arXiv 0905.31932009-05-20hep-ph

QCD矩阵元的R-演化

The R-evolution of QCD matrix elements

Andre H. Hoang, Ambar Jain, Ignazio Scimemi, Iain W. Stewart

备注：: International Workshop on Effective Field Theories: from the Pion to the Upsilon 1-6 February 2009,Valencia, Spain

摘要：

QCD中的微扰级数通常是渐近的，并且存在所谓的红外重正子模糊性。在MS-bar中的标准算子乘积展开的上下文中，这些模糊性由更高维算子的矩阵元素补偿，但是由于大的数值取消，该过程可能难以控制。取决于减法尺度R的矩阵元素和系数的显式减法可以避免这个问题。对于不同的过程，威尔逊系数中R的适当选择可以有很大的不同。在这次演讲中，我们讨论了重整化群的发展与规模R，并表明，它总结了大规模的过程与广泛不同的R的差异。我们还证明了R-发展方程的解可以用来恢复扰动级数的Borel变换中奇点的所有阶渐近形式。对于这些奇异性的归一化，我们得到了一个快速收敛的求和规则，只需要已知的微扰系数作为输入。该求和规则可以作为一种新的检验重正马龙歧义的方法，而不需要回答大β_0近似。

英文摘要：

Perturbation series in QCD are generally asymptotic and suffer from so-called infrared renormalon ambiguities. In the context of the standard operator product expansion in MS-bar these ambiguities are compensated by matrix elements of higher dimension operators, but the procedure can be difficult to control due to large numerical cancellations. Explicit subtractions for matrix elements and coefficients, depending on a subtraction scale R, can avoid this problem. The appropriate choice for R in the Wilson coefficients can widely vary for different processes. In this talk we discuss renormalization group evolution with the scale R, and show that it sums large logarithms in the difference of processes with widely different R's. We also show that the solution of the R-evolution equations can be used to recover the all order asymptotic form of the singularities in the Borel transform of the perturbative series. For the normalization of these singularities we obtain a quickly converging sum rule that only needs the known perturbative coefficients as an input. This sum rule can be used as a novel test for renormalon ambiguities without replying on the large-beta_0 approximation.

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摘要：

英文摘要：

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