Lepton Flavor Violating $h\to\tau\mu$ decay induced by leptoquarks

The flavor changing neutral current decay $h\to\tau\mu$ is studied in a renormalizable scalar leptoquark model with no proton decay. Analytical expressions for the one-loop level contributions of a scalar leptoquark to the decay width of the process $h\to\tau\mu$ are presented. We find a viable model parameter space via the current constraints on the muon ($g-2$), the decay $\tau\to\mu\gamma$, the LHC Higgs boson data and the direct leptoquark searches at the LHC. Then, we evaluate branching ratio of the decay $h\to\tau\mu$induced by leptoquarks; we find that it is of the order of $10^{-8}-10^{-7}$ ($10^{-8}$; $10^{-9}-10^{-8}$)for a scalar leptoquark mass equal to $m_{\Omega_{5/3}}=1$ TeV ($m_{\Omega_{5/3}}=2$; $m_{\Omega_{5/3}}=10$ TeV). Finally, we evaluate the number of events produced at future hadron colliders from both the $h\to\tau\mu$ decay and the potential Standard Model background finding a potentialevidence for the $h\to\tau\mu$ decay.