[Paper Review] Mass Terms in Two-Higgs Doublet Models

Rui Santos, Sancho Oliveira+1 more|ArXiv.org|Dec 14, 2001

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper analyzes how different mass terms in CP-conserving, renormalizable two-Higgs doublet models (THDMs) lead to distinct physical predictions despite similar theoretical frameworks. By systematically adding or removing dimension-two terms to the two main classes of THDMs—those with Z₂ or global U(1) symmetry—it demonstrates that such modifications induce significant differences in loop-induced processes, particularly in top quark decay width and Higgs boson decay to diphotons, with enhancements up to a factor of four in fermiophobic scenarios.

ABSTRACT

We take a closer look at the mass terms of all renormalizable and CP conserving two-Higgs doublet models (THDM). We show how some of the dimension two parameters in the potential can be set equal to zero leading to relations among the tree-level parameters of the potential. The different versions of the THDM obtained give rise to different amplitudes for physical processes. We will illustrate this with two examples. The first one is the one-loop weak correction to the top decay width, t -> b W. The second one is the decay h -> gamma gamma in the fermiophobic limit.

Motivation & Objective

• To investigate the physical consequences of adding or removing mass terms in renormalizable, CP-conserving two-Higgs doublet models (THDMs).
• To clarify how different symmetry structures—Z₂ or global U(1)—and their soft breaking via mass terms affect scalar sector parameters and physical amplitudes.
• To demonstrate that seemingly minor changes in the scalar potential lead to measurable differences in loop-induced processes such as top quark decay and Higgs diphoton decay.
• To analyze the fermiophobic limit in constrained THDM variants and quantify deviations in Higgs decay widths compared to standard models.

Proposed method

• Derives the most general CP-conserving, renormalizable scalar potential for two Higgs doublets, including all possible dimension-two mass terms.
• Classifies models into two main classes: $V_A$ (Z₂ symmetric) and $V_B$ (U(1) symmetric), and studies their variants by setting specific mass terms to zero.
• Applies vacuum stability and CP-conserving minimum conditions to eliminate unphysical configurations, particularly enforcing $\mu_4^2 = 0$ to prevent spontaneous CP violation.
• Calculates one-loop corrections to top quark decay $t \to bW$ using the modified scalar potential parameters, focusing on differences between $V_A$ and $V_B$ types.
• Analyzes the $h \to \gamma\gamma$ decay amplitude in the fermiophobic limit, emphasizing the role of the $hH^+H^-$ vertex, which differs between $V_A$ and $V_B$ models.
• Introduces dimensionless ratios $R_A$ and $R_B$ to quantify deviations in $h \to \gamma\gamma$ decay widths relative to the standard $V_A$ and $V_B$ models.

Experimental results

Research questions

• RQ1 How do the inclusion or exclusion of specific mass terms in the two-Higgs doublet potential affect the physical amplitudes of loop-induced processes?
• RQ2 To what extent do the $V_A$ (Z₂-symmetric) and $V_B$ (U(1)-symmetric) models differ in their predictions for the top quark decay width $\Gamma(t \to bW)$ at one-loop level?
• RQ3 Can a fermiophobic Higgs state be consistently realized in all variants of $V_A$ and $V_B$ models, and how do the $h \to \gamma\gamma$ decay rates vary across these variants?
• RQ4 What are the quantitative bounds on the enhancement or suppression of $h \to \gamma\gamma$ decay width in constrained models compared to the standard $V_A$ and $V_B$ models?

Key findings

• The one-loop correction to the top quark decay width $t \to bW$ can be enhanced by up to a factor of ten over the Standard Model prediction in certain parameter regions of the constrained models.
• For the $h \to \gamma\gamma$ decay in the fermiophobic limit, the ratio $R_A$ (relative to standard $V_A$) reaches approximately 4 when $\beta = \pi/3$, indicating a significant enhancement in model $V_A^{iii}$.
• In model $V_B^{iii}$, the ratio $R_B$ for $h \to \gamma\gamma$ reaches values above 4 for $M_h \approx 120\,\text{GeV}$ and $\beta = \pi/3$, showing even larger deviations than in $V_A^{iii}$.
• The $hH^+H^-$ vertex, which governs the $h \to \gamma\gamma$ amplitude in the fermiophobic limit, differs fundamentally between $V_A$ and $V_B$ models, leading to distinct decay rate predictions.
• Models $V_A^{i}$ and $V_A^{ii}$ do not allow a fermiophobic Higgs: setting $\alpha = \pi/2$ leads to a vanishing $M_h$ or $M_H$, respectively.
• The constraints from $\Delta\rho$ and positivity of mass parameters restrict the viable parameter space, especially in models $V_B^{i,ii,iii}$, excluding certain ranges of $\alpha$.