Precision measurement of the J/ψ→μ⁺μ⁻μ⁺μ⁻ branching fraction and search for a new gauge boson Z^ at BESIII

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We present a precision measurement of the branching fraction of the rare decay J/ψ→μ⁺μ⁻μ⁺μ⁻, and a search for a new gauge boson Z^ that couples only to the second and third lepton generations, using a data sample of (8998 ± 39) × 10⁶ $J/ψ$ events collected by the BESIII detector. The branching fraction of the J/ψ→μ⁺μ⁻μ⁺μ⁻ decay is measured to be B(J/ψ→μ⁺μ⁻μ⁺μ⁻)=[0.91±0.04~ (stat.)±0.07~ (syst.)]× 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/ψ→μ⁺μ⁻μ⁺μ⁻ decay and determine the T-odd observable to be AT = [0.05± 0.04~ (stat.)±0.01~ (syst.)], which is consistent with $CP$ conservation. In the search for J/ψ→ Z^μ⁺μ⁻ via Z^→μ⁺μ⁻, no significant Z^ signal is observed in the μ⁺μ⁻ invariant mass region of $(0.212,~2.6)$~GeV/c², and we set upper limits on the U(1)L_μ-L_τ model coupling constant g^ 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^ masses below $0.7$~GeV/c².