Interpreting the current Higgs excesses at the LHC in the 2HD+a framework

There are several excesses of events in current LHC data, yet not exceeding the level of significance which would make them to be considered as firm. They point to the possibility of the presence of a new Higgs particle in the spectrum, in addition to the already observed 125 GeV state. In particular, there are excesses involving a diphoton resonance at invariant masses of about 95 GeV, 152 GeV and 650 GeV accompanied to an extra scalar. We have, in addition, the recent observation of a toponium at a mass of about 350 GeV. In this paper, we aim to explain such experimental hints in the framework of a two Higgs doublet model supplemented by a relatively light pseudoscalar Higgs boson a which would correspond to the putative resonance in most cases. This realistic 2HD+a scenario is attractive as it is has the virtue to pass all experimental constraints from high-precision experiments and collider searches and, at the same time, to allow for a viable explanation of the dark matter in the universe. We first update the present constraints on the model, in particular taking into account the latest results on dark matter and Higgs searches, as well the high-precision measurements, including those from Higgs and flavor physics. We then show that the additional Higgs states with the proper mass spectrum and adjusted couplings to fermions, would explain all the LHC excesses (but individually) while passing the former experimental constraints as well as the theoretical ones.