H\to\gamma\gamma in the Complex Two Higgs Doublet Model

We explore the parameter regions in the complex Two Higgs Doublet Model (c2HDM) with explicit CP violation that can describe current LHC hints for one or more Higgs boson signals at 125 GeV. Such a simple extension of the Standard model has three neutral Higgs bosons and a pair charged Higgs and leads to rich CP-violating sources including the CP-even CP-odd mixing of the neutral Higgs bosons. Within this model we present the production of light Higgs boson at the LHC followed by its decay into two photons. Our numerical study takes into account theoretical and experimental constraints on the Higgs potential like positivity, unitarity and perturbativity as well as $\rho$-parameter, $b\to s\gamma$ and $R_b$. These requirement together with the minimum conditions could explain the di-photon excess observed at the LHC. We also discuss the effects of the CP violating phases on the CP violation observable which is the difference between left-circular and right-circular polarization.