Lightest Higgs Boson and Relic Neutralino in the MSSM with CP Violation

We discuss the lower bound to the lightest Higgs boson H_1 in the minimal supersymmetric extension of the standard model (MSSM) with explicit CP violation, and the phenomenology of the lightest relic neutralino in the same scenario. In particular, adopting the CPX benchmark scenario, we find that the combination of experimental constraints coming from LEP, Thallium Electric Dipole Moment (EDM) measurements, quorkonium decays, and B_s -> mu mu decay favours a region of the parameter space where the mass of H_1 is in the range 7 GeV < M_{H_1} < 10 GeV, while 3 < tan(beta) < 5. Assuming a departure from the usual GUT relation among gaugino masses (|M_1| << |M_2|), we find that through resonant annihilation to H_1 a neutralino as light as 2.9 GeV can be a viable dark matter candidate in this scenario. We call this the CPX light neutralino scenario, and discuss its phenomenology showing that indirect Dark Matter searches are compatible with the present experimental constraints, as long as m_\chi < M_{H_1}/2. On the other hand, part of the range m_\chi > M_{H_1}/2 which is allowed by cosmology is excluded by antiproton fluxes.