Measurement of branching fractions for D meson decaying into ϕ meson and a pseudoscalar meson

The four decay modes D⁰→ϕπ⁰, D⁰→ϕη, D⁺→ϕπ⁺, and D⁺→ϕK⁺ are studied by using a data sample taken at the centre-of-mass energy s=3.773 GeV with the BESIII detector, corresponding to an integrated luminosity of 2.93 fb⁻¹. The branching fractions of the first three decay modes are measured to be B(D⁰→ϕπ⁰)=(1.168±0.028±0.028)×10⁻³, B(D⁰→ϕη)=(1.81±0.46±0.06)×10⁻⁴, and B(D⁺→ϕπ⁺)=(5.70±0.05±0.13)×10⁻³, respectively, where the first uncertainties are statistical and the second are systematic. In addition, the upper limit of the branching fraction for D⁺→ϕK⁺ is given to be 2.1×10⁻⁵ at the 90% confidence level. The ratio of B(D⁰→ϕπ⁰) to B(D⁺→ϕπ⁺) is calculated to be (20.49±0.50±0.45)%, which is consistent with the theoretical prediction based on isospin symmetry between these two decay modes.