Leptoquark induced rare decay amplitudes $h \to \tau^\mp \mu^\pm$ and $\tau\to \mu\gamma$

Rare decay modes of the newly discovered standard-model-like Higgs boson $h$ may test the flavor changing couplings in the leptoquark sector through the process $h \to \tau^\mp\mu^\pm$. Motived by the recently reported excess in LHC data from the CMS detector, we found that a predicted branching fraction Br($h \to \tau^\mp\mu^\pm$) at the level of 1\% is possible even though the coupling parameters are subjected to the stringent constraint from the null observation of $\tau\to\mu\gamma$, where the destructive cancellation among amplitudes is achievable by fine tuning.