We update the constraints on Two-Higgs-Doublet Models of Type I and II discussed in arXiv:1405.3584 using the latest LHC measurements of the ~125.5 GeV Higgs signal as of Summer 2014. We provide explicit comparisons of the results before and after th
e Summer 2014 ATLAS and CMS updates. Overall, the changes with respect to arXiv:1405.3584 are rather small; to a large extent this is due to the fact that both the ATLAS and the CMS updates of the $gammagamma$ decay mode moved closer to SM expectations.
We analyze the Two-Higgs-Doublet Models (2HDMs) of Type I and II for consistency with the latest measurements of the ~125.5 GeV Higgs-like signal at the LHC. To this end, we perform scans of the 2HDM parameter space taking into account all relevant p
re-LHC constraints as well as the most recent limits coming from searches for heavy Higgs-like states at the LHC. The current status of the 2HDMs of Type I and II is discussed assuming that the observed 125.5 GeV state is one of the two CP-even Higgs bosons, either the lighter h or the heavier H. Implications for future experiments, including expectations regarding other lighter or heavier Higgs bosons are given. The possible importance of heavier Higgs bosons feeding the signals for the 125.5 GeV state is also evaluated.
We develop diagnostic tools that would provide incontrovertible evidence for the presence of more than one Higgs boson near 125 GeV in the LHC data.
We examine GUT-scale NMSSM scenarios in which {it both} $h_1$ and $h_2$ lie in the 123 -- 128 GeV mass range. Very substantially enhanced $gammagamma$ and other rates are possible. Broadened mass peaks are natural.
We assess the extent to which various constrain
