An extension of two-Higgs-doublet model and the excesses of 750 GeV diphoton, muon g-2 and $h\to\mu\tau$

In this paper we simultaneously explain the excesses of the 750 GeV diphoton, muon g-2 and $h\to \mu\tau$ in an extension of the two-Higgs-doublet model (2HDM) with additional vector-like fermions and a CP-odd scalar singlet ($P$) which is identified as the 750 GeV resonance. This 750 GeV resonance has a mixing with the CP-odd scalar ($A$) in 2HDM, which leads to a coupling between $P$ and the SM particles as well as a coupling between $A$ and the vector-like fermions. Such a mixing and couplings are strongly constrained by $\tau\to\mu\gamma$, muon g-2 and the 750 GeV diphoton data. We scan over the parameter space and find that such an extension can simultaneously account for the observed excesses of 750 GeV diphoton, muon g-2 and $h\to \mu\tau$. The 750 GeV resonance decays in exotic modes, such as $P\to hA$, $P\to HZ$, $P\to HA$ and $P\to W^\pm H^\mp$, and its width can be dozens of GeV and is sensitive to the mixing angle.