[Paper Review] Update of the 2HDM-III with a four-zero texture in the Yukawa matrices and phenomenology of the charged Higgs Boson

J. Hernández-Sánchez, Stefano Moretti+2 more|arXiv (Cornell University)|Feb 1, 2013

Particle physics theoretical and experimental studies3 references4 citations

TL;DR

This paper revisits the 2HDM-III with a four-zero texture in the Yukawa matrices, showing that the charged Higgs boson $H^\pm$ can have a dominant branching ratio into $cb$ final states—up to 90%—due to large, flavor-violating couplings driven by off-diagonal terms in the Yukawa matrices. Unlike models with $\mathcal{Z}_2$ symmetry, this scenario allows $H^\pm c\bar{b}$ couplings to be significantly enhanced, making $H^\pm \to cb$ a key signature for LHC discovery.

ABSTRACT

We update the flavor-violating constraints on the charged Higgs sector of the 2-Higgs Doublet Model Type-III (2HDM-III), using a four-zero texture in the Yukawa matrices. We give a generic Lagrangian of the 2HDM-III. In order to show the relevance of the off-diagonal terms of such a texture, we utilize the main constraints from $B$-physics, $μ-e$ universality in $τ$ decays and the radiative decay $Z o b \bar{b}$ presented recently in arXiv:1212.6818 [hep-ph]. In particular, we show that the $H^- c \bar{b}$ coupling can be very large and very different with respect to 2HDMs with a flavor discrete symmetry (i.e., ${\mathcal{Z}}_2$). We also discuss the possible enhancements of the vertices $H^\pm W^\mp V$ ($V=Z, γ$) that arise at one-loop level.

Motivation & Objective

• To re-evaluate the 2HDM-III model with a four-zero texture in the Yukawa matrices, focusing on flavor-violating constraints.
• To assess the phenomenological implications of large off-diagonal Yukawa couplings, particularly for $H^\pm \to cb$ decay.
• To explore the potential for enhanced $H^\pm W^\mp V$ vertices ($V = Z, \gamma$) at one-loop level due to sizable $\lambda_6, \lambda_7$ parameters.
• To identify distinctive signatures—especially $H^\pm \to cb$—that could distinguish 2HDM-III from other 2HDM variants with $\mathcal{Z}_2$ symmetry.
• To guide future LHC searches by identifying viable parameter regions where $H^\pm$ couplings and branching ratios are maximized.

Proposed method

• Construct a generic 2HDM-III Lagrangian with two Higgs doublets and a four-zero texture in the Yukawa matrices, assuming Hermitian Yukawa matrices.
• Use the relation $Y_{ij}^{f} \propto \sqrt{m_i^f m_j^f} \chi_{ij}^{f}$ to express off-diagonal Yukawa couplings in terms of fermion masses and dimensionless parameters $\chi_{ij}^{f}$.
• Apply constraints from $B$-physics, $\mu$-$e$ universality in $\tau$ decays, and the radiative $Z \to b\bar{b}$ decay from arXiv:1212.6818 to limit the parameter space.
• Compute the decay widths for $H^\pm \to cb$, $cs$, $\tau\nu$, and $W^\pm \gamma/Z$ using the effective Lagrangian and one-loop contributions.
• Analyze the role of self-interactions $H^+H^-\phi^0$ via $\lambda_6, \lambda_7$ parameters in enhancing $H^\pm \to W^\pm \gamma$ and $H^\pm \to W^\pm Z$ branching ratios.
• Compare the branching ratio ratios $R_{sb} = \text{BR}(H^\pm \to cb)/\text{BR}(H^\pm \to cs)$ under different $\chi_{ij}^{f}$ configurations to identify model-specific signatures.

Experimental results

Research questions

• RQ1 How do off-diagonal terms in the four-zero Yukawa texture affect the $H^\pm$ couplings and branching ratios in 2HDM-III?
• RQ2 Can the $H^\pm \to cb$ decay channel dominate in 2HDM-III, and under what conditions does this occur?
• RQ3 What is the impact of the $\lambda_6, \lambda_7$ parameters on the one-loop induced $H^\pm W^\mp V$ vertices?
• RQ4 How does the $H^\pm \to cb$ branching ratio in 2HDM-III differ from that in $\mathcal{Z}_2$-symmetric 2HDMs?
• RQ5 What are the viable parameter regions where $H^\pm \to cb$ reaches BR > 90%, and how can they be probed at the LHC?

Key findings

• The $H^\pm \to cb$ branching ratio can reach up to 90% in 2HDM-III with a four-zero Yukawa texture, especially when $Y_{ij} \gg X_{ij}, Z_{ij}$, due to large contributions from $\sqrt{m_t m_c} \chi_{23}^u$ terms.
• The ratio $R_{sb} = \text{BR}(H^\pm \to cb)/\text{BR}(H^\pm \to cs) \sim |V_{tb}|^2 / |V_{ts}|^2 \approx 10$ when $Y \gg X,Z$, leading to a dominant $H^\pm \to cb$ decay.
• When $X \gg Y,Z$, the ratio $R_{sb} \sim |V_{cs}|^2 / |V_{cb}|^2 \approx 0.1$ or $R_{sb} \sim m_b^2 |V_{cb}|^2 / (m_s^2 |V_{cs}|^2) \approx 100$ if $\chi_{ij}^d$ is negative and $O(1)$, offering two distinct exotic scenarios.
• One-loop contributions to $H^\pm \to W^\pm \gamma$ and $H^\pm \to W^\pm Z$ can reach branching ratios of $10^{-4}$ to $10^{-3}$ and $10^{-3}$ to $10^{-2}$, respectively, due to large $\lambda_6, \lambda_7$ parameters.
• The $H^\pm c\bar{b}$ coupling can be significantly larger than in $\mathcal{Z}_2$-symmetric 2HDMs, making $H^\pm \to cb$ a unique and dominant decay mode in 2HDM-III.
• The model allows for a $H^\pm$ that is effectively leptophobic ($\text{BR}(H^\pm \to \tau\nu) \ll 1\%$) when $m_{H^\pm} < m_t - m_b$, with $H^\pm \to cb$ and $H^\pm \to cs$ dominating.