Gauge hierarchy and metastability from Higgs-driven crunching

TL;DR

This work links the Higgs hierarchy problem to vacuum metastability via a dynamical vacuum selection mechanism in a landscape that scans the Higgs mass. Patches with a natural $m^2$ crunch to a large negative-energy vacuum, while patches with $m^2<m_{ m crit}$ develop a metastable electroweak-like vacuum whose existence is tied to the RG running of the quartic coupling and the instability scale $\mu_I$. To make this mechanism viable and testable, the authors introduce TeV-scale vector-like fermions in two minimal models—a heavy neutral lepton and a singlet-doublet system—that lower $\mu_I$ and yield a calculable $m_{ m crit}$; their parameter spaces are shown to be accessible to future lepton colliders (FCC-ee, ILC) and possibly a muon collider or FCC-hh. The analysis combines tree-level and loop-level potential modeling with RG running and higher-dimensional operators, and discusses vacuum decay, stabilization scales, and finite-temperature effects, providing a concrete phenomenological program to probe vacuum selection physics at colliders and in cosmology.

Abstract

We present a new solution to the Higgs hierarchy problem based on dynamical vacuum selection in a landscape scanning the Higgs mass. In patches where the Higgs mass parameter takes a natural value, the Higgs potential only admits a minimum with a large and negative energy density. This causes a cosmological crunch, removing such patches from the landscape. Conversely, in patches where the Higgs mass parameter is smaller than a critical value, the Higgs potential admits a metastable minimum with the standard cosmological history. This critical value is determined by the instability scale, where the quartic coupling turns negative due to its running. The ability of this mechanism to explain the observed Higgs mass hinges on new physics at the TeV scale, such as vector-like fermions. We study two simple realizations of this scenario in a heavy neutral lepton model and in the singlet-doublet model, the latter mimicking a Higgsino-bino system. We show that the relevant parts of their parameter spaces can be probed by proposed future colliders, such as the FCC-ee or a muon collider.

Figures (6)

• Figure 1: A sketch of the effective Higgs potential with $\lambda (\mu = \Lambda) <0$ stabilized by a higher-dimensional operator $\Delta V = h^6/\Lambda^2$. We note that while this effect implies a strong dependence of the potential around the EW vacuum on the scanned parameter $m^2$ (left panel), while the behavior of the potential around the natural minimum is mostly independent of $m^2$. For values of the mass parameter smaller than some critical value $m_{\rm crit}^2\sim \mu_I^2$ (see Eq. \ref{['eq:mcrit']}), a second metastable minimum can form. Due to the logarithmic running of this coupling, this happens at field values several orders of magnitude smaller than $\Lambda$. Here, we have for concreteness chosen $\beta_\lambda (\mu_I)=-0.1$ and $\Lambda=100 \mu_I$.
• Figure 2: A visualization of Eq. \ref{['eq:criteqfull']}. The curves represent the function $F$ for different values of the parameter $c = C_6 \mu_I^2/(\Lambda^2 |\beta_\lambda (\mu_I)|)$, which encodes the corrections from higher-dimensional operators. For small enough or vanishing values of this parameter, the function $F$ has a local maximum. If $m^2$ is larger than this maximum, the function $F$ intersects the $y=m^2$-line once, corresponding to the quantum phase of a unique minimum. For smaller values of $m^2$, the three intersections correspond to an additional minimum with adjacent potential barrier. For large enough values of $c$, corresponding to a small UV scale $\Lambda$, there always exists a unique minimum, independent of $m^2$. In this regime, the dimension-six operator becomes important already in the regime where $\lambda >0$.
• Figure 3: The elevation of the radiatively generated vacuum as a function of $m^2$ in units of $\mu_I^4 |\beta_\lambda (\mu_I)|$ and $\mu_I^2 |\beta_\lambda (\mu_I)|$, respectively, for different hierarchies between the instability scale and the scale of new physics.
• Figure 4: The elevation of the radiatively generated vacuum relative to its adjacent natural vacuum in units of $\mu_I^4/|\beta_\lambda (\mu_I)|$ as a function of the parameter $c$ for $m^2=0$. For $0.046 \leq c < c_{\rm max}$, the second minimum still exists, but has a larger energy density than its counterpart at $h=0$.
• Figure 5: Higgs mass bounds and experimental constraints for the heavy neutral lepton model. The black lines show contours of constant $m_{\rm crit} = 1,2, 5$ TeV. The red solid line and shaded area correspond to experimental constraints from EW precision observables delAguila:2008pwdeBlas:2013glaBasso:2013jkaDeppisch:2015qwa, and the red broken lines are projected reach from EW precision at FCC-ee (dashed) Antusch:2015miaAntusch:2016ejd and ILC (dash-dotted) Antusch:2015mia. The blue solid line and shaded region depicts constraints from a CMS direct search CMS:2024xdq, and the purple solid line and shaded region correspond to constraints from requiring perturbativity of $y$.