IMPROVED METASTABILITY BOUNDS ON THE STANDARD MODEL HIGGS MASS

TL;DR

The paper tackles the question of Higgs-sector stability in the Standard Model by deriving metastability bounds on the Higgs mass $M_H$ as a function of the top-quark mass $M_t$ and the cutoff scale $\Lambda$ beyond which new physics appears. It advances the analysis by computing a zero-temperature effective potential with next-to-leading-log corrections and physical pole masses, and by evaluating finite-temperature corrections using Debye-mass ring resummation; all quantities are obtained numerically to avoid analytic approximations. The authors obtain absolute lower bounds on $M_H$ from the requirement that the electroweak vacuum not decay to a deeper high-field minimum via thermal fluctuations or quantum tunnelling, presenting simple fits $M_H/{\rm GeV}=A(\Lambda)(M_t/{\rm GeV})-B(\Lambda)$ and quantifying the dependence on $\alpha_S(M_Z)$. These results have practical implications for LEP-200 Higgs searches and offer a way to bound or infer the scale of new physics $\Lambda_{\max}$ from measured $M_H$ and $M_t$, while also providing a framework to differentiate the SM from MSSM scenarios depending on parameters.

Abstract

Depending on the Higgs-boson and top-quark masses, $M_H$ and $M_t$, the effective potential of the Standard Model at finite (and zero) temperature can have a deep and unphysical stable minimum $\langle φ(T)\rangle$ at values of the field much larger than $G_F^{-1/2}$. We have computed absolute lower bounds on $M_H$, as a function of $M_t$, imposing the condition of no decay by thermal fluctuations, or quantum tunnelling, to the stable minimum. Our effective potential at zero temperature includes all next-to-leading logarithmic corrections (making it extremely scale-independent), and we have used pole masses for the Higgs-boson and top-quark. Thermal corrections to the effective potential include plasma effects by one-loop ring resummation of Debye masses. All calculations, including the effective potential and the bubble nucleation rate, are performed numerically, and so the results do not rely on any kind of analytical approximation. Easy-to-use fits are provided for the benefit of the reader. Conclusions on the possible Higgs detection at LEP-200 are drawn.

Figures (9)

• Figure 1: Plot of the effective potential for $M_t=175$ GeV, $M_H\sim 122$ GeV at $T=0$ (thick solid line) and $T=T_t=2.5\times 10^{15}$ GeV (thin solid line).
• Figure 2: Plot of $E_b$, the energy of the critical bubble, as a function of the temperature for the same values of $M_t$ and $M_H$ as in Fig. 1.
• Figure 3: Plot of $dP/d\log_{10}T$ as a function of the temperature for the same values of $M_t$ and $M_H$ as in Fig. 1. The temperature $T_t=2.5\times 10^{15}$ GeV at which the integrated probability is equal to 1 is indicated with a dashed line.
• Figure 4: Plot of the effective potential at $T_t=2.5\times 10^{15}$ GeV, for the same values of $M_t$ and $M_H$ as in Fig. 1, normalized with respect to its maximum value, as a function of $\phi$, arbitrarily normalized with $\phi_0=6.0\times 10^{15}$ GeV. The arrow indicates the value of the bounce solution $\phi_B(0)$.
• Figure 5: Plot of the logarithm of the total probability ($\log P$) as a function of $M_H$ for $M_t=175$ GeV.