Search for baryon and lepton number violating decay ${D}^{±}\to n\left(\overline{n}\right){e}^{±}$

Using a data set of electron-positron collisions corresponding to an integrated luminosity of $293\text{}\text{}{\mathrm{fb}}^{-1}$ taken with the BESIII detector at a center-of-mass energy of 3.773 GeV, a search for the baryon ($B$) and lepton ($L$) number violating decays ${D}^{±}\to n\left(\overline{n}\right){e}^{±}$ is performed. No signal is observed and the upper limits on the branching fractions at the 90% confidence level are set to be $1.43×{10}^{-5}$ for the decays ${D}^{+\left(-\right)}\to \overline{n}\left(n\right){e}^{+\left(-\right)}$ with $\Delta |B-L|=0$, and $2.91×{10}^{-5}$ for the decays ${D}^{+\left(-\right)}\to n\left(\overline{n}\right){e}^{+\left(-\right)}$ with $\Delta |B-L|=2$, where $\Delta |B-L|$ denotes the change in the difference between baryon and lepton numbers.