD-loop correction is a positive Coleman–Weinberg–like term, δV ∝ ξ_{σφ}^{2} σ_{cl}^{4} [2 ln(σ_{cl}^{2}) − 1 + ln(ξ_{σφ}^{2})], which ensures UV stability despite ghost contributions. This work informs the UV behavior of HD theories and bears on gravity-motivated models like quadratic gravity, where ghost fields and derivative couplings play a crucial role in determining high-energy consistency; future work will extend the analysis to RG running and include σ/gauge loops.

Abstract

We consider the theory of a higher-derivative (HD) real scalar field $φ$ coupled to a complex scalar $σ$, the coupling of the $φ$ and $σ$ being given by two types, $λ_{σφ}σ^\dagger σφ^{2}$ and $ξ_{σφ}σ^\dagger σ\left(\partial_μφ\right)^{2}$. We evaluate $φ$ one-loop corrections $δV(σ)$ to the effective potential of $σ$, both the contribution from the positive norm part of $φ$ and that from the {\it negative norm part} (ghost). We show that $δV(σ_{\rm cl})$ at $σ_{\rm cl}\to \infty$, where $σ_{\rm cl}$ is a classical value of $σ$, is positive, implying the stability of $δV(σ_{\rm cl})$ by the HD 1-loop radiative corrections at high energy.