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arXiv 1507.06326hep-phhep-exhep-lat
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大N QCD的ε ′/ε ′参数B_6^{(1/2)}和B_8^{(3/2)}的上界及其它

Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News

Andrzej J. Buras, Jean-Marc Gerard

摘要:

我们证明了在作者与Barclay合作发展的大N方法中,参数化主QCD和电弱算符的K \to ππ矩阵元_0和_2的参数B_6^{(1/2)}和B_8^{(3/2)}<Q_6><Q_8>都受到负的O(1/N)修正,使得B_6^{(1/2)} &lt; B_8^{(3/2)}&lt;1与RBC-UKQCD合作的最近晶格结果一致。我们还指出,通过格点合作得到的所有QCD和电弱企鹅算符Q_i对K \to ππ振幅A_0和A_2的贡献的强子矩阵元的大小模式,为我们的大N方法提供了进一步的支持。特别地,矩阵元素_0的非常精确的晶格结果<Q_8>意味着对应的参数B_8^{(1/2)}=1.0 \pm 0.2与大的N值B_8^{(1/2)}=1.1 \pm 0.1相比较。我们简要地讨论了这些发现的比值ε '/ε ′的影响。事实上,根据RBC-UKQCD合作的B_8^{(3/2)}的精确值,我们关于B_6^{(1/2)}的上限意味着SM中的ε '/ε大约比其实验值(16.6 PDMATHAMN 2.3)\times 10^{-4}低两倍。对参数\hat B_K和ΔI=1/2规则也作了简要的评述。

英文摘要:

We demonstrate that in the large N approach developed by the authors in collaboration with Bardeen, the parameters B_6^{(1/2)} and B_8^{(3/2)} parametrizing the K\toππmatrix elements <Q_6>_0 and <Q_8>_2 of the dominant QCD and electroweak operators receive both negative O(1/N) corrections such that B_6^{(1/2)} < B_8^{(3/2)}<1 in agreement with the recent lattice results of the RBC-UKQCD collaboration. We also point out that the pattern of the size of the hadronic matrix elements of all QCD and electroweak penguin operators Q_i contributing to the K\to ππamplitudes A_0 and A_2, obtained by this lattice collaboration, provides further support to our large N approach. In particular, a very precise lattice result for the matrix element <Q_8>_0 implies for the corresponding parameter B_8^{(1/2)}=1.0\pm 0.2 to be compared with large N value B_8^{(1/2)}=1.1\pm 0.1. We discuss briefly the implications of these findings for the ratio epsilon'/epsilon. In fact, with the precise value for B_8^{(3/2)} from RBC-UKQCD collaboration, our upper bound on B_6^{(1/2)} implies epsilon'/epsilon in the SM roughly by a factor of two below its experimental value (16.6\pm 2.3)\times 10^{-4}. We also briefly comment on the parameter \hat B_K and the ΔI=1/2$ rule.

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