Novel Higgs-to-125 GeV Higgs boson decays in the complex NMSSM

In the next-to-minimal supersymmetric standard model (NMSSM) a variety of parameter configurations yields a Higgs boson consistent with the one observed at the LHC. Additionally, the Higgs sector of the model can contain explicit charge parity (CP)-violating phases even at the tree level, in contrast with the minimal supersymmetric standard model (MSSM). In this article we present the one-loop Higgs boson mass matrix of the complex NMSSM in the renormalization-group-improved effective potential approach. We also present the trilinear Higgs boson self couplings as well as various partial decay widths of a generic CP-mixed Higgs boson in the model. We then analyze a very interesting phenomenological scenario wherein the decay of a relatively light pseudoscalar-like Higgs boson into similar to 125 GeV standard model-like Higgs boson(s) is induced by nonzero CP-violating phases. We discuss in detail a few benchmark cases in which such a decay can contribute significantly to the production of SM-like Higgs bosons at the LHC on top of the gluon fusion process. It can thus be partially responsible for the gamma gamma excess near 125 GeV due to the subsequent decay of the SM-like Higgs boson. Such a scenario is extremely difficult to realize in the complex MSSM and, if probed at the LHC, it could provide an indication of the nonminimal nature of supersymmetry.