By analyzing $2.93{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data taken at the center-of-mass energy $\sqrt{s}=3.773\mathrm{GeV}$ 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 $(1.135\pm 0.034\pm 0.031)\%$ and $(1.091\pm 0.027\pm 0.035)\%$, 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.

• Received 15 August 2019

DOI:https://doi.org/10.1103/PhysRevD.100.072006

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Published by the American Physical Society