The KM phase in semi-realistic heterotic orbifold models Original Research Article

In string-inspired semi-realistic heterotic orbifolds models with an anomalous U(1)X, a nonzero Kobayashi–Masakawa (KM) phase is shown to arise generically from the expectation values of complex scalar fields, which appear in nonrenormalizable quark mass couplings. Modular covariant nonrenormalizable superpotential couplings are constructed. A toy Z3 orbifold model is analyzed in some detail. Modular symmetries and orbifold selection rules are taken into account and do not lead to a cancellation of the KM phase. We also discuss attempts to obtain the KM phase solely from renormalizable interactions.