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

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