Lepton flavour violating decay of 125 GeV Higgs boson to $\mu\tau$ channel and excess in $t\bar t H$

A recent search for the lepton flavor violating (LFV) decays of the Higgs boson, performed by CMS collaboration, reports an interesting deviation from the standard model (SM). The search conducted in the channel $H\rightarrow \mu\tau_e$ and $H\rightarrow \mu\tau_{\textrm{had}}$ shows an excess of $2.4\sigma$ signal events with 19.7 fb$^{-1}$ data at a center-of-mass energy $\sqrt s=8$ TeV. On the other hand, a search performed by CMS collaboration for the SM Higgs boson produced in association with a top quark pair ($t\bar t H$) also showed an excess in the same-sign di-muon final state. In this work we try to find out if these two seemingly uncorrelated excesses are related or not. Our analysis reveals that a lepton flavour violating Higgs decay ($H\rightarrow\mu\tau$) can partially explain the excess in the same sign di-muon final state in the $t\bar t H$ search, infact brings down the excess well within 2$\sigma$ error of the SM expectation. Probing such non-standard Higgs boson decay is of interest and might contain hints of new physics at the electroweak scale.