Improved measurements of the absolute branching fractions of the inclusive decays ${D}^{+\left(0\right)}\to \varphi X$

By analyzing $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ of ${e}^{+}{e}^{-}$ annihilation data taken at the center-of-mass energy $\sqrt{s}=3.773\text{}\text{}\mathrm{GeV}$ with the BESIII detector, we determine the branching fractions of the inclusive decays ${D}^{+}\to \varphi X$ and ${D}^{0}\to \varphi X$ to be $\left(1.135±0.034±0.031\right)%$ and $\left(1.091±0.027±0.035\right)%$, respectively, where $X$ denotes any possible particle combination. The first uncertainties are statistical, and the second are systematic. We also determine the branching fractions of the decays $D\to \varphi X$ and their charge conjugate modes $\overline{D}\to \varphi \overline{X}$ separately for the first time, and no significant $CP$ asymmetry is observed.