Gravitational corrections to Standard Model vacuum decay

TL;DR

The paper analyzes gravitational corrections to Standard Model vacuum decay by performing a perturbative expansion in the Newton constant and derives analytic corrections to the decay rate, showing that gravity only modestly shifts the metastability border in the Higgs-top mass plane. It also shows that Planck-suppressed operators can be as relevant as gravitational effects. In addition, it investigates the prospect of Standard Model–driven inflation via a near-flat Higgs potential but finds the predicted perturbation spectrum incompatible with observations. Overall, current precision data suggest the SM vacuum can remain metastable or stable up to the Planck scale, with gravity-induced corrections being subdominant within uncertainties.

Abstract

We refine and update the metastability constraint on the Standard Model top and Higgs masses, by analytically including gravitational corrections to the vacuum decay rate. Present best-fit ranges of the top and Higgs masses mostly lie in the narrow metastable region. Furthermore, we show that the SM potential can be fine-tuned in order to be made suitable for inflation. However, SM inflation results in a power spectrum of cosmological perturbations not consistent with observations.

Figures (4)

• Figure 1: Probability $p(R)$ that the SM vacuum decayed so far for $m_h=115\,{\rm GeV}$, $m_t = 174.4\,{\rm GeV}$, $\alpha_3(M_Z)=0.118$, due to bounces with size $R$, without including gravitational effects (dashed curve IRS) and including gravitational effects (continuous line). The correction is relevant only at $1/R\,\hbox{$>$$\sim$}\,10^{17}\,{\rm GeV}$. Uncertainties due to higher-order corrections are not shown.
• Figure 2: Metastability region of the Standard Model vacuum in the $(m_h,m_t)$ plane, for $\alpha_s(m_Z)=0.118$ (solid curves). Dashed and dot-dashed curves are obtained for $\alpha_s(m_Z)=0.118\pm 0.002$. The shaded half-ellipses indicates the experimental range for $m_t$ and $m_h$ at $68\%$ and $90\%$ confidence level. Sub-leading effects could shift the bounds by $\pm 2\,{\rm GeV}$ in $m_t$.
• Figure 3: Examples of fine-tuned SM potentials that might allow inflation. The right handed axis shows the value of the slow-roll parameter $\varepsilon$ that would give the observed amount of anisotropies.
• Figure 4: Bounds on the Higgs mass derived by the conditions of absolute stability (lower bound), sufficient metastability (yellow region) and perturbativity (upper dotted lines, derived by the conditions $\lambda < 3,6$), as function of the scale of validity of the SM. This plot assumes $m_t=173\,{\rm GeV}$ and $\alpha_3(M_Z)=0.118$.