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The two Higgs doublet model emerges as a minimal scenario in which toaddress, at the same time, the $\gamma\gamma$ excess at 750 GeV and the leptonflavour 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 apeculiar pattern for the lepton Yukawa couplings. We add TeV scale vector-likefermions and find parameter space consistent with both excesses, as well aswith Higgs and electroweak precision observables.

Two Higgs doublets to explain the excesses $pp\rightarrow \gamma\gamma(750\ {\rm GeV})$ and $h \to \tau^\pm \mu^\mp$