Muon g-2 anomaly and μ–τ-philic Higgs doublet with a light CP-even component

We examine the possibilities of accommodating the muon g - 2 anomaly released by Fermilab in the 2HDM with a discrete Z 4 symmetry in which an inert Higgs doublet field ( H , A , H ± ) has the lepton flavor violation μ – τ interactions. We assume the Yukawa matrices to be real and symmetrical and investigate the case of light H (5 GeV < m H < 115 GeV). After imposing relevant theoretical and experimental constraints, especially for the multi-lepton searches at the LHC, we find that the muon g - 2 anomaly can be explained within 2 σ confidence level in the region of 5 GeV < m H < 20 GeV, 130 GeV < m A ( m H ± ) < 610 GeV, and 0.005 < ρ < 0.014. Meanwhile, the χ τ 2 fitting the data of lepton flavour universality in the τ decays approaches to the SM prediction.