We report on a precision measurement of the ratio ${cal R}_{taumu}^{Upsilon(3S)} = {cal B}(Upsilon(3S)totau^+tau^-)/{cal B}(Upsilon(3S)tomu^+mu^-)$ using data collected with the BaBar detector at the SLAC PEP-II $e^+e^-$ collider. The measurement is based on a 28 fb$^{-1}$ data sample collected at a center-of-mass energy of 10.355 GeV corresponding to a sample of 122 million $Upsilon(3S)$ mesons. The ratio is measured to be ${cal R}_{taumu}^{Upsilon(3S)} = 0.966 pm 0.008_mathrm{stat} pm 0.014_mathrm{syst}$ and is in agreement with the Standard Model prediction of 0.9948 within 2 standard deviations. The uncertainty in ${cal R}_{taumu}^{Upsilon(3S)}$ is almost an order of magnitude smaller than the only previous measurement.
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