Higgs decay mediated by top-quark with flavor-changing neutral scalar interactions

We explore the flavor-changing parameters mediated by a Higgs boson within the THDM-III context. In particular, the $h\to t^* c$ processes, and check the high suppression for the FC in the THDM-III context for the low $t_\beta$ parameters. Our exploration in the $\chi_{ij}^{u}-\chi_{ij}^{d}-$parameter space shows the allowed regions for different $t_\beta^{}$ values. We explored different modes for Higgs decays, considered the experimental constraints to get scattering plots for the FC parameters and some relevant decay modes. We expect future results to figure out the FC and its implications in the scalar sector.