[Paper Review] Interpreting the $\boldsymbol{W}$-Mass and Muon $\boldsymbol{(g_μ-2)}$ Anomalies within a 2-Higgs Doublet Model

Rachid Benbrik, Mohammed Boukidi+1 more|arXiv (Cornell University)|Apr 25, 2022

Computational Physics and Python Applications4 citations

TL;DR

This paper proposes a Type III two-Higgs-doublet model (2HDM) with lepton-flavour violation to simultaneously explain the Fermilab muon $(g_\mu-2)$ anomaly and the CDF-II $W$-boson mass measurement. By introducing non-zero mass splittings among the charged and neutral Higgs bosons ($H^\pm$, $A$, $H$), the model successfully reconciles both anomalies within experimental and theoretical constraints, favoring negative $S$-parameter values and a $m_W$ consistent with CDF-II's 2022 result.

ABSTRACT

In this study, we investigate the anomalous magnetic moment of the muon $(g_μ-2)$ as reported by Fermilab (FNAL), along with the recent measurement of the $W$-boson mass by the CDF-II collaboration. Both findings show significant deviations from the predictions of the Standard Model (SM), hinting at the possibility of new physics. Our focus is on the Type III two-Higgs-doublet model (2HDM), wherein both Higgs doublets couple with all fermions, leading to the induction of flavour-changing neutral currents (FCNCs) at the tree level. Within this framework, we investigate a lepton-flavour-violating (LFV) scenario, aiming to explain both observed anomalies, while satisfying the up-to-date theoretical and experimental constraints.

Motivation & Objective

• To address the 5.0σ discrepancy in the muon anomalous magnetic moment ($g_\mu-2$) measured by Fermilab’s Muon $g-2$ experiment.
• To reconcile the CDF-II 2022 measurement of the $W$-boson mass ($m_W = 80.4335 \pm 0.0094$ GeV), which deviates by 7σ from the SM prediction.
• To explore a lepton-flavour-violating ($\mu\!\to\!\tau$) scenario in the Type III 2HDM that induces tree-level flavour-changing neutral currents (FCNCs).
• To satisfy current theoretical and experimental constraints, including electroweak precision observables (EWPOs), $\sin^2\theta_{\mathrm{eff}}$, and $\Delta a_\mu$ within 2σ.
• To determine whether a single 2HDM framework can simultaneously explain both anomalies without violating existing limits.

Proposed method

• Adopting a Type III 2HDM with two complex SU(2)$_L$ Higgs doublets ($\Phi_1$, $\Phi_2$), where both couple to all fermions, leading to tree-level FCNCs.
• Implementing a lepton-flavour-violating Yukawa interaction via $\chi_{ij}^{\ell}$ couplings to mediate $\mu\!\to\!\tau$ transitions.
• Performing a reduced parameter scan over $m_H - m_{H^\pm}$ and $m_H - m_A$, fixing $m_H = 125.09$ GeV and $c_{\beta-\alpha}$, $\tan\beta$, and $\chi_{ij}^{\ell}$.
• Using the $S$ and $T$ parameters to constrain the model, with $S$ parameter values disfavoring mass degeneracy.
• Comparing predictions against CDF-II and PDG 2021 data for $m_W$ and $\sin^2\theta_{\mathrm{eff}}$, and against the Fermilab $\Delta a_\mu$ measurement.
• Applying constraints from $\Delta a_\mu$ (within 2σ), $\sin^2\theta_{\mathrm{eff}}$ measurements (world average and SLD), and theoretical bounds on Higgs masses and couplings.

Experimental results

Research questions

• RQ1 Can a Type III 2HDM with lepton-flavour violation simultaneously explain the $g_\mu-2$ anomaly and the CDF-II $W$-boson mass measurement?
• RQ2 What are the required mass splittings among the charged and neutral Higgs bosons ($H^\pm$, $A$, $H$) to satisfy both anomalies and constraints?
• RQ3 How do the $S$ and $T$ parameters constrain the model, and what values are favored by the CDF-II and Fermilab data?
• RQ4 Is the observed $m_W$ value from CDF-II compatible with the 2HDM framework when combined with the $\Delta a_\mu$ measurement?
• RQ5 What role does the effective weak mixing angle $\sin^2\theta_{\mathrm{eff}}$ play in distinguishing between the SM and the 2HDM predictions in this scenario?

Key findings

• The model successfully explains the CDF-II $W$-boson mass measurement ($m_W = 80.4335 \pm 0.0094$ GeV) within 2σ, with the $m_W$ prediction aligning best with the CDF-II data and SLD measurement.
• The $\Delta a_\mu$ value from the model lies within the 2σ range of the Fermilab measurement ($\Delta a_\mu = (25 \pm 4.8) \times 10^{-10}$), indicating consistency with the observed anomaly.
• Mass degeneracy among $H$, $A$, and $H^\pm}$ is disfavored; a non-zero and negative $m_H - m_{H^\pm}$ splitting is required to satisfy both anomalies.
• The $S$ parameter is found to be negative and non-zero, favoring the CDF-II $m_W$ measurement and distinguishing the model from the SM.
• The $\sin^2\theta_{\mathrm{eff}}$ predictions from the model lie in the ranges [0.23107, 0.23130] (CDF-II) and [0.2314, 0.2316] (PDG), consistent with experimental data.
• Parameter points satisfying all constraints—including $\Delta a_\mu$, $m_W$, $\sin^2\theta_{\mathrm{eff}}$, and theoretical limits—exist only when $m_H - m_{H^\pm}$ is non-zero, indicating a key role for Higgs mass splitting.