A Private SUSY 4HDM with FCNC in the Up-sector

Abstract: We present a SUSY model with four Higgs doublets of the ``private type", where each fermion type (up, down, and charged leptons) obtain their masses from a different Higgs doublet H_f ( f = u_1, d, e). The conditions for anomaly cancellation, imply that the remaining Higgs doublet of the model (H_{u_2}), must have the same hypercharge as H_{u_1}, and thus can only couple to up-type quarks, which opens the possibility to have FCNC's only in this sector. We study the Lagrangian of the model, and in particular the Higgs potential, in order to identify the Higgs mass-eigenstates and their interactions; for the Yukawa matrices we consider the 4-texture case. We obtain constraints on the model parameters by using LHC measurements on the properties of the 125 GeV Higgs boson ($h$), and identify viable regions of parameter space. These constraints are then used to evaluate the prospects to detect the FCNC decay mode t -> ch at the future high-luminosity (HL) option for the LHC, which are compared with current limits from LHC-run2. Then, we also evaluate the FCNC decay of the next heavier Higgs boson H_2 -> tc, which can reach typically BR(H_2 -> tc) = O(10^{-4}-10^{-5} ); the search for the signal at HL-LHC is also studied, finding that it could be detectable for some specific regions of the model parameter space.