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arXiv 1007.0684hep-ph
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次次领头阶级的Epsilon_K:粲顶夸克贡献

Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution

Joachim Brod, Martin Gorbahn

摘要:

我们对粲顶夸克对标准模型中有效Delta S = 2 Hamilton量的贡献eta_ct进行了次次领头阶(NNLO)QCD分析。eta_ct表示短距离对参数k_K的贡献的重要部分。我们计算了主导算符Q_S2的三圈反常维数、电流-电流算符和企鹅算符在Q_S2中的三圈混合以及相应的电弱、底夸克和粲夸克尺度下的双圈匹配条件。作为我们的最终数值结果,我们得到eta_ct = 0.496 +/- 0.047,这比次首阶(NLO)值eta_ct(NLO)= 0.457 +/- 0.073大约大7%。这导致预测为η_K =(1.90 +/- 0.26)x 10^(-3),其对应于相对于使用eta_ct(NLO)获得的值的约3.3%的增强。

英文摘要:

We perform a next-to-next-to-leading order (NNLO) QCD analysis of the charm-top-quark contribution eta_ct to the effective Delta S = 2 Hamiltonian in the Standard Model. eta_ct represents an important part of the short distance contribution to the parameter epsilon_K. We calculate the three-loop anomalous dimension of the leading operator Q_S2, the three-loop mixing of the current-current and penguin operators into Q_S2, and the corresponding two-loop matching conditions at the electroweak, the bottom-quark, and the charm-quark scale. As our final numerical result we obtain eta_ct = 0.496 +/- 0.047, which is roughly 7% larger than the next-to-leading-order (NLO) value eta_ct(NLO) = 0.457 +/- 0.073. This results in a prediction for epsilon_K = (1.90 +/- 0.26) x 10^(-3), which corresponds to an enhancement of approximately 3.3% with respect to the value obtained using eta_ct(NLO).

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