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

Abstract We examine the possibilities of accommodating the muon $$g-2$$ g - 2 anomaly released by Fermilab in the 2HDM with a discrete $$Z_4$$ Z 4 symmetry in which an inert Higgs doublet field ( $$H,~A,~H^\pm $$ H , A , H ± ) has the lepton flavor violation $$\mu $$ μ – $$\tau $$ τ interactions. We assume the Yukawa matrices to be real and symmetrical and investigate the case of light H (5 GeV $$<m_H<$$ < 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 $$g-2$$ g - 2 anomaly can be explained within $$2\sigma $$ 2 σ confidence level in the region of 5 GeV $$<m_H<20$$ < m H < 20 GeV, 130 GeV $$< m_A~(m_{H^\pm })<$$ < m A ( m H ± ) < 610 GeV, and 0.005 $$<\rho<$$ < ρ < 0.014. Meanwhile, the $$\chi ^2_\tau $$ χ τ 2 fitting the data of lepton flavour universality in the $$\tau $$ τ decays approaches to the SM prediction