Electroweak production of light scalar-pseudoscalar pairs from extended Higgs sectors

In models with extended Higgs sectors, it is possible that the Higgs boson discovered at the LHC is not the lightest one. We show that in a realistic model (the Type I 2-Higgs Doublet Model), when the sum of the masses of a light scalar and a pseudoscalar ($h$ and $A$) is smaller than the $Z$ boson mass, the Electroweak (EW) production of an $hA$ pair can dominate over QCD production by orders of magnitude, a fact not previously highlighted. This is because in the $gg$-initiated process, $hA$ production via a resonant $Z$ in the $s$-channel is prohibited according to the Landau-Yang theorem, which is not the case for the $q\bar{q}$-initiated process. We explore the parameter space of the model to highlight regions giving such $hA$ solutions while being consistent with all constraints from collider searches, $b$-physics and EW precision data. We also single out a few benchmark points to discuss their salient features, including the $hA$ search channels that can be exploited at Run II of the LHC.