Observation of $eta^primerightarrowpi^+pi^-mu^+mu^-$

Using $(1310.6 pm 7.0) times 10^{6}~J/psi$ events acquired with the BESIII detector at the BEPCII storage rings, the decay $eta^primerightarrowpi^+pi^-mu^+mu^-$ is observed for the first time with a significance of 8$sigma$ via the process $J/psirightarrowgammaeta$. We measure the branching fraction of $eta^primerightarrowpi^+pi^-mu^+mu^-$ to be $mathcal{B}(eta^primerightarrowpi^+pi^-mu^+mu^-)$=(1.97$pm$0.33(stat.)$pm$0.18(syst.))$times10^{-5}$, where the first and second uncertainties are statistical and systematic, respectively.