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arXiv 1702.01767hep-phhep-exhep-lat
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$τ$ $|V_{us}|$问题的解决方案

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

Renwick J. Hudspith, Randy Lewis, Kim Maltman, James Zanotti

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15 pages, 4 figures. Updated treatment of strange hadronic tau decay data; expanded discussion of the breakdown of the conventional implementation approach. Final version to appear in Physics Letters B
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摘要：

我们重新审视的难题$|V_{us}|$值从传统的实施强子$τ$衰变为基础的味道打破有限能量和规则躺在$>3 σ$低于三族幺正性的期望。显着的非物理依赖$|V_{us}|$上的选择的重量，w，和上限，$s_0$，进入分析的实验光谱积分的确认，并在估计更高的维度，$D>4$，OPE的贡献的假设故障被确定为这些问题的主要来源。一个连续和晶格的结果相结合，提出了一个新的实施的风味打破总和规则的方法，其中不仅$|V_{us}|$，但也$D>4$有效的冷凝物，适合的数据。晶格结果还用于阐明如何可靠地处理缓慢收敛的D=2 OPE系列。新的总和规则的实施被证明是治愈的问题的非物理的W-和$s_0$ -$|V_{us}|$的依赖性，并产生结果$\sim 0.0020$高于传统的实施。与B工厂的输入，并使用，此外，分散约束的结果的$Kπ$分支分数，我们发现$\vert V_{us}\vert =0.2231(27)_{exp}(4)_{th}$，在极好的协议与结果从$K_{\ell 3}$，并兼容的错误与预期的三个家庭的酉性，从而解决了长期以来的包容性$τ$ $|V_{us}|$难题。

英文摘要：

We revisit the puzzle of $|V_{us}|$ values obtained from the conventional implementation of hadronic-$τ$-decay-based flavor-breaking finite-energy sum rules lying $>3 σ$ below the expectations of three-family unitarity. Significant unphysical dependences of $|V_{us}|$ on the choice of weight, w, and upper limit, $s_0$, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, $D>4$, OPE contributions is identified as the main source of these problems. A combination of continuum and lattice results is shown to suggest a new implementation of the flavor-breaking sum rule approach in which not only $|V_{us}|$, but also $D>4$ effective condensates, are fit to data. Lattice results are also used to clarify how to reliably treat the slowly converging D=2 OPE series. The new sum rule implementation is shown to cure the problems of the unphysical w- and $s_0$-dependence of $|V_{us}|$ and to produce results $\sim 0.0020$ higher than those of the conventional implementation. With B-factory input, and using, in addition, dispersively constrained results for the $Kπ$ branching fractions, we find $\vert V_{us}\vert =0.2231(27)_{exp}(4)_{th}$, in excellent agreement with the result from $K_{\ell 3}$, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive $τ$ $|V_{us}|$ puzzle.

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