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

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 $ϕ^{6}$ and $ϕ^{8}$ operators at the one-loop level with novel couplings $η_{1/2}$. 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 ($η_{1/2}(m_\text{t})> 0.01$). 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 $η_{1/2}$.