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We report on a precision measurement of the ratio ${\calR}_{\tau\mu}^{\Upsilon(3S)} = {\cal B}(\Upsilon(3S)\to\tau^+\tau^-)/{\calB}(\Upsilon(3S)\to\mu^+\mu^-)$ using data collected with the BaBar detector atthe 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 toa sample of 122 million $\Upsilon(3S)$ mesons. The ratio is measured to be${\cal R}_{\tau\mu}^{\Upsilon(3S)} = 0.966 \pm 0.008_\mathrm{stat} \pm0.014_\mathrm{syst}$ and is in agreement with the Standard Model prediction of0.9948 within 2 standard deviations. The uncertainty in ${\calR}_{\tau\mu}^{\Upsilon(3S)}$ is almost an order of magnitude smaller than theonly previous measurement.

Precision measurement of the ${\cal B}(\Upsilon(3S)\to\tau^+\tau^-)/{\cal B}(\Upsilon(3S)\to\mu^+\mu^-)$ ratio