CP violation in supersymmetric U ( 1 ) ′ models

The supersymmetric CP problem is studied within superstring-motivated extensions of the MSSM with an additional U(1) ′ gauge symmetry broken at the TeV scale. This class of models offers an attractive solution to the µ problem of the MSSM, in which U(1) ′ gauge invariance forbids the bare µ term, but an effective µ parameter is generated by the vacuum expectation value of a Standard Model singlet S which has superpotential coupling of the form SHuHd to the electroweak Higgs doublets. The effective µ parameter is thus dynamically determined as a function of the soft supersymmetry breaking parameters, and can be complex if the soft parameters have nontrivial CP-violating phases. We examine the phenomenological constraints on the reparameterization invariant phase combinations within this framework, and find that the supersymmetric CP problem can be greatly alleviated in models in which the phase of the SU(2) gaugino mass parameter is aligned with the soft trilinear scalar mass parameter associated with the SHuHd coupling. We also study how the phases filter into the Higgs sector, and find that while the Higgs sector conserves CP at the renormalizable level to all orders of perturbation theory, CP violation can enter at the nonrenormalizable level at one-loop order. In the majority of the parameter space, the lightest Higgs boson remains essentially CP even but the heavier Higgs bosons can exhibit large CP-violating mixings, similar to the CP-violating MSSM with large µ parameter.