Revisiting the $\mu$-$\tau$-philic Higgs doublet in light of the muon $g-2$ anomaly, $\tau$ decays, and multi-lepton searches at the LHC.

2021 
Considering relevant theoretical and experimental constraints, especially for the lepton flavour universality in the $\tau$ decays and multi-lepton searches at the LHC, we revisit the possibilities of accommodating the muon $g-2$ anomaly reported by Fermilab in the 2HDM with a discrete $Z_4$ symmetry in which an inert Higgs doublet field ($H,~A,~H^\pm$) has the lepton flavor violation $\mu$-$\tau$ interactions. We assume the Yukawa matrices are real and symmetrical, and find two allowed regions. In the region of 590 GeV $
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