Measurements of Charged Current Lepton Universality and $|V_{us}|$ using Tau Lepton Decays to $e^- \barν_e ν_τ$, $μ^- \barν_μν_τ$, $π^- ν_τ$, and $\K^- ν_τ$
Using 467 $fb^{-1}$ of $e^+e^-$ annihilation data collected with the BaBar detector, we measure $\frac{\cal{B}(τ^- \to μ^- \barν_μν_τ)}{\cal{B}(τ^- \to e^- \barν_e ν_τ)} = (0.9796 \pm 0.0016 \pm 0.0036)$, $\frac{\cal{B}(τ^- \to π^- ν_τ)}{\cal{B}(τ^- \to e^- \barν_e ν_τ)} = (0.5945 \pm 0.0014 \pm 0.0061)$, and $\frac{\cal{B}(τ^- \to \K^- ν_τ)}{\cal{B}(τ^- \to e^- \barν_e ν_τ)} = (0.03882 \pm 0.00032 \pm 0.00057)$, where the uncertainties are statistical and systematic, respectively. From these precision $τ$ measurements, we test the Standard Model assumption of $μ$-$e$ and $τ$-$μ$ 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.