Search for a lighter Higgs in Two Higgs Doublet Models

We consider present constraints on Two Higgs Doublet Models, both from the LHC at Run 1 and from other sources in order to explore the possibility of constraining a neutral scalar or pseudo-scalar particle lighter than the 125 GeV Higgs boson. Such a lighter particle is not yet completely excluded by present data. We show with a simplified analysis that some new constraints could be obtained at the LHC if such a search is performed by the experimental collaborations, which we therefore encourage to continue carrying out light diphoton resonance searches at $\sqrt{s}=$ 13 TeV in the context of Two Higgs Doublet Models.