Lattice Input on the Inclusive \(\tau\) Decay \(V_{us}\) Puzzle

Recent analyses of flavor-breaking hadronic-\(\tau\)-decay-based sum rules produce values of \(\vert V_{us}\vert\) \(\sim 3\sigma\) low compared to 3-family unitarity expectations. An unresolved systematic issue is the significant variation in \(\vert V_{us}\vert\) produced by different prescriptions for treating the slowly converging \(D=2\) OPE series. We investigate the reliability of these prescriptions using lattice data for various flavor-breaking correlators and show the fixed-scale prescription is clearly preferred. Preliminary updates of the conventional \(\tau\)-based, and related mixed \(\tau\)-electroproduction-data-based, sum rule analyses incorporating B-factory results for low-multiplicity strange \(\tau\) decay mode distributions are then performed. Use of the preferred FOPT \(D=2\) OPE prescription is shown to significantly reduce the discrepancy between 3-family unitarity expectations and the sum rule results.