Protecting the Stability of the EW Vacuum from Planck-Scale Gravitational Effects

We investigate the stability of the Standard-Model Electroweak (EW) vacuum in the presence of Planck-scale suppressed operators of the type $\phi^{2n}/M^{2n-4}_{\rm P}$ that involve the Higgs field $\phi$ and could in principle be induced by quantum gravity effects. We show how minimal embeddings of the Standard Model (SM) in supergravity (SUGRA) can stabilize the EW vacuum against such operators up to very high values of the induced supersymmetry breaking scale $M_{\cal S}$, which may well be above the onset of the so-called SM metastability scale of $10^{11}$ GeV. In particular, we explicitly demonstrate how discrete $R$ symmetries could be invoked to suppress the occurrence of harmful Planck-scale operators of the form $\phi^{2n}/M^{2n-4}_{\rm P}$ to arbitrary higher powers of $n$. We analyze different scenarios of Planck-scale gravitational physics and derive lower limits on the power $n$ that is required in order to protect our EW vacuum from dangerous rapid decay. The significance of our results for theories of low-scale quantum gravity is illustrated.