Precision measurement of the $\mathcal{B}(\mathrm{{\rm Y}}(3S)\to {\tau }^{+}{\tau }^{-})\mathrm{/}\mathcal{B}(\mathrm{{\rm Y}}(3S)\to {\mu }^{+}{\mu }^{-})$ 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 $\mathrm{{\rm Y}}(3S)$ mesons. The ratio is measured to be ${\cal R}{\tau\mu}^{\Upsilon(3S)} = 0.966 \pm 0.008_$\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}$ \pm 0.014_$\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}$$ 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.