[Paper Review] Light scalars, ($g_{\mu}-2$) muon anomaly and dark matter in a model with a Higgs democracy

Nikolai Krasnikov|arXiv (Cornell University)|Jul 3, 2017

Particle physics theoretical and experimental studies10 references3 citations

TL;DR

This paper proposes a renormalizable extension of the Standard Model with Higgs democracy—where each lepton has its own Higgs isodoublet—augmented by a light isosinglet scalar and a Dirac dark matter fermion. The scalar mixes with the leptonic Higgses, generating small Yukawa couplings to muons that explain the muon $g_\mu - 2$ anomaly without conflicting with rare kaon or B-meson decay bounds. The model simultaneously accounts for the observed dark matter relic density via the dark fermion, which annihilates through the scalar mediator. The addition of a $L_\mu - L_\tau$-coupled vector boson further enables explanation of both the $g_\mu - 2$ anomaly and dark matter density.

ABSTRACT

In this paper we consider isosinglet scalar extension of a model with a Higgs democracy - multihiggs extension of the SM where each quark and lepton has its own Higgs isodoublet. The addition of light isosinglet scalar allows to solve muon $(g_{\\mu}-2)$ anomaly and it can serve as a messenger between the SM matter and dark matter. Due to small mixing of isosinglet scalar with the Higgs boson responsible for top quark mass the proposed model escapes bounds from rare $K$- and $B$-meson decays and solves both muon $(g_{\\mu}-2)$ and dark matter problems. Also we point out that an extension of the model with $L_{\\mu} - L_{\ au}$ vector interaction allows not only explain muon $(g_{\\mu} - 2)$ anomaly but also dark matter density.

Motivation & Objective

• To resolve the long-standing $g_\mu - 2$ anomaly, which shows a 3.6σ deviation from the Standard Model prediction.
• To simultaneously account for the observed dark matter relic density in the universe.
• To construct a renormalizable model that avoids stringent constraints from rare kaon and B-meson decays while generating small muon Yukawa couplings via scalar mixing.
• To explore the viability of light scalar and vector mediators ($\phi$, $Z'$) that couple preferentially to muons and dark matter.

Proposed method

• Introduces a model with three lepton-specific Higgs isodoublets ($H_e, H_\mu, H_\tau$), a singlet scalar $\phi$, and a Dirac dark matter fermion $\psi_d$.
• Imposes a discrete symmetry ($Z_2$) to forbid tree-level mixing between $\phi$ and the SM Higgs, ensuring the model is safe from rare decay bounds.
• Uses vacuum misalignment: $\langle \phi \rangle \neq 0$ triggers mixing between $\phi$ and the leptonic Higgses via trilinear couplings $\sqrt{2} M_l H^+ H \phi$.
• Derives the mixing angles $\theta_{h\phi} \sim \frac{M_l \langle H \rangle}{m_{h_l}^2}$, which generate small effective Yukawa couplings to muons.
• Computes one-loop contributions to $g_\mu - 2$ from the scalar and vector mediators using loop integrals involving $F(x)$ and $\Delta a_\mu$ formulae.
• Estimates dark matter relic density via the Boltzmann equation, using freeze-out cross sections $\langle \sigma v_{\text{rel}} \rangle \sim 10^{-8} \, \text{GeV}^{-2}$ for s-wave and p-wave annihilation.

Experimental results

Research questions

• RQ1 Can a light isosinglet scalar in a Higgs democracy model explain the $g_\mu - 2$ anomaly without violating constraints from rare $K$ and $B$ decays?
• RQ2 Can the same scalar mediator simultaneously account for the observed dark matter relic density?
• RQ3 Does the inclusion of a $L_\mu - L_\tau$-coupled vector boson ($Z'$) enhance the model’s ability to explain both $g_\mu - 2$ and dark matter density?
• RQ4 What are the viable parameter ranges for the scalar mass, mixing angle, and dark matter mass that satisfy both anomalies?

Key findings

• The model explains the $g_\mu - 2$ anomaly with a scalar mediator via a small effective Yukawa coupling $g_{\mu\phi} \sim 10^{-3}$, induced by mixing with the muon Higgs.
• The scalar coupling to muons is naturally suppressed due to $\theta_{h\phi} \sim \mathcal{O}(10^{-3})$, avoiding conflict with $K$ and $B$ meson decay bounds.
• The dark matter fermion $\psi_d$ with mass $m_d \sim 100$ MeV and coupling $g_\psi \sim 10^{-5}$ achieves the correct relic density via s-wave annihilation with $\langle \sigma v_{\text{rel}} \rangle \approx 0.28 \times 10^{-8} \, \text{GeV}^{-2}$.
• For the $L_\mu - L_\tau$ vector model, a $Z'$ boson with mass $m_{Z'} \sim 120$ keV to 400 keV and coupling $\alpha'_V \sim 10^{-8}$ can explain both $g_\mu - 2$ and dark matter density.
• The model predicts a dark matter annihilation cross section consistent with Planck observations, with $\Omega h^2 \approx 0.12$ for $m_d \sim 100$ MeV and $T_d \sim 10$ MeV.
• The model is viable for direct detection: the scattering cross section is too small to be detected in current experiments, but future muon beam experiments (e.g., NA64 at CERN) may probe the $Z'$.