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.
Highlights
The problem of stability of the electroweak (EW) vacuum [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] has been central in our understanding of the standard model (SM) and in demystifying the very nature of possible new physics (NP)
Before we carry on studying the impact of NP on the stability of the EW vacuum, we present in Table I the results of our analysis of the tunneling time τ in the SM: τSM=TU ∼ 10639 and τSM=TU ∼ 10661
We have studied the stability of the EW vacuum along the radial direction φ of the Higgs doublet in the presence of Planck-scale suppressed operators of the form φ2n=M2n−4, where M is of order the Planck mass MP
Summary
The problem of stability of the electroweak (EW) vacuum [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] has been central in our understanding of the standard model (SM) and in demystifying the very nature of possible new physics (NP). EW minimum; (ii) the EW vacuum has become a metastable state representing a relative minimum of VðφÞ, but its lifetime turns out to be larger than the age of the Universe [2,11,16,17]; (iii) any possible higher-scale minimum of VðφÞ happens to be degenerate with that of the EW vacuum, obeying some ad hoc principle of multiple criticality [18] Postulating the latter principle enabled the authors of [18] to obtain predictions for the masses of the Higgs boson H and the top quark t, well before their discovery.
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