Search for baryon and lepton number violation decay $D^{\pm }\to n(\bar{n})e^{\pm }$

Using a data set of electron-positron collisions corresponding to an integrated luminosity of $2.93\mathrm{f}{\mathrm{b}}^{-1}$ 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 $D^{\pm }\to n(\bar{n})e^{\pm }$ is performed. No signal is observed and the upper limits on the branching fractions at the $90\mathrm{\%}$ confidence level are set to be $1.43\times {10}^{-5}$ for the decays $D^{+(-)}\to \bar{n}(n)e^{+(-)}$ with $\mathrm{\Delta }\mathrm{\mid }B-L\mathrm{\mid }=0$, and $2.91\times {10}^{-5}$ for the decays $D^{+(-)}\to n(\bar{n})e^{+(-)}$ with $\mathrm{\Delta }\mathrm{\mid }B-L\mathrm{\mid }=2$ , where $\mathrm{\Delta }\mathrm{\mid }B-L\mathrm{\mid }$ denotes the change in the difference between baryon and lepton numbers.