Quantum Gravitational Contributions to the Standard Model Effective Potential and Vacuum Stability

TL;DR

This paper investigates how quantum gravitational effects influence the standard model effective potential and vacuum stability, revealing that gravity-induced operators can significantly alter the Higgs vacuum's nature and stability at high energies.

Contribution

It introduces the calculation of gravity-induced higher dimension operators and their beta functions, analyzing their impact on electroweak vacuum stability within effective field theory.

Findings

Gravity induces $oldsymbol{ ext{phi}^6}$ and $oldsymbol{ ext{phi}^8}$ operators at one-loop.

The true vacuum minimum shifts below the Planck scale in most parameter regions.

Quantum gravity effects contribute at the percent level to the effective potential's minimal value.

Abstract

We compute the quantum gravitational contributions to the standard model effective potential and analyze their effects on the Higgs vacuum stability in the framework of effective field theory. Non-renormalizability of Einstein gravity induces higher dimension $\phi^{6}$ and $\phi^{8}$ operators at the one-loop level with novel couplings $\eta_{1/2}$. The beta functions of these couplings are established and the impact of the gravity induced contributions on electroweak vacuum stability is studied. We find that the true minimum of the standard model effective potential now lies below the Planck scale for almost the entire parameter space ($\eta_{1/2}(m_\text{t})> 0.01$). In addition quantum gravity is shown to contribute to the minimal value of the standard model NLO effective potential at the percent level. The quantum gravity induced contributions yield a metastable vacuum for a large fraction of the parameter space in the flowing couplings $\eta_{1/2}$.