Large pseudoscalar Yukawa couplings in the complex 3HDM

As LHC's Run3 unfolds, we peer deeper into the couplings of the 125GeV Higgs ($h_{125}$) and also test for extra scalars. Even before such extra scalars are found, one can probe them by using the fact that theories with multiple Higgs doublets allow for substantial deviations of the couplings of $h_{125}$ from their SM values. Indeed, the observed couplings already place stringent limits on such theories. We investigate the curious possibility that $h_{125}$ couples to the top quark mostly as a scalar, while it couples to the bottom quark mostly as a pseudoscalar. This possibility was allowed by 2017 data for the so-called C2HDM; a two Higgs doublet model with a single source of explicit CP violation. It was shown recently that this possibility disappears when using the full experimental data of 2024. Here we discuss a three Higgs doublet with explicit CP violation (C3HDM), and show that the curious CP-even/CP-odd $t$/$b$ possibility is partly resuscitated, prompting further experimental exploration of this prospect.