Higgs bosons in the minimal supersymmetric standard model with explicit CP violation

We study the Higgs-boson mass spectrum of the minimal supersymmetric standard model, in which the tree-level CP invariance of the Higgs potential is broken explicitly by loop effects of soft-CP-violating Yukawa interactions related to scalar quarks of the third generation. The analysis is performed by considering the CP-non-invariant renormalization-group improved effective potential through next-to-leading order that includes leading logarithms due to two-loop Yukawa and QCD corrections. We find that the three neutral Higgs particles predicted by the theory may strongly mix with one another, thereby significantly modifying their tree-level couplings to fermions and to the W sup+- and Z bosons. We analyze the phenomenological consequences of such a minimal supersymmetric scenario of explicit CP violation on the production rates of the lightest Higgs particle, and discuss strategies for its potential discovery at high-energy colliders.