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arXiv · 1312.1716

Lattice Input on the Inclusive $τ$ Decay $V_{us}$ Puzzle

P. A. Boyle·L. Del Debbio·N. Garron·R. J. Hudspith·E. Kerrane·K. Maltman·J. M. Zanotti
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Abstract

Recent analyses of flavor-breaking hadronic-$τ$-decay-based sum rules produce values of $\vert V_{us}\vert$ $\sim 3σ$ 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 $τ$-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.

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P. A. Boyle, L. Del Debbio, N. Garron, R. J. Hudspith, E. Kerrane, K. Maltman, J. M. Zanotti. 2013-12-05. Lattice Input on the Inclusive $τ$ Decay $V_{us}$ Puzzle. https://doi.org/10.1142/s2010194514604414

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