The phenomenology of the di-photon excess and $h\to\tau\mu$ within 2HDM

The diphoton excess around $m_S=750$ GeV observed at ATLAS and CMS can be interpreted as coming from $S=H$ and $A$, the neutral components of a second Higgs doublet. If so, then the consistency of the light Higgs decays with the Standard Model predictions provides upper bounds on the rates of $S\to VV, hZ, hh$ decays. On the other hand, if $h\to\tau\mu$ decay is established, then a lower bound on the rate of $S\to\tau\mu$ decay arises. Requiring that $\Gamma_S\lesssim45$ GeV gives both an upper and a lower bound on the rotation angle from the Higgs basis $(\Phi_v,\Phi_A)$ to the mass basis $(\Phi_h,\Phi_H)$. The charged scalar, with $m_{H^\pm}\simeq750$ GeV, is produced in association with a top quark, and can decay to $\mu^\pm\nu$, $\tau^\pm\nu$, $tb$ and $W^\pm h$