A private SUSY 4HDM with FCNC in the up-sector

Abstract We present a SUSY model with four Higgs doublets of the "private type," in which all fermion types (up, down, and charged leptons) obtain their masses from different doublet . The conditions for anomaly cancellation imply that remaining ( $H_{u_2}$?> ) must have same hypercharge as $H_{u_1}$?> , thus, can only couple to up-type quarks, opens possibility FCNCs this sector. study Lagrangian model, particular, potential, identify mass-eigenstates interactions; Yukawa matrices, we consider four-texture case. constraints on parameters by using LHC measurements properties 125 GeV boson h ), viable regions parameter space. Subsequently, these are used evaluate prospects detecting FCNC decay mode $t \to ch$?> at future high-luminosity (HL) option LHC, compared current limits LHC-run2. Moreover, next heavier $H_2\to tc$?> typically reach $BR(H_2 \rightarrow tc) \approx {\cal{O}}(10^{-4}-10^{-5} )$?> search signal HL-LHC is also studied, it found may be detectable specific