Search for the charged lepton flavor violating decay $\eta \to e^{\pm }{\mu }^{\mp }$

Based on $(10.087\pm 0.044)\times {10}^{9}J\mathrm{/}\psi$ events collected at the center-of-mass energy $\sqrt{s}=3.097$~GeV with the BESIII detector, we search for the charged lepton flavor violating decay $\eta \to e^{\pm }{\mu }^{\mp }$ through the process $J\mathrm{/}\psi \to \gamma {\eta }^{\mathrm{\prime }}$ with ${\eta }^{\mathrm{\prime }}\to {\pi }^{+}{\pi }^{-}\eta$. No signal is observed, and an upper limit on the branching fraction is determined to be $\mathcal{B}(\eta \to e^{\pm }{\mu }^{\mp })<6.8\times {10}^{-7}$ at the 90% confidence level. This result improves the previous best limit by one order of magnitude.