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Recent measurements of the CMS experiment at the LHC show possibly, withabout $3\sigma$ significance, a resonance in di-photon events with an invariantmass of 95.4 GeV. If this resonance can be confirmed, this could be a hint fora new elementary particle beyond the Standard Model. An additionalStandard-model like Higgs boson with this mass could be excluded by the CMSexperiment. We investigate whether this resonance could fit into a two-Higgsdoublet model highly constrained by CP symmetry, the so-calledmaximally-CP-symmetric model (MCPM). Our finding shows that indeed theenhancement measured by CMS could originate from the pseudoscalar Higgs-boson$h''$ of this model. According to the model the boson $h''$ would mainly beproduced in the Drell-Yan reaction by charm-anticharm-quark fusion. The maindecay mode of $h''$ is predicted to be $h'' \to c\bar{c}$.

CMS results for the $\gamma \gamma$ production at the LHC: do they give  a hint for a Higgs boson of the maximally CP symmetric two-Higgs-doublet  model?