Towards precise baryogenesis in the 2HDM$+a$

We perform a detailed investigation of the viable baryogenesis parameter space of a non-minimal Higgs sector consisting of two Higgs doublets and a singlet pseudoscalar (2HDM$+a$). In such a model, an early Universe period of transient CP violation may occur, driven by a nonvanishing vacuum expectation value of the CP-odd scalar $a$. This naturally avoids the stringent electric dipole moment experimental constraints on beyond-the-Standard-Model sources of CP violation. We provide a state-of-art computation of the baryon asymmetry, providing several important improvements over existing baryogenesis computations for this model. We show that the required thermal history and successful baryogenesis lead to a predictive scenario, testable in the near future by a combination of LHC searches and low-energy flavour measurements. Our improved predictions for the baryon asymmetry find that it is rather suppressed compared to earlier predictions, requiring larger mixing between the singlet and 2HDM pseudoscalars and hence leading to a more easily testable model at colliders.