A mini review on CP-violating minimal supersymmetric Standard Model Higgs

We discuss the present status of the Higgs sector of the CP-violating minimal supersymmetric Standard Model (CPVMSSM). In the Standard Model (SM) of particle physics, the only source of CP violation is the complex phase in the Cabibbo-Kobayashi-Maskawa (CKM) matrix. By now we all know that this single phase is not large enough to explain the observed baryon asymmetry of our Universe. Hence, one require additional sources of CP violation. The MSSM with several complex phases is one such scenario. The tree-level CP invariance of the MSSM Higgs potential is broken at one-loop level in the presence of complex phases in the MSSM Lagrangian. The presence of these additional phases modifies Higgs masses, mixings and couplings significantly. These additional phases have non-trivial impact on several low-energy observables; like the electric dipole moments (EDMs) of atoms and molecules, the CP asymmetry in rare b-decays etc. We first present a brief outline of the CPVMSSM Higgs sector, and then discuss the current limits/bounds obtained from the measurements of several low-energy observables. We also comment on the current bounds coming from the high-energy collider experiments, specially the Large Electron Positron (LEP) Collider and the ongoing Large Hadron Collider (LHC) at the CERN.