Impacts of the Higgs mass on vacuum stability, running fermion masses and two-body Higgs decays

TL;DR

This work analyzes how a relatively light Higgs mass around $M_H \simeq 125$ GeV affects SM vacuum stability, running fermion masses, and two-body Higgs decays using two-loop renormalization-group equations. It identifies a vacuum-stability cutoff $\Lambda_{\rm VS} \sim 4\times10^{12}$ GeV for $M_H \simeq 125$ GeV, implying new physics at or below this scale, with sensitivity to the top-quark mass. The authors update running masses up to $\Lambda_{\rm VS}$ and recalculate Higgs branching ratios with inputs at $\mu \sim M_H$, providing data useful for model-building and flavor physics, including potential links to neutrino mass mechanisms. Overall, the paper connects Higgs-sector phenomenology to high-scale stability and flavor dynamics, highlighting the potential role of a seesaw-scale and leptogenesis near $\Lambda_{\rm VS}$.

Abstract

The latest results of the ATLAS and CMS experiments indicate 116 GeV \lesssim M_H \lesssim 131 GeV and 115 GeV \lesssim M_H \lesssim 127 GeV, respectively, for the mass of the Higgs boson in the standard model (SM) at the 95% confidence level. In particular, both experiments point to a preferred narrow mass range M_H \simeq (124 ... 126) GeV. We examine the impact of this preliminary result of M_H on the SM vacuum stability by using the two-loop renormalization-group equations (RGEs), and arrive at the cutoff scale Λ_VS \sim 4 \times 10^{12} GeV (for M_H = 125 GeV, M_t = 172.9 GeV and α_s(M_Z) = 0.1184) where the absolute stability of the SM vacuum is lost and some kind of new physics might take effect. We update the values of running lepton and quark masses at some typical energy scales, including the ones characterized by M_H, 1 TeV and Λ_VS, with the help of the two-loop RGEs. The branching ratios of some important two-body Higgs decay modes, such as H \to b\bar{b}, H \to τ^+ τ^-, H\to γγ, H\to W^+ W^- and H \to Z Z, are also recalculated by inputting the values of relevant particle masses at M_H.

Figures (4)

• Figure 1: Correlation between the energy scale $\Lambda^{}_{\rm VS}$ and the Higgs mass $M^{}_H$ based on the requirement of vacuum stability, where the solid curve corresponds to the best-fit value of the top-quark pole mass $M^{}_t = 172.9~{\rm GeV}$, and the dashed lines stand for the $1\sigma$ lower and upper limits.
• Figure 2: The running behaviors of $R^{}_t(\mu)$, $R^{}_b(\mu)$ and $R^{}_\tau(\mu)$ with respect to the energy scale $\mu$ in the SM, where the vertical dashed line indicates the cutoff scale $\Lambda^{}_{\rm VS} \simeq 4\times 10^{12}~{\rm GeV}$ as required by the vacuum stability for $M^{}_H \simeq 125~{\rm GeV}$.
• Figure 3: The evolution of $R^{}_i(\mu)$ with respect to the energy scale $\mu$, where the red band corresponds to the variation of the Higgs mass in the range $M^{}_H \simeq (124 \cdots 126)~{\rm GeV}$, and the vertical dashed line indicates the cutoff scale $\Lambda^{}_{\rm VS} \simeq 4\times 10^{12}~{\rm GeV}$. Note that $R^{}_1(\mu) \simeq R^{}_2(\mu) \simeq R^{}_3 (\mu)$ holds to an excellent degree of accuracy.
• Figure 4: The branching ratios of two-body Higgs decays versus the Higgs mass $M^{}_H$. The thick lines stand for the dominant $H \to f \bar{f}$ modes: $b \bar{b}$ (solid line), $\tau^+ \tau^-$ (dashed line) and $c \bar{c}$ (dotted line); and the thin lines denote $H \to g g$ (solid line), $\gamma \gamma$ (dashed line), $Z \gamma$ (dotted line), $W^+ W^-$ (dotted-dashed line) and $Z Z$ (double-dotted dashed line).