Top mass determination, Higgs inflation, and vacuum stability

TL;DR

This work shows that Planck-scale new physics can drastically alter electroweak vacuum stability, metastability, and instability boundaries, invalidating the notion of a universal SM phase diagram derived without UV completion. By incorporating higher-dimension operators $φ^6$ and $φ^8$ with couplings $λ_6$ and $λ_8$, the authors demonstrate that the running quartic coupling $λ_{eff}$ and the stability line shift, making the SM point move between regions depending on the UV details. They also reveal that the EW vacuum lifetime in metastability can be dramatically affected by UV terms, exemplified by lifetimes changing from $ au ≈ 10^{613} T_U$ to $ au_{new} ≈ 10^{-64} T_U$. Additionally, the results cast serious doubt on Higgs inflation scenarios that rely on $λ(M_P) ≈ 0$ and $β(λ(M_P)) ≈ 0$, highlighting the need for a dedicated stability test for any BSM theory rather than relying on a universal SM picture.

Abstract

The possibility that new physics beyond the Standard Model (SM) appears only at the Planck scale $M_P$ is often considered. However, it is usually argued that new physics interactions at $M_P$ do not affect the SM stability phase diagram, so the latter is obtained neglecting these terms. According to this diagram, for the current experimental values of the top and Higgs masses, our universe lives in a metastable state (with very long lifetime), near the edge of stability. Contrary to these expectations, however, we show that the stability phase diagram strongly depends on new physics and that, despite claims to the contrary, a more precise determination of the top (as well as of the Higgs) mass will not allow to discriminate between stability, metastability or criticality of the electroweak vacuum. At the same time, we show that the conditions needed for the realization of Higgs inflation scenarios (all obtained neglecting new physics) are too sensitive to the presence of new interactions at $M_P$. Therefore, Higgs inflation scenarios require very severe fine tunings that cast serious doubts on these models.

Figures (8)

• Figure 1: The stability phase diagram obtained according to the standard analysis. The $M_H-M_t$ plane is divided in three sectors, stability (green), metastability (yellow), and instability (red) regions (see text). The dot is for $M_H\sim 125.7$ GeV and $M_t\sim 173.34$ GeV (current experimental values). The $1\sigma$, $2\sigma$ and $3\sigma$ ellipses are also shown, the experimental uncertainties being $\Delta M_H=\pm 0.3$ GeV and $\Delta M_t=\pm 0.76$ GeV.
• Figure 2: The solid (blue) line shows the running of $\lambda_{eff}(\phi)$ for $M_H=125.7$ GeV and $M_t$ adjusted so that $\min_\phi\lambda_{eff}(\phi)=0$ (see Eq.(\ref{['lamco']})). We get $M_t\sim 171.43$ GeV, while the minimum is at $\bar{\phi}_{_{M_H, M_t}}\sim 2.22 \cdot 10^{18}$ GeV. The dotted (red) line shows the running of $\lambda_{eff}^{new}(\phi)$ (Eq. (\ref{['lanew']})) for the same values of $M_H$ and $M_t$ and for $\lambda_6=-0.4$ and $\lambda_8=0.7$. The minimum is formed well below zero. Keeping fixed the values of $M_H$, $\lambda_6$ and $\lambda_8$, the dashed (green) line shows the running of $\lambda_{eff}^{new}(\phi)$ for that value of $M_t$ such that $\min_\phi\lambda_{eff}^{new}(\phi)=0$. In this case, we get $M_t= 163.3$ GeV.
• Figure 3: The solid (blue) line shows the function $\log_{10}\cal T(\mu)$ for $M_H=125.7$ GeV and $M_t=173.34$ GeV (current experimental values). The minimum forms at $\mu \sim 3.6 \cdot 10^{17}$ GeV, that gives $\tau \sim 10^{613} T_U$. The dashed (red) line shows $\log_{10}{\cal T}_{new}(\mu)$ for the same values of $M_H$ and $M_t$ and for $\lambda_6=-0.4$ and $\lambda_8=0.7$. In this case the minimum is obtained for $\mu\sim 0.62\, M_P$, that gives $\tau_{new} \sim 10^{-64} T_U$.
• Figure 4: The stability phase diagram for the potential $V(\phi)=\lambda\phi^4/4+\lambda_6\phi^6/(6M_P^2) +\lambda_8\phi^8/(8M_P^4)$ with $\lambda_6=-0.22$ and $\lambda_8=0.4$. The $M_H-M_t$ plane is divided in three sectors, stability, metastability, and instability regions. The dot indicates $M_H\sim 125.7$ GeV and $M_t\sim 173.34$ GeV. The $1\sigma$, $2\sigma$ and $3\sigma$ ellipses are obtained for the experimental uncertainties $\Delta M_H=\pm 0.3$ GeV and $\Delta M_t=\pm 0.76$ GeV. The stability and instability lines of fig.\ref{['smphase']} (dashed lines) are reported for comparison.
• Figure 5: The stability phase diagram for the potential of fig.\ref{['smphase2']} with $\lambda_6=-0.4$ and $\lambda_8=0.7$. The $M_H-M_t$ plane is divided in three sectors, stability, metastability, and instability regions. The dot indicates $M_H\sim 125.7$ GeV and $M_t\sim 173.34$ GeV. The $1\sigma$, $2\sigma$ and $3\sigma$ ellipses are obtained for the experimental uncertainties $\Delta M_H=\pm 0.3$ GeVand $\Delta M_t=\pm 0.76$ GeV.