Precision Measurements of ${\cal B}[ψ(3686) \to π^+π^- J/ψ]$ and ${\cal B}[J/ψ\to l^+l^-]$

Based on $(106.41 \pm 0.86)\times 10^{6}$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII collider, the branching fractions of $ψ(3686) \to π^+π^- J/ψ$, $J/ψ\to e^+e^- $, and $J/ψ\to μ^+μ^-$ are measured. We obtain ${\cal B}[ψ(3686) \to π^+π^-J/ψ]=(34.98\pm 0.02\pm 0.45)%$, ${\cal B}[J/ψ\to e^+e^-] = (5.983 \pm 0.007 \pm 0.037)%$ and ${\cal B}[J/ψ\to μ^+μ^-] = (5.973 \pm 0.007 \pm 0.038)%$. The measurement of ${\cal B}[ψ(3686) \to π^{+}π^{-}J/ψ]$ confirms the CLEO-c measurement, and is apparently larger than the others. The measured $J/ψ$ leptonic decay branching fractions agree with previous experiments within one standard deviation. These results lead to ${\cal B}[J/ψ\to l^+l^-] = (5.978 \pm 0.005 \pm 0.040)%$ by averaging over the $e^{+}e^{-}$ and $μ^{+}μ^{-}$ channels and a ratio of ${\cal B}[J/ψ\to e^+e^-] / {\cal B}[J/ψ\to μ^+μ^-] = 1.0017 \pm 0.0017 \pm 0.0033$, which tests $e$-$μ$ universality at the four tenths of a percent level. All the measurements presented in this paper are the most precise in the world to date.