Lattice investigation of custodial two-Higgs-doublet model at weak quartic couplings

TL;DR

This work provides the first non-perturbative lattice study of the SU(2)-gauged custodial two-Higgs-doublet model in the weak-quartic regime, confirming spontaneous breaking of the custodial SU(2) in a dedicated sector and mapping how SM-like physics can be realized on a line of constant SM parameters. It develops a lattice framework with gradient-flow based scale setting to tune to $R=m_h/m_W=1.5$ and $g_{GF}^2(mu=m_W)=0.5$, and explores the non-SM scalar spectrum, finding a lower bound for a BSM scalar mass well below $m_W$ that is robust against the cutoff. The gauge coupling running exhibits asymptotic freedom at high energies and screening effects around the $W$ mass, consistent with a mass-dependent treatment. Finite-temperature analysis shows a smooth crossover near the electroweak scale, aligning with SM expectations and suggesting that weak quartic couplings do not yield a first-order EWPT in this setup. The study lays groundwork for future work at larger quartics to probe potential strong-EWPT scenarios and their phenomenological implications.

Abstract

The $SU(2){-}$gauged custodial two-Higgs-doublet model, which shares the same global-symmetry properties with the standard model, is studied non-perturbatively on the lattice. The additional Higgs doublet enlarges the scalar spectrum and opens the possibility for spontaneous breaking of the global symmetry. In this work we start by showing the occurrence of spontaneous breaking of the custodial symmetry in a region of the parameter space of the model. Following this, both the spectrum and the running of the gauge coupling are examined at weak quartic couplings in the presence of the custodial symmetry. The calculations are performed with energy cutoffs ranging from 300 to 600 GeV on a line of constant standard model physics, obtained by tuning bare couplings to fix the ratio between the masses of the Higgs and the $W$ bosons, as well as the value of the renormalized gauge coupling at the scale of the $W$ boson mass. The realizable masses for the additional scalar states are explored. For the choice of bare quartic couplings in this work, the estimated lower bound of these masses is found to be well below the $W$ boson mass, and independent of the cutoff. We also study the finite temperature electroweak transition along this line of constant standard model physics, revealing properties of a smooth crossover behavior.

Figures (13)

• Figure 1: Summary of the cutodial 2HDM parameter space with the global symmetries and spectrum content for each of the sectors $H_{0}$, $H_{1}$, $H_{2}$, $H_{12}$. $1^{-}$, and $0^{+}$ represent a vector and a scalar state, respectively.
• Figure 2: Expectation values for $L_{\alpha_{12}}^{3}$ (left) and $L_{\alpha_{1}}$ (right) as a function of $\kappa_{1}$ signaling the transition between $(H_{2})$ and $(H_{12})$. The constant bare couplings are those from the $\beta=8.56$ point of the LPCP. Two lattice volumes are shown, $12^{4}$, and $16^{4}$.
• Figure 3: Expectation value of the $SU(2)$ non-invariant quantity $L_{\alpha_{12}}^{3}$ as a function of the symmetry breaking parameter $\varepsilon$ for different values of the hopping parameter $\kappa_{1}$ below and above the transition. Two different volumes are shown.
• Figure 4: Expectation value of the $SU(2)$ non-invariant quantity $L_{\alpha_{12}}^{3}$ as a function of the symmetry breaking parameter $\varepsilon$ in the thermodynamic limit for different values of the hopping parameter, $\kappa_{1}$.
• Figure 5: Order parameter $\langle L_{\alpha_{12}}^{3} \rangle$ in the thermodynamic limit and with the $\varepsilon\rightarrow0$ extrapolation.