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

Abstract

We revisit the puzzle of |Vus| values obtained from the conventional implementation of hadronic-τ- decay-based flavor-breaking finite-energy sum rules lying >3σ below the expectations of three-family unitarity. Significant unphysical dependences of |Vus| on the choice of weight, w, and upper limit, s0, 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 , but also |Vus|, 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 s0-dependence of |Vus| 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 |Vus| = 0.2231(27)exp(4)th, in excellent agreement with the result from Kℓ3 and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive τ |Vus| puzzle.