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

TL;DR

This paper explores how embedding the Standard Model in supergravity with discrete R symmetries can prevent Planck-scale suppressed operators from destabilizing the electroweak vacuum, ensuring stability up to high energy scales.

Contribution

It demonstrates that supergravity embeddings with discrete R symmetries can suppress harmful operators, protecting the EW vacuum from quantum gravity effects at high scales.

Findings

Supergravity embeddings can stabilize the EW vacuum against Planck-scale operators.

Discrete R symmetries effectively suppress dangerous operators of arbitrary high order.

Lower bounds on operator powers are derived to ensure vacuum stability.

Abstract

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.