The Muonic Portal to Vector Dark Matter:connecting precision muon physics, cosmology, and colliders

TL;DR

The MPVDM model links dark matter to the muon sector via a dark SU(2) gauge symmetry and vector-like muons, yielding a vector dark matter candidate $V_D$ and a near-resonant annihilation mechanism that suppresses late-time annihilation to satisfy CMB bounds while reproducing the relic density. The authors perform analytical and numerical analyses of the muon anomalous magnetic moment contributions, and explore the full five-parameter space under two $(g-2)_\mu$ interpretations: a tension scenario with a positive excess and a compatibility scenario consistent with SM predictions within uncertainties. They combine cosmological and collider constraints, recasting LHC searches to bound vector-like muons to $m_{\mu_D}\gtrsim 850$ GeV, and predict striking multi-lepton signatures up to 6–10 muons at the HL-LHC. The work reveals a predictive, testable framework that connects precision muon physics, cosmology, and collider phenomenology, with a robust near-resonant mechanism enabling light DM to coexist with current data and clear collider targets for future exploration.

Abstract

We present a comprehensive study of the Muonic Portal to Vector Dark Matter (MPVDM), a minimal yet phenomenologically rich extension of the Standard Model featuring a new SU(2)_D gauge symmetry and vector-like muons. In this framework the dark sector interacts with the Standard Model only through these heavy leptons, linking dark matter and the muon sector. The MPVDM can simultaneously explain the observed relic abundance and the muon anomalous magnetic moment a_mu under both the "tension" and "compatibility" scenarios motivated by recent (g-2)_mu results. A key finding is a generic off-resonance velocity suppression mechanism that allows light (<1 GeV) vector dark matter to evade CMB limits near 2*m_DM ~ m_H_D. Unlike scenarios based on ultra narrow Breit-Wigner resonances and early kinetic decoupling, the suppression follows from the temperature evolution of the annihilation cross section in a moderately detuned near resonant regime, where being 10-20 percent below resonance gives the required CMB era suppression without fine tuning. A five dimensional parameter scan shows that the tension scenario requires sub GeV dark matter with g_D ~ 1e-3 and TeV scale vector like muons, while the compatibility scenario admits a broad mass range up to multi TeV. Recasting ATLAS and CMS searches for mu+ mu- + E_T^miss sets a lower bound of about 850 GeV on vector like muons. The MPVDM thus offers a unified, predictive, and experimentally accessible framework linking dark matter and muon physics across cosmological and collider frontiers.

Figures (11)

• Figure 1: Diagrams contributing to $a_\mu$ in the MPVDM. Those involving only SM particles provide a new physics contribution through the muon mixing angles.
• Figure 2: Loop functions appearing in the scalar and vector contributions to $a_\mu$ in the MPVDM. The blue line corresponds to the contribution from scalar-$\mu'$ loop. The brown line shows the loop function for scalar-$\mu$ loop. The red line corresponds to the $V^\prime\mu^\prime$ loop contribution, the green line to $Z\mu^\prime$, and the olive line to $V^\prime\mu$. When relations are valid only in specific limits (see text), the regions where the limit is not achieved are represented by dashed lines. The range of $r_{V_D}$ and $r_{V^\prime}$ is strictly bounded between 0 and 1 due to the model hierarchy: $m_{V^\prime} < m_{V_D} < m_{\mu_D} < m_{\mu^\prime}$.
• Figure 3: Colour map of $\Delta \hat{a}_\mu$ (from Eq. \ref{['eq:amu_hat']}) obtained from a five-dimensional scan of the parameter space (Eq. \ref{['eq:pert_constraints']}), projected onto the $(m_{V_D}, g_D)$ plane. The selected points reproduce the experimental value of $a_\mu$ within $5\sigma$. Perturbativity constraints from Eq. \ref{['eq:pert_constraints']} have been applied.
• Figure 4: $\Delta a_\mu^{\mathrm{NP}}$ versus $m_{V_D}$ for different values of $g_D$. The dotted, solid, and dashed blue lines correspond respectively to $\Delta a_\mu^{\mathrm{NP}} = \{\Delta a_\mu^{\mathrm{EXP}} - 2\sigma, \Delta a_\mu^{\mathrm{EXP}}, \Delta a_\mu^{\mathrm{EXP}} + 2\sigma\}$. Here we choose $g_D \in \{0.001, 0.003, 0.005, 0.01, 0.1, 1\}$, $m_{\mu_D} = 800~\mathrm{GeV}$, $m_{\mu^\prime} = 1000~\mathrm{GeV}$, and $m_{H_D} = 0.677~\mathrm{GeV}$, one of which corresponds to the benchmark point in \ref{['tab:BPs for g2 + cosmo']}.
• Figure 5: Colour map of $\Delta \hat{a}_\mu$ (from Eq. \ref{['eq:amu_hat']}) obtained from a five-dimensional scan of the parameter space (Eq. \ref{['eq:pert_constraints']}), projected onto the $(m_{V_D}, g_D)$ plane. The selected points reproduce the experimental value of $a_\mu$ within $5\sigma$ under the assumption of no $a_\mu$ excess. Perturbativity constraints from Eq. \ref{['eq:pert_constraints']} have been applied.