Continuum and lattice methods are used to investigate systematic issues in the sum rule determination of $V_{ us}$ using inclusive hadronic $\tau$ decay data. Results for $V_{ us}$ employing assumptions for $D>4$ OPE contributions used in previous conventional implementations of this approach are shown to display unphysical dependence on the sum rule weight, $w$, and choice of upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest a new implementation of the sum rule approach with not just $\vert V_{ us}\vert$, but also $D>4$ effective condensates, fit to data. Lattice results are also shown to provide a quantitative assessment of truncation uncertainties for the slowly converging $D=2$ OPE series. The new sum rule implementation yields $\vert V_{ us}\vert$ results free of unphysical $s_0$- and $w$-dependences and $\sim 0.0020$ higher than that obtained using the conventional implementation. With preliminary new experimental results for the $K\pi$ branching fraction, the resulting $\vert V_{ us}\vert$ is in excellent agreement with that based on $K_{ \ell 3}$, and compatible within errors with expectations from three-family unitarity.
Categories: hep-ph hep-ex hep-lat