A resolution of the inclusive flavor-breaking $\ddot{I}„$ $|V_{us}|$ puzzle

Abstract

We revisit the puzzle of $|V_{us}|$ values obtained from the conventional implementation of hadronic-$\ddot{I}„$-decay-based flavor-breaking finite-energy sum rules lying $>3\ddot{I}ƒ$ below the expectations of three-family unitarity. Significant unphysical dependences of $|V_{us}|$ 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 is 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 $|V_{us}|$, 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 $|V_{us}|$ and to produce results $\sim 0.0020$ higher than those of the conventional implementation. With B-factory input, and using, in addition, dispersively constrained results for the $K\ddot{I}€$ branching fractions, we find $|V_{us}|=0.2231(27{)}_{exp}(4{)}_{th}$, 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 $\ddot{I}„$ $|V_{us}|$ puzzle.

15 pages, 4 figures. Updated treatment of strange hadronic tau decay data; expanded discussion of the breakdown of the conventional implementation approach. Final version to appear in Physics Letters B