Measurement of branching fractions for Meson Decaying Into Meson and a Pseudoscalar Meson

The four decay modes ${D}^{0}\to \varphi {\pi }^{0}$, ${D}^{0}\to \varphi \eta $, ${D}^{+}\to \varphi {\pi }^{+}$, and ${D}^{+}\to \varphi {K}^{+}$ are studied by using a data sample taken at the centre-of-mass energy $\sqrt{s}=3.773$ 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 $B\left({D}^{0}\to \varphi {\pi }^{0}\right)=\left(1.168±0.028±0.028\right)×{10}^{-3}$, $B\left({D}^{0}\to \varphi \eta \right)=\left(1.81±0.46±0.06\right)×{10}^{-4}$, and $B\left({D}^{+}\to \varphi {\pi }^{+}\right)=\left(5.70±0.05±0.13\right)×{10}^{-3}$, respectively, where the first uncertainties are statistical and the second are systematic. In addition, the upper limit of the branching fraction for ${D}^{+}\to \varphi {K}^{+}$ is given to be $2.1×{10}^{-5}$ at the 90% confidence level. The ratio of $B\left({D}^{0}\to \varphi {\pi }^{0}\right)$ to $B\left({D}^{+}\to \varphi {\pi }^{+}\right)$ is calculated to be $\left(20.49±0.50±0.45\right)\text{%}$, which is consistent with the theoretical prediction based on isospin symmetry between these two decay modes.