In this paper, we explore the parameter space for processes with fermionic flavor violation within the Two Higgs Doublets Model (2HDM) type III, processes of Flavor Changing Neutral Currents (FCNCs) are present at Leading Order (LO) as dynamics beyond the Standard Model (SM) are included. We analyze the possible Yukawa couplings beyond the SM involving the quark top, as the experimental signatures would be a clear signal to conclude about the model. The processes we analyzed are same sign top pair production at the [Formula: see text] collisions, and single top quark production in [Formula: see text] collisions, through Deep Inelastic Scattering (DIS). To examine the scenarios that could exhibit such exotic events, we perform a scan in the parameter space to determine the observation possibilities for FCNC. We show the results considering the model parameters, coming from modified Yukawa interactions, [Formula: see text] of the order one. In addition, we explore the order of magnitude of possible single top production via [Formula: see text], at the proposed muon–proton collider. We found scattering values for these exotic processes of up to [Formula: see text].
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