[Paper Review] Current bounds on the Type-Z $Z_3$ three Higgs doublet model

Rafael Boto, Jorge C. Romão+1 more|arXiv (Cornell University)|Jun 22, 2021

Particle physics theoretical and experimental studies27 references4 citations

TL;DR

This paper investigates the Type-Z $Z_3$-symmetric three Higgs doublet model (3HDM), showing that cancellations between the two charged Higgs bosons in $B\to X_s\gamma$ and $h\to\gamma\gamma$ decays significantly relax lower bounds on their masses. By relaxing the exact alignment condition and applying stringent theoretical and experimental constraints, the study identifies viable benchmark points with lighter additional Higgs states than previously assumed.

ABSTRACT

Type-Z models, where charged leptons, up type quarks, and down type quarks each couple to a different scalar, are only possible when there are three or more Higgs doublets. We consider the Type-Z three Higgs doublet model imposed by a softly broken $Z_3$ symmetry. We take into account all theoretical and experimental constraints, highlighting the importance of perturbative unitarity and bounded from below conditions that we develop here, and which have a strong impact on $B ightarrow X_s γ$. Since there can be cancellations between the two charged Higgs in $B ightarrow X_s γ$ (and in $h ightarrow γγ$), the lower bounds obtained on the charged Higgs masses are alleviated. We also discuss in detail the important physical differences between exact alignment and approximate alignment, and present some useful benchmark points.

Motivation & Objective

• To investigate the viability of the Type-Z $Z_3$-symmetric three Higgs doublet model under current theoretical and experimental constraints.
• To assess how cancellations between the two charged Higgs bosons affect constraints from $B\to X_s\gamma$ and $h\to\gamma\gamma$ decays.
• To explore parameter regions beyond exact alignment, identifying viable benchmark points with lighter Higgs masses.
• To systematically apply perturbative unitarity, bounded-from-below (BFB) conditions, and HiggsBounds-5.9.1 to constrain the model.
• To clarify the physical differences between exact and approximate alignment in the context of the $Z_3$ 3HDM.

Proposed method

• Implements a softly broken $\mathbbm{Z}_3$ symmetry to construct the scalar potential and Yukawa interactions in a three Higgs doublet model.
• Derives explicit expressions for Higgs couplings, including $hH^{\pm}H^{\mp}$ and $AH^{\pm}H^{\mp}$, using rotation matrices and vacuum alignment parameters.
• Applies perturbative unitarity and bounded-from-below (BFB) conditions to constrain the model's parameter space.
• Uses the HiggsBounds-5.9.1 package to test compatibility with LHC Higgs search results.
• Performs a global scan over parameters, varying from exact alignment to approximate alignment, to identify viable regions.
• Considers the impact of opposite-sign contributions from two charged Higgs states in $h\to\gamma\gamma$ and $B\to X_s\gamma$, enabling mass suppression.

Experimental results

Research questions

• RQ1 How do cancellations between the two charged Higgs bosons in $h\to\gamma\gamma$ and $B\to X_s\gamma$ affect the lower bounds on their masses in the Type-Z $Z_3$ 3HDM?
• RQ2 What are the implications of relaxing the exact alignment condition in the $Z_3$ 3HDM for the viability of the model under current experimental constraints?
• RQ3 How do perturbative unitarity and bounded-from-below (BFB) conditions constrain the parameter space of the $Z_3$ 3HDM beyond the alignment limit?
• RQ4 Which benchmark points in the $Z_3$ 3HDM remain viable after applying all theoretical and experimental constraints, including HiggsBounds-5.9.1?
• RQ5 What are the key physical differences between exact and approximate alignment in the context of the $Z_3$ 3HDM, and how do they affect phenomenology?

Key findings

• Cancellations between the two charged Higgs bosons in $h\to\gamma\gamma$ and $B\to X_s\gamma$ decays allow for significantly lighter charged Higgs masses than previously assumed, relaxing lower bounds.
• The model remains viable even when the 125 GeV Higgs boson is not in the exact alignment limit, with several benchmark points satisfying all constraints.
• Recent LHC measurements exclude all points from Fig. 2 of Chakraborti:2021bpy, even when using the same parameter choices, due to updated HiggsBounds-5.9.1 constraints.
• Perturbative unitarity and bounded-from-below (BFB) conditions are derived and applied, providing essential theoretical constraints on the model's parameter space.
• The study identifies viable benchmark points with charged Higgs masses below 500 GeV, demonstrating that the model can remain consistent with current data without requiring heavy new scalars.
• The physical differences between exact and approximate alignment are shown to be crucial, as approximate alignment allows for lighter Higgs states while preserving compatibility with experimental data.