Global fits of the two-loop renormalized Two-Higgs-Doublet model with soft $Z_2$ breaking

TL;DR

This paper performs comprehensive global fits of the Two-Higgs-Doublet model with two-loop renormalization, identifying parameter regions consistent with stability up to the Planck scale and experimental data, and analyzing implications for Higgs physics.

Contribution

It provides the first next-to-leading order renormalization group equations for the model and combines them with experimental constraints to delineate viable parameter space.

Findings

Higgs potential couplings cannot exceed magnitude 1 for stability.

Heavy Higgs masses are constrained to be above 340-360 GeV.

The model does not solve the hierarchy problem beyond 5 TeV.

Abstract

We determine the next-to-leading order renormalization group equations for the Two-Higgs-Doublet model with a softly broken $Z_2$ symmetry and CP conservation in the scalar potential. We use them to identify the parameter regions which are stable up to the Planck scale and find that in this case the quartic couplings of the Higgs potential cannot be larger than 1 in magnitude and that the absolute values of the S-matrix eigenvalues cannot exceed 2.5 at the electroweak symmetry breaking scale. Interpreting the 125 GeV resonance as the light CP-even Higgs eigenstate, we combine stability constraints, electroweak precision and flavour observables with the latest ATLAS and CMS data on Higgs signal strengths and heavy Higgs searches in global parameter fits to all four types of $Z_2$ symmetry. We quantify the maximal deviations from the alignment limit and find that in type II and Y the mass of the heavy CP-even (CP-odd) scalar cannot be smaller than 340 GeV (360 GeV). Also, we pinpoint the physical parameter regions compatible with a stable scalar potential up to the Planck scale. Motivated by the question how natural a Higgs mass of 125 GeV can be in the context of a Two-Higgs-Doublet model, we also address the hierarchy problem and find that the Two-Higgs-Doublet model does not offer a perturbative solution to it beyond 5 TeV.