Determination of $J/\psi$ leptonic branching fraction via $\psi \mathrm{}\left(2S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}J/\psi$

A comparison of the rates for $\psi \mathrm{}\left(2S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}J/\psi ,$ $J/\overrightarrow{\psi }{l}^{+}{l}^{-}$ and $J/\overrightarrow{\psi }$ anything is used to determine the $J/\psi$ leptonic branching fractions. The results are $B(J/\overrightarrow{\psi }{e}^{+}{e}^{-})=(5.90\mathrm{}\pm 0.05\pm 0.10)\%$ and $B(J/\overrightarrow{\psi }{\mu }^{+}{\mu }^{-})=(5.84\mathrm{}\pm 0.06\pm 0.10)\%,$ where the first error is statistical and the second is systematic. Assuming lepton universality, the leptonic branching fraction of the $J/\psi$ is $B(J/\overrightarrow{\psi }{l}^{+}{l}^{-})=(5.87\mathrm{}\pm 0.04\pm 0.09)\%$ per species. This result is used to estimate the QCD scale factor ${\Lambda }_{\mathrm{MS}¯}^{\mathrm{}\left(4\right)\mathrm{}}$ and the strong coupling constant ${\alpha }_s.$