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arXiv 2212.03052hep-phgr-qchep-th
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引力对电弱真空衰变的修正:度规形式与Palatini形式

Gravitational corrections to electroweak vacuum decay: metric vs. Palatini

Ioannis D. Gialamas, Alexandros Karam, Thomas D. Pappas

AI总结:

本文在度规和Palatini两种引力表述下,通过微扰方法研究引力对电弱真空衰变的修正,发现Palatini形式中引力抑制衰变更弱,并给出幺正性所需的下界$ξ>-1/12$。

摘要:

我们考虑标准爱因斯坦-希尔伯特-希格斯作用量,其中希格斯场通过$ξh^2 \mathcal{R}$项与引力非最小耦合,并在度规和Palatini两种引力表述中研究引力修正对电弱真空稳定性的影响。为了解析地识别两种形式之间的差异,我们采用微扰方法,通过引力耦合常数的前导阶展开来纳入引力修正。我们的分析表明,在Palatini形式中,引力抑制真空衰变概率这一众所周知的效果,对于任何非最小耦合$ξ$值,其抑制程度都比度规情形更温和。此外,我们发现,在Palatini形式中,引力修正的正定性(这是理论幺正性的必要条件)要求下界$ξ>-1/12$。

英文摘要:

We consider the standard Einstein-Hilbert-Higgs action where the Higgs field couples nonminimally with gravity via the term $ξh^2 \mathcal{R}$, and investigate the stability of the electroweak vacuum in the presence of gravitational corrections in both the metric and Palatini formulations of gravity. In order to identify the differences between the two formalisms analytically, we follow a perturbative approach in which the gravitational corrections are taken into consideration via a leading order expansion in the gravitational coupling constant. Our analysis shows that in the Palatini formalism, the well-known effect of gravity suppressing the vacuum decay probability, becomes milder in comparison with the metric case for any value of the nonminimal coupling $ξ$. Furthermore, we have found that in the Palatini formalism, the positivity of the gravitational corrections, which is a necessary requirement for the unitarity of the theory, entails the lower bound $ξ>-1/12$.

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