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

We report on a precision measurement of the ratio ${\cal R}_{\tau\mu}^{\Upsilon(3S)} = {\cal B}(\Upsilon(3S)\to\tau^+\tau^-)/{\cal B}(\Upsilon(3S)\to\mu^+\mu^-)$ 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 ${\cal R}_{\tau\mu}^{\Upsilon(3S)} = 0.966 \pm 0.008_\mathrm{stat} \pm 0.014_\mathrm{syst}$ and is in agreement with the Standard Model prediction of 0.9948 within 2 standard deviations. The uncertainty in ${\cal R}_{\tau\mu}^{\Upsilon(3S)}$ is almost an order of magnitude smaller than the only previous measurement.