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arXiv · 1510.06954

A resolution of the inclusive flavor-breaking sum rule $τ$ $V_{us}$ puzzle

K. Maltman·R. J. Hudspith·R. Lewis·C. E. Wolfe·J. Zanotti
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Abstract

A combination of continuum and lattice methods is used to investigate systematic issues in the finite-energy-sum-rule determination of $V_{us}$ based on flavor-breaking combinations of hadronic $τ$ decay data. Results for $V_{us}$ obtained using assumptions for $D>4$ OPE contributions employed in previous conventional implementations of this approach are shown to display significant unphysical dependences on the choice of sum rule weight, $w$, and upper limit, $s_0$, of the relevant experimental spectral integrals. Continuum and lattice results suggest the necessity of a new implementation of the flavor-breaking sum rule approach, in which not only $\vert V_{us}\vert$, but also $D>4$ effective condensates are fit to data. Lattice results also provide a means of quantifying the truncation error for the slowly converging $D=2$ OPE series. The new implementation is shown to produce $\vert V_{us}\vert$ results free of unphysical $s_0$- and $w$-dependences and typically $\sim 0.0020$ higher than the (unstable) results found using the conventional implementation. With preliminary new experimental results for the $Kπ$ branching fraction, the resulting $\vert V_{us}\vert$ is in excellent agreement with that obtained from $K_{\ell 3}$, and compatible within errors with expectations from three-family unitarity.

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K. Maltman, R. J. Hudspith, R. Lewis, C. E. Wolfe, J. Zanotti. 2015-10-23. A resolution of the inclusive flavor-breaking sum rule $τ$ $V_{us}$ puzzle. https://arxiv.org/abs/1510.06954

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