Higgs boson and Top quark masses as tests of Electroweak Vacuum Stability

TL;DR

The paper performs a NNLO renormalization-group analysis of the Standard Model Higgs potential up to the Planck scale to test electroweak vacuum stability using the Higgs mass in the LHC range and treating the running top mass $\overline{m_t}(m_t)$ as a free parameter. It shows that current data allow a stable electroweak vacuum within uncertainties, while also exploring a near-critical regime that could admit a shallow false minimum near $M_{\rm Pl}$ with implications for primordial inflation. The authors derive boundary conditions for such a shallow minimum and provide a conservative upper bound on type I seesaw right-handed neutrino masses consistent with vacuum stability. They emphasize that improved measurements of $\overline{m_t}(m_t)$ and $\alpha_3(m_Z)$, as well as potential future $e^+e^-$ colliders, are essential to decisively determine the vacuum’s nature and its cosmological connections, while noting that gravitational effects are not included in the analysis.

Abstract

The measurements of the Higgs boson and top quark masses can be used to extrapolate the Standard Model Higgs potential at energies up to the Planck scale. Adopting a NNLO renormalization procedure, we: i) find that electroweak vacuum stability is at present allowed, discuss the associated theoretical and experimental errors and the prospects for its future tests; ii) determine the boundary conditions allowing for the existence of a shallow false minimum slightly below the Planck scale, which is a stable configuration that might have been relevant for primordial inflation; iii) derive a conservative upper bound on type I seesaw right-handed neutrino masses, following from the requirement of electroweak vacuum stability.

Figures (11)

• Figure 1: Value of $\lambda(m_H)$ obtained by performing the matching at different scales $\mu$, indicated by the labels, as a function of $m_H$. The solid (dashed) lines are obtained by including corrections up to 2-loop (1-loop). We fixed $m_t=172$ GeV (for different values see eq.(\ref{['eq-lmh']})).
• Figure 2: Values of $h_t(m_t)$ and $\overline{m_t}(m_t)$ as a function of $m_t$. The curves are obtained by matching at different scales, which are indicated by the labels. We fixed $m_H=126$ GeV for definiteness but the results do not significantly dependent on $m_H$, provided it is chosen in its experimental range.
• Figure 3: The SM Higgs potential (left) and the quartic Higgs coupling (right) as functions of the renormalization scale $\mu$, for $m_H=126$ GeV and different values of $\overline{m_t}(m_t)$, increasing from top to bottom by the amount indicated by the labels. The dashed curve in the right plot shows the associated value of $\beta_\lambda(\mu)$. The other input parameters are fixed at the central values discussed in the previous section.
• Figure 4: The scale $\mu_\beta$ as a function of $\overline{m_t}(m_t)$ and for different values of $m_H$, as indicated by the labels.
• Figure 5: The solid (black) line marks the points in the plane $[m_H,\overline{m_t}(m_t)]$ where a second vacuum, degenerate with the electroweak one, is obtained just below the Planck scale. The (red) diagonal arrow shows the effect of varying $\alpha_3(m_Z)=0.1196\pm 0.0017$PDG; the (blue) horizontal one shows the effect of varying $\mu_\lambda$ (the matching scale of $\lambda$) from $m_Z$ up to $2 m_H$. The shaded (yellow) vertical region is the $2\sigma$ ATLAS :2012gk and CMS :2012gu combined range, $m_H=125.65 \pm 0.85$ GeV; the shaded (green) horizontal region is the range $\overline{m_t} (m_t)=163.3 \pm 2.7$ GeV, equivalent to $m_t=173.3\pm2.8$ GeV Alekhin:2012py.