Constraining CP4 3HDM with top quark decays

CP4 3HDM is a unique three-Higgs-doublet model equipped with a higher-order CP symmetry in the scalar and Yukawa sector. Based on a single assumption (the minimal model with a CP-symmetry of order 4 and no accidental symmetry), it leads to a remarkable correlation between its scalar and Yukawa sectors, which echoes in its phenomenology. A recent scan of the parameter space of CP4 3HDM under the assumption of scalar alignment identified a few dozens of points which passed many flavour constraints. In the present work we show, however, that almost all of these points are now ruled out by the recent LHC searches of $t \to H^+ b$ with subsequent hadronic decays of $H^+$. Apart from a few points with charged Higgses heavier than the top quark, only one point survives all the checks, the model with an exotic, non-2HDM-like generation pattern of $H^+$ couplings with quarks. One can expect many more points with exotic $H^+$ couplings to quarks if the scalar alignment assumption is relaxed.