A resolution of the inclusive flavor-breaking τ |Vus| puzzle

We revisit the puzzle of $\left|V_{us}\right|$ values obtained from the conventional implementation of hadronic-τ- decay-based flavor-breaking finite-energy sum rules lying $>3\sigma$ below the expectations of three-family unitarity. Significant unphysical dependences of $\left|V_{us}\right|$ on the choice of weight, w, and upper limit, $s_0$, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, $D>4$, OPE contributions identified as the main source of these problems. A combination of continuum and lattice results is shown to suggest a new implementation of the flavor-breaking sum rule approach in which not only $\left|V_{us}\right|$, but also $D>4$ effective condensates, are fit to data. Lattice results are also used to clarify how to reliably treat the slowly converging $D=2$ OPE series. The new sum rule implementation is shown to cure the problems of the unphysical w- and $s_0$-dependence of $\left|V_{us}\right|$ and to produce results ∼0.0020 higher than those of the conventional implementation employing the same data. With B-factory input, and using, in addition, dispersively constrained results for the Kπ branching fractions, we find $\left|V_{us}\right|=0.2231{\left(27\right)}_{exp}{\left(4\right)}_{th}$, in excellent agreement with the result from $K_{\ell 3}$, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive τ $\left|V_{us}\right|$ puzzle.