Two Higgs doublets to explain the excesses pprightarrow γγ(750\ {rm GeV}) and h to τ^pm μ^mp

The two Higgs doublet model emerges as a minimal scenario in which to address, at the same time, the $\gamma\gamma$ excess at 750 GeV and the lepton flavour violating decay into $\tau^\pm \mu^\mp $ of the 125 GeV Higgs boson. The price to pay is additional matter to enhance the $\gamma\gamma$ rate, and a peculiar pattern for the lepton Yukawa couplings. We add TeV scale vector-like fermions and find parameter space consistent with both excesses, as well as with Higgs and electroweak precision observables.