| Abstract |
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Using 467 $fb^{-1}$ of $e^+e^-$ annihilation data collected with the BaBar detector, we measure
$\frac{{\cal{B}}(\tau^- \to \mu^- \bar{\nu}_\mu \nu_\tau)}{{\cal{B}}(\tau^- \to e^- \bar{\nu}_e \nu_\tau)} = (0.9796 \pm 0.0016 \pm 0.0036)$,
$\frac{{\cal{B}}(\tau^- \to \pi^- \nu_\tau)}{{\cal{B}}(\tau^- \to e^- \bar{\nu}_e \nu_\tau)} = (0.5945 \pm 0.0014 \pm 0.0061)$, and
$\frac{{\cal{B}}(\tau^- \to \K^- \nu_\tau)}{{\cal{B}}(\tau^- \to e^- \bar{\nu}_e \nu_\tau)} = (0.03882 \pm 0.00032 \pm 0.00057)$,
where the uncertainties are statistical and systematic, respectively.
From these precision $\tau$ measurements,
we test the Standard Model assumption of $\mu$-$e$ and $\tau$-$\mu$ charge current lepton universality and
provide determinations of $|V_{us}|$ experimentally
independent of the decay of a kaon and which we compare with the value
predicted from the unitarity of the Cabibbo-Kobayashi-Maskawa matrix.
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