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.