Stability, Higgs Boson Mass and New Physics

TL;DR

It is found that the stability of the electroweak (EW) vacuum strongly depends on new physics interaction at the Planck scale MP, despite of the fact that they are higher-dimensional interactions, apparently suppressed by inverse powers of MP.

Abstract

When the particle with mass $\sim 126$ GeV discovered at LHC is identified with the Higgs boson of the Standard Model, intriguing and challenging questions arise. Among them, the issue of the EW vacuum stability. We find that, despite claims to the contrary, the latter strongly depends on new physics interactions. In particular, if $τ$ is the lifetime of the EW vacuum, new physics can turn $τ$ from $τ>> T_U$ to $τ<< T_U$, where $T_U$ is the age of the Universe.

Figures (3)

• Figure 1: In this picture we repeat the analysis of isidoisiunoisidue, which is done in the absence of new interactions at the Planck scale. The $M_H-M_t$ plane is divided in three sectors: absolute stability, metastability and instability regions. The dot indicates $M_H\sim 126$ GeV and $M_t\sim 173.1$ GeV.
• Figure 2: For $M_H \sim 126$ GeV and $M_t\sim 173.1$ GeV, the running of $\lambda(\mu)$ as determined by $SM$ model interactions only (solid line) and in the presence of $\lambda_6$ and $\lambda_8$. Dashed-dotted line: $\lambda_6(M_P)=1$ and $\lambda_8(M_P)=0.5$. Dashed line: $\lambda_6(M_P)=-2$ and $\lambda_8(M_P)=2.1$. Clearly, the tree lines coincide for values of $\mu$ below the Planck scale.
• Figure 3: (a) The effective potential $V_{eff}(\phi)$ (solid line) for $M_H \sim 126$ GeV and $M_t\sim 173.1$ GeV. Note that the new minimum forms at $\phi_{min}^{(2)} \sim 10^{31}$ GeV. For the same values of $M_H$ and $M_t$, $V_{eff}^{new}(\phi)$ for $\lambda_6=-2$ and $\lambda_8=2.1$ (dashed line); $V_{eff}^{new}(\phi)$ for $\lambda_6=1$ and $\lambda_8=0.5$ (dashed-dotted line). In order to include such a vaste range of scales, a log-log plot has been considered. (b) Zoom of the panel (a) figure near the Planck scale. $V_{eff}(\phi)$, $V_{eff}^{new}(\phi)$ and $\phi$ are normalized to Planck units (in this range no log-log plot is needed). $V_{eff}^{new}(\phi)$ for $\lambda_6 <0$ bends down steeply and forms a new minimum at $\phi_{min}^{(2)}=0.979 M_P$. With $\lambda_6 > 0$, $V_{eff}^{new}(\phi)$ falls down less steeply than $V_{eff}(\phi)$ and in the picture we cannot resolve the minimum which forms at $\phi=0.119 M_P$.