3-family Unitarity Research Articles

Lattice Input on the τ[formula omitted] Puzzle

|Vus| values obtained from recent hadronic-τ-decay-based flavor-breaking sum rule analyses are significantly lower than expectations based on 3-family unitarity and results obtained from other sources. We use lattice data to investigate the accuracy/reliability of the OPE representation of the flavor-breaking correlator combination entering these analyses. The behavior of an alternate combination, chosen to reduce problems associated with the slow convergence of the D=2 OPE series, and entering an alternate mixed τ-electroproduction sum rule, is also investigated. Preliminary updates of both analyses, predicated on lessons learned from the lattice data, are also presented.

LATTICE INPUT ON THE INCLUSIVE τ DECAY Vus PUZZLE

Recent analyses of flavor-breaking hadronic-τ-decay-based sum rules produce values of |Vus| ~ 3σ low compared to 3-family unitarity expectations. An unresolved systematic issue is the significant variation in |Vus| 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 τ-based, and related mixed τ-electroproduction-data-based, sum rule analyses incorporating B-factory results for low-multiplicity strange τ 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.

A critical look at [formula omitted] determinations from hadronic τ decay data

A critical review of hadronic tau decay data based determinations of |V_{us}| is given, focussing on the impact of the slow convergence of the integrated D=2 OPE series for the conventional flavor-breaking sum rule determination and the potential role of as-yet-unmeasured multiparticle contributions to the strange spectral distribution. Additional information obtainable from analyses of inclusive strange decay data alone, and from mixed electroproduction-tau sum rules with much reduced OPE uncertainties, is also discussed. Self-consistency tests are shown to favor determinations which reduce somewhat discrepancies with 3-family unitarity expectations.

Status of the Hadronic τ Decay Determination of [formula omitted

We update the hadronic τ determination of | V u s | , showing that current strange branching fractions produce results 2 − 3 σ lower than 3-family unitarity expectations. Issues related to the size of theoretical uncertainties and results from an alternate, mixed τ-electroproduction sum rule determination are also considered.

A mixed τ-electroproduction sum rule for [formula omitted

The interpretation of results of recent τ decay determinations of |Vus|, which yield values ∼3σ low compared to 3-family unitarity expectations, is complicated by the slow convergence of the relevant integrated D=2 OPE series. We introduce a class of new sum rules involving both electroproduction and τ decay data designed to deal with this problem by strongly suppressing D=2 OPE contributions at the correlator level. Experimental complications are briefly discussed and an example of the improved control over theoretical errors presented. The uncertainty on the resulting determination, |Vus|=0.2202(39), is entirely dominated by experimental errors, and should be subject to significant near-term improvement.

STATUS OF THE HADRONIC τ DETERMINATION OF Vus

We update the extraction of Vus 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.