# Quartic Coupling Unification in the Maximally Symmetric 2HDM

## TL;DR

This paper explores how the Maximally Symmetric Two-Higgs Doublet Model (MS-2HDM) achieves quartic coupling unification at high energy scales, offering a minimal, predictive extension of the Standard Model with testable Higgs coupling deviations.

## Contribution

It demonstrates quartic coupling unification in the MS-2HDM at high RG scales and analyzes vacuum stability, providing a minimal, predictive framework with specific Higgs coupling predictions.

## Key findings

- Quartic couplings unify at scales around 10^{11} to 10^{20} GeV.
- Unification occurs at conformally invariant points where all quartic couplings vanish.
- Model predicts deviations in Higgs couplings to W, Z, top, and bottom quarks.

## Abstract

We consider the Maximally Symmetric Two-Higgs Doublet Model (MS-2HDM) in which the so-called Standard Model (SM) alignment can be naturally realised as a consequence of an accidental SO(5) symmetry in the Higgs sector. This symmetry is broken (i) explicitly by renormalization-group (RG) effects and (ii) softly by the bilinear scalar mass term $m^2_{12}$. We find that in the MS-2HDM all quartic couplings can unify at large RG scales $\mu_X \sim 10^{11}\,$-$\,10^{20}$ GeV. In particular, we show that quartic coupling unification can take place in two different conformally invariant points, where all quartic couplings vanish. We perform a vacuum stability analysis of the model in order to ensure that the electro-weak vacuum is sufficiently long-lived. The MS-2HDM is a minimal and very predictive extension of the SM governed by only three additional parameters: the unification scale $\mu_X$, the charged Higgs mass $M_{h^{\pm}}$ (or $m^2_{12}$) and $\tan\beta$, which allow one to determine the entire Higgs sector of the model. In terms of these input parameters, we present illustrative predictions of misalignment for the SM-like Higgs-boson couplings to the $W^\pm$ and $Z$ bosons and, for the first time, to the top and bottom quarks.