Nonstrange D-meson decay modes with η and η′. Sensitive tests for small amplitudes, final state interactions and CP violation

Abstract

Interference terms between weak amplitudes producing the η and η′ nonstrange components belonging to different weak generations have opposite signs for the two states and may have nontrivial CP-violating phases. Such interference effects are suggested by the experimentally observed enhancements of D s→πη′, D s→ϱη′ and D→Kη′ decays over corresponding η decay modes and their absence in D +- decays, where the analogous interference term has the same sign for η and η′ and should produce no enhancement. General relations testing different weak decay modes are derived for charmed meson decays into isovector two-body final states emphasizing the role of linear interference effects as a much more sensitive test for small amplitudes than quadratic direct contributions. Particularly simple relations between D s decays follow from assuming dominance of the tree diagram c→su d and neglecting OZI-violating final state rescattering.