We report a new precise determination of the leptonic widths of the J/psi
meson performed with the KEDR detector at the VEPP-4M $e^{+}e^{-}$ collider.
The measured values of the J/psi parameters are:
Gamma_{ee} imesGamma_{ee}/Gamma = 0.3323 pm 0.0064 (stat.) pm 0.0048
(syst.) keV Gamma_{ee} imesGamma_{mumu}/Gamma=0.3318 pm 0.0052 (stat.)
pm 0.0063 (syst.) keV. Assuming $emu$ universality and using the table value
of the branching ratios the leptonic Gamma_{ll}= 5.59 pm 0.12 keV width and
the total Gamma=94.1 pm 2.7 keV widths were obtained. We also discuss in
detail a method to calculate radiative corrections at a narrow resonance.
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