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Determinations of $V_{u s}$ $V_{u s}$ using inclusive hadronic $τ$ $τ$ decay data

Kim Maltman

Mathematics and Statistics, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada

CSSM, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia

E-mail Address: kmaltman@yorku.ca

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Renwick James Hudspith

Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada

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Randy Lewis

Physics and Astronomy, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada

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Taku Izubuchi

RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA

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Hiroshi Ohki

RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA

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, and

James M. Zanotti

CSSM, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia

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https://doi.org/10.1142/S0217732316300305Cited by:4 (Source: Crossref)

Abstract

Two methods for determining $| V_{u s} |$ $| V_{u s} |$ employing inclusive hadronic $τ$ $τ$ decay data are discussed. The first is the conventional flavor-breaking sum rule determination whose usual implementation produces results $\sim 3 σ$ $\sim 3 σ$ low compared to three-family unitary expectations. The second is a novel approach combining experimental strange hadronic $τ$ $τ$ distributions with lattice light-strange current–current two-point function data. Preliminary explorations of the latter show the method promises $| V_{u s} |$ $| V_{u s} |$ determinations competitive with those from $K_{ℓ 3}$ $K_{ℓ 3}$ and $Γ [K_{μ 2}] / Γ [π_{μ 2}]$ $Γ [K_{μ 2}] / Γ [π_{μ 2}]$ . For the former, systematic issues in the conventional implementation are investigated. Unphysical dependences of $| V_{u s} |$ $| V_{u s} |$ on the choice of sum rule weight, $w$ $w$ , and upper limit, $s_{0}$ $s_{0}$ , 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 $D = 2$ $D = 2$ OPE series. The results for $| V_{u s} |$ $| V_{u s} |$ from this new implementation are shown to be free of unphysical $w$ $w$ - and $s_{0}$ $s_{0}$ -dependences, and $\sim 0.0020$ $\sim 0.0020$ higher than those produced by the conventional implementation. With preliminary new $K π$ $K π$ branching fraction results as input, we find $| V_{u s} |$ $| V_{u s} |$ in excellent agreement with that obtained from $K_{ℓ 3}$ $K_{ℓ 3}$ , and compatible within errors with expectations from three-family unitarity.

Keywords:

PACS: 12.15.Hh, 11.55.Hx, 12.38.Gc

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