Two Higgs doublets to explain the excesses $pp\to \gamma \gamma (750\mathrm{G}\mathrm{e}\mathrm{V})$ and $h\to {\tau }^{\pm }{\mu }^{\mp }$

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.