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

We revisit the puzzle of vertical bar V-us vertical bar values obtained from the conventional implementation of hadronic-tau-decay-based flavor-breaking finite-energy sum rules lying > 3 sigma below the expectations of three-family unitarity. Significant unphysical dependences of vertical bar V-us vertical bar 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 vertical bar V-us vertical bar, 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 wand s(0)-dependence of vertical bar V-us vertical bar and to produce results similar to 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 K pi branching fractions, we find vertical bar V-us vertical bar = 0.2231(27)(exp)(4)(th), in excellent agreement with the result from K-l3, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive t vertical bar V-us vertical bar puzzle. (c) 2018 The Authors. Published by Elsevier B.V.