The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
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DOI：
10.1016/j.nuclphysb.2004.03.030
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发表时间：
2004-03
期刊：
影响因子：
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通讯作者：
S. Moch;J. Vermaseren;A. Vogt
中科院分区：
文献类型：
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作者：
S. Moch;J. Vermaseren;A. Vogt
计算了微扰QCD中非极化非单重态夸克密度组合演化的三个分裂函数的次-次-主导阶（NNLO）贡献。我们的结果与文献中的部分结果一致。我们发现，正确的领先对数（LL）预测小动量分数x不提供一个很好的估计各自的完整结果。一个新的，不可预测的LL贡献被发现的颜色因子dabcdabcentering在三个循环的第一次。我们调查的修正的大小和稳定性的NNLO演化下的重整化标度的变化。除了非常小的x的校正被发现是相当小的，即使是大的值的强耦合常数，原则上促进微扰演化到子GeV政权。
We compute the next-to-next-to-leading order (NNLO) contributions to the three splitting functions governing the evolution of unpolarized non-singlet combinations of quark densities in perturbative QCD. Our results agree with all partial results available in the literature. We find that the correct leading logarithmic (LL) predictions for small momentum fractions x do not provide a good estimate of the respective complete results. A new, unpredicted LL contribution is found for the colour factor dabcdabcentering at three loops for the first time. We investigate the size of the corrections and the stability of the NNLO evolution under variation of the renormalization scale. Except for very small x the corrections are found to be rather small even for large values of the strong coupling constant, in principle facilitating a perturbative evolution into the sub-GeV regime.