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Leptoquark induced rare decay amplitudes $h \to τ^\mp μ^\pm$ and $τ\to μγ$

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 $h \to τ^\mpμ^\pm$. Motived by the recently reported excess in LHC data from the CMS detector, we found that a predicted branching fraction Br($h \to τ^\mpμ^\pm$) at the level of 1\% is possible even though the coupling parameters are subjected to the stringent constraint from the null observation of $τ\toμγ$, where the destructive cancellation among amplitudes is achievable by fine tuning.