On the metastability of the Standard Model vacuum

TL;DR

This work provides a rigorous, next-to-leading order assessment of the Standard Model vacuum's metastability by performing a complete one-loop calculation of the tunnelling rate from the electroweak minimum, augmented with two-loop renormalization-group evolution of the Higgs quartic coupling and other SM couplings. The authors resolve scale ambiguities inherent in the semi-classical bounce by explicitly computing the one-loop action around the flat-space bounce and summing finite contributions from Higgs, top, gauge, and Goldstone sectors. Their results yield concrete bounds in the (m_H,m_t) plane, showing that for m_H≈115 GeV the electroweak vacuum remains long-lived unless m_t is above about 175 GeV, with the dominant contributions arising from high-scale bubbles around 10^16 GeV and little dependence on Planck-scale physics. The analysis demonstrates that the metastability bound is robust against ultraviolet uncertainties and highlights the precision needed in top-quark mass determinations to test the stability landscape of the SM vacuum.

Abstract

If the Higgs mass m_H is as low as suggested by present experimental information, the Standard Model ground state might not be absolutely stable. We present a detailed analysis of the lower bounds on m_H imposed by the requirement that the electroweak vacuum be sufficiently long-lived. We perform a complete one-loop calculation of the tunnelling probability at zero temperature, and we improve it by means of two-loop renormalization-group equations. We find that, for m_H=115 GeV, the Higgs potential develops an instability below the Planck scale for m_t>(166\pm 2) GeV, but the electroweak vacuum is sufficiently long-lived for m_t < (175\pm 2) \GeV.

Figures (4)

• Figure 1: Running of the quartic Higgs coupling for $m_H = 115~{\rm GeV}$ and $m_t= 165, 170, 175,180$ and $185~{\rm GeV}$$[\alpha_s(m_Z)=0.118]$. Absolute stability $[\lambda > 0]$ is still possible if $m_t < 166~{\rm GeV}$. The hatched region indicates the metastability bound.
• Figure 2: Numerical results for the subtracted part of the correction to the action from top loops $[f_t(g_t^2/|\lambda|)$, solid curve$]$ and gauge boson loops $[f_g(g^2/|\lambda|)$, dashed curve$]$. Relevant values of $g^2/|\lambda|$ are $4\div 8$.
• Figure 3: Contribution to the tunnelling rate (in arbitrary units) from bubbles of different $R$, as a function of $1/R$, for $m_H = 115~{\rm GeV}$ and $m_t = 175~{\rm GeV}$.
• Figure 4: 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 area indicates the experimental range for $m_t$. Sub-leading effects could shift the bounds by $\pm 2~{\rm GeV}$ in $m_t$.