Anatomy of non-leptonic two-body decays of charmed mesons into final states with η′

Abstract

We show that D → Pη′ decay amplitudes, where P = K, π, η, cannot be simply related to their D → Pη counterparts with a single η₀–η₈ mixing angle. We propose a novel, consistent treatment of η₀–η₈ mixing for application in D → Pη and D → Pη′ decays. Using this framework, we perform a global analysis of D → Pη′ decays employing SU(3)_F symmetry including linear SU(3)_F breaking. We find that the assumption of 30% SU(3)_F breaking is in slight tension (2.5σ) with the data when compared to a fit that allows for 50% SU(3)_F breaking, the latter giving a perfect description of the data. In order to allow for further scrutinization of SU(3)_F-breaking effects in the future, we give branching ratio predictions for all D → Pη′ modes. Our predictions deviate from the current data in case of the branching ratios \( \mathcal{B} \)(\( {D}_s^{+} \) → K⁺η′) and \( \mathcal{B} \)(D⁺ → K⁺η′). Future more precise measurements of these channels are therefore highly important in order to clarify the quality of the SU(3)_F expansion in nonleptonic D → Pη′ decays.