Narrow Results

The decay constant of is the key quantity to determine the production rate of in τ decays. By assuming is the lowest scalar bound state of , the decay constant can be calculated reliably in QCD sum rule. Then the decay branching ratio of is predicted to be about (7.9±3.1)×10^-5. If this branching ratio can be measured by experiment, it should be helpful to make clear the structure of .

Two methods for determining $\left|V_{us}\right|$ employing inclusive hadronic $\tau$ decay data are discussed. The first is the conventional flavor-breaking sum rule determination whose usual implementation produces results $\sim 3\sigma$ low compared to three-family unitary expectations. The second is a novel approach combining experimental strange hadronic $\tau$ distributions with lattice light-strange current–current two-point function data. Preliminary explorations of the latter show the method promises $\left|V_{us}\right|$ determinations competitive with those from $K_{\ell 3}$ and $\mathrm{\Gamma }[K_{\mu 2}]/\mathrm{\Gamma }[{\pi }_{\mu 2}]$. For the former, systematic issues in the conventional implementation are investigated. Unphysical dependences of $\left|V_{us}\right|$ on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the weighted experimental spectral integrals are observed, the source of these problems identified and a new implementation which overcomes these problems developed. Lattice results are shown to provide a tool for quantitatively assessing truncation uncertainties for the slowly converging $D=2$ OPE series. The results for $\left|V_{us}\right|$ from this new implementation are shown to be free of unphysical $w$- and $s_0$-dependences, and $\sim 0.0020$ higher than those produced by the conventional implementation. With preliminary new $K\pi$ branching fraction results as input, we find $\left|V_{us}\right|$ in excellent agreement with that obtained from $K_{\ell 3}$, and compatible within errors with expectations from three-family unitarity.

We update the extraction of V_us from hadronic τ decay data in light of recent BaBar and Belle results on the branching fractions of a number of important strange decay modes. A range of sum rule analyses is employed, particular attention being paid to those based on “non-spectral weights”, developed previously to bring the slow convergence of the relevant integrated D = 2 OPE series under improved control. Results from the various sum rules are in good agreement with one another, but ~ 3σ below expectations based on 3-family unitarity.