Investigation of Higgs boson anomalous FCNC interactions in the simple 3-3-1 model

We study phenomenological constraints on a simple $3-3-1$ model with flavor violating Yukawa couplings. Both triplets Higgs couple to leptons and quarks, which generates flavor violating signals in both lepton and quark sectors. We have shown that this model can allow for large Higgs lepton flavor-violating rate decay $h\to \mu \tau$ and also can be reached to perfect agreements with other experimental constraints such as $\tau \rightarrow \mu \gamma$and$(g-2)_\mu$. The contributions of flavor-changing neutral current (FCNC) couplings, Higgs-quark-quark couplings, to the mesons mixing are investigated. Br$(h\to q{q}^{\mathrm{\prime }})$ can be enhanced with keeping from the measurements of meson mixing. The branching ratio for $t\to qh$ can reach up to ${10}^{-3}$, but it could be as low as ${10}^{-8}$.