[Paper Review] $(g-2)_\mu$ in the 2HDM and slightly beyond -- an updated view

P. M. Ferreira, B. L. Gonçalves+2 more|arXiv (Cornell University)|Apr 7, 2021

Computational Physics and Python Applications1 references4 citations

TL;DR

This paper revisits the muon anomalous magnetic moment $(g-2)_\mu$ in the context of the Two-Higgs-Doublet Model (2HDM), particularly focusing on the type-X and muon-specific 2HDM with vector-like leptons (VLLs). It demonstrates that VLLs—without mixing with the muon—significantly extend the viable parameter space for explaining the $(g-2)_\mu$ anomaly, especially in the lepton-specific (type-X) model, while maintaining consistency with electroweak precision and Higgs decay constraints. The inclusion of VLLs allows for lighter pseudoscalar Higgs bosons and larger $\tan\beta$, improving the fit to the experimental anomaly at 4.2$\sigma$.

ABSTRACT

The recent measurement of the muon $g - 2$ anomaly continues to defy a Standard Model explanation, but can be accommodated within the framework of two Higgs doublet models. If one further includes extra fermion content in the form of a generation of vector like leptons, the allowed parameter range that explains the anomaly is even further extended, and thorny issues of perturbativity and clashes with $B$-decay constraints avoided. We will show how the muon magnetic moment anomaly can be fit within these models, under the assumption that the vector-like leptons do not mix with the muon. We update previous analyses and include all theoretical and experimental constraints, including searches for extra scalars. It is shown that the inclusion of vector-like fermions allows the lepton-specific and muon-specific models to perform much better in fitting the muon's $g - 2$. These fits do require the Yukawa coupling between the Higgs and the vector-like leptons to be large, causing potential problems with perturbativity and unitarity, and thus models in which the vector-like leptons mix with the muon may be preferred.

Motivation & Objective

• To re-evaluate the ability of the 2HDM, particularly the type-X and muon-specific models, to explain the observed $(g-2)_\mu$ anomaly in light of the new Fermilab measurement.
• To investigate how the inclusion of vector-like leptons (VLLs) without muon mixing affects the parameter space and viability of 2HDMs in explaining the anomaly.
• To update and include all theoretical and experimental constraints—such as electroweak precision, Higgs decays, B-decay bounds, and unitarity—on the 2HDM with VLLs.
• To assess whether the VLL contribution via two-loop Barr-Zee diagrams can resolve tensions with B-decay constraints that plague the standard type-II 2HDM.
• To compare the performance of the type-X and muon-specific 2HDM with VLLs against the standard 2HDM and evaluate perturbative and unitarity constraints on Yukawa couplings.

Proposed method

• Adopts the 2HDM with a $\mathbb{Z}_2$ symmetry to forbid tree-level flavor-changing neutral currents, focusing on type-X and muon-specific models.
• Incorporates vector-like leptons (VLLs) that couple to the Higgs sector but do not mix with the muon, contributing to $\Delta a_\mu$ via two-loop Barr-Zee diagrams.
• Applies constraints from electroweak precision observables, $B \to K^{(*)} \ell^+\ell^-$ decays, $\tau$ lepton decays, and Higgs invisible decay modes to restrict parameter space.
• Uses the latest Fermilab $\mu$-g-2 measurement ($\Delta a_\mu = (251 \pm 59) \times 10^{-11}$) as input for the anomaly fit.
• Performs a global fit including unitarity and perturbativity bounds on the Yukawa couplings between the Higgs and VLLs, setting limits on $\lambda_{L,R}$.
• Employs numerical scans over $m_A$, $\tan\beta$, $m_{H^+}$, and VLL masses, with benchmark points (B1, B2) to illustrate allowed regions in the $(m_A, \tan\beta)$ plane.

Experimental results

Research questions

• RQ1 Can the inclusion of vector-like leptons (VLLs) without muon mixing significantly extend the viable parameter space in the type-X 2HDM to explain the $(g-2)_\mu$ anomaly?
• RQ2 How do constraints from $B$-meson decays, $\tau$ lepton decays, and Higgs invisible decays affect the allowed parameter space in the 2HDM with VLLs?
• RQ3 To what extent do the two-loop Barr-Zee contributions from VLLs improve the fit to the $(g-2)_\mu$ anomaly compared to the standard 2HDM?
• RQ4 What are the implications of large Yukawa couplings between the Higgs and VLLs for perturbativity and unitarity in the model?
• RQ5 Can the muon-specific 2HDM with VLLs simultaneously satisfy the $(g-2)_\mu$ anomaly and avoid conflicts with $B$-decay constraints that exclude the standard type-II model?

Key findings

• The inclusion of vector-like leptons (VLLs) without muon mixing allows the type-X and muon-specific 2HDMs to explain the $(g-2)_\mu$ anomaly with $m_A$ as low as 10 GeV and $\tan\beta$ between 30 and 50, consistent with the 4.2$\sigma$ anomaly.
• The VLL contribution via two-loop Barr-Zee diagrams significantly widens the viable parameter space, enabling solutions that were previously excluded due to $B$-decay constraints.
• The model remains viable under unitarity and perturbativity constraints only if the Yukawa couplings $\lambda_{L,R}$ between the Higgs and VLLs are large, with $\lambda_{\text{max}} \lesssim 4\pi$ for benchmark points B1 and B2.
• The allowed region in the $(m_A, \tan\beta)$ plane for the muon-specific 2HDM with VLLs extends to lower $m_A$ and higher $\tan\beta$ compared to the standard 2HDM, improving the fit to the anomaly.
• Constraints from $\tau$ lepton decays and $h \to AA$ invisible decays further restrict the parameter space, but do not rule out viable solutions in the VLL-extended model.
• The study confirms that models with VLLs mixing with the muon may be preferred due to reduced Yukawa coupling demands, though non-mixing VLLs still provide a viable path to explaining the anomaly.