Precision measurement of the $J/\psi \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ branching fraction and search for a new gauge boson $Z^{\prime }$ at BESIII

Abstract

We present a precision measurement of the branching fraction of the rare decay $J/\psi \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$, and a search for a new gauge boson $Z^{\prime }$ that couples only to the second and third lepton generations, using a data sample of $(8998\pm 39)\times 10^6$ $J/\psi$ events collected by the BESIII detector. The branching fraction of the $J/\psi \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ decay is measured to be $B(J/\psi \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-})=[0.91\pm 0.04(stat.)\pm 0.07(syst.)]\times 10^{-6}$, representing the most precise measurement to date and consistent with the theoretical prediction within one standard deviation. Additionally, we search for $CP$ asymmetry in the $J/\psi \to {\mu }^{+}{\mu }^{-}{\mu }^{+}{\mu }^{-}$ decay and determine the T-odd observable to be $A_T=[0.05\pm 0.04(stat.)\pm 0.01(syst.)]$, which is consistent with $CP$ conservation. In the search for $J/\psi \to Z^{\prime }{\mu }^{+}{\mu }^{-}$ via $Z^{\prime }\to {\mu }^{+}{\mu }^{-}$, no significant $Z^{\prime }$ signal is observed in the ${\mu }^{+}{\mu }^{-}$ invariant mass region of $(0.212,2.6)$~GeV$/c^2$, and we set upper limits on the $\mathrm{U}(1{)}_{L_{\mu }-L_{\tau }}$ model coupling constant $g^{\prime }$ ranging from 0.001 to 0.294 at the 90\% confidence level, which is comparable to the upper limits set by Belle II for $Z^{\prime }$ masses below $0.7$~GeV$/c^2$.

arXiv comment19 pages, 6 figures