Dark leptophilic scalar with the updated muon $g-2$ anomaly

The muon $g-2$ anomaly was strengthened by recent experimental results at Fermilab, which may be signatures of new physics. A scenario of leptophilic scalar $ϕ_L$ accounting for the muon $g-2$ anomaly is investigated in this paper. Though a light $ϕ_L$ mainly decaying into standard model (SM) particles has been excluded by experiments, a dark leptophilic scalar $ϕ_L$ predominantly decaying into invisible fermionic dark matter (DM) $χ\barχ$ is still allowed. Considering the decay mode $ϕ_L \to χ\barχ$ opened (here $m_{ϕ_L} = 3 m_χ$), the coupling preferred by the muon $g-2$ and the $ϕ_L-χ$ coupling are derived. The light/heavy $ϕ_L$ (roughly 1 GeV as a benchmark value) can be tested by future experiments via DM/SM decay modes, and $ϕ_L$'s contribution to the anomalous magnetic moment of tau lepton could be investigated at lepton colliders. The search of $χ$ via $χ-$electron scattering in DM direct detection is not sensitive due to a tiny $ϕ_L-$electron coupling, especially for $m_χ\gtrsim m_μ$.

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