Leptoquark explanation of $h \to \mu\tau$ and muon $(g-2)$

We consider lepton flavor violating Higgs decay, specifically $h \to \mu\tau$, in a leptoquark model. We introduce two scalar leptoquarks with the $SU(3)_c \times SU(2)_L \times U(1)_Y$ quantum numbers, $(3,2,7/6)$ and $(3,2,1/6)$, which do not generate the proton decay within renormalizable level. They can mix with each other by interactions with the standard model Higgs. The constraint from the charged lepton flavor violating process, $\tau^{-} \to \mu^{-} \gamma$, is very strong when only one leptoquark contribution is considered. However, we demonstrate that significant cancellation is possible between the two leptoquark contributions. We show that we can explain the CMS (ATLAS) excess in $h \to \mu \tau$. We also show that muon $(g-2)$ anomaly can also be accommodated.