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arXiv 1611.03371hep-ph
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超越定阶精度的分段函数

Fragmentation Functions Beyond Fixed Order Accuracy

Daniele P. Anderle, Tom Kaufmann, Felix Ringer, Marco Stratmann

摘要:

详细描述了半包容电子正电子湮没中强子在小动量分数下的物理增强贡献的全阶近似现象和部分子到强子碎裂函数的类时尺度演化.在梅林矩空间中进行重正化的形式主义进行了简要的回顾,并推导出所有相关的表达式,直到下一个到下一个到领先的对数阶,包括其明确的依赖于因式分解和重正化尺度。我们讨论了一个适当的数值实现的delimmed的结果,包括一个迭代的解决方案,已知的固定顺序表达式的匹配,并在梅林逆变换的轮廓的选择的细节。第一次提取的部分子到π介子碎裂函数的半包容性的湮灭数据进行在不同的对数阶的的双折射,以估计它们的唯象相关性。为此,我们将我们的结果与相应的拟合进行比较,以达到固定的,下一个到下一个到领先的阶精度,并研究在每种情况下对因子分解尺度的残差依赖性。

英文摘要:

We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the time-like scale evolution of parton-to-hadron fragmentation functions. The formalism to perform resummations in Mellin moment space is briefly reviewed, and all relevant expressions up to next-to-next-to-leading logarithmic order are derived, including their explicit dependence on the factorization and renormalization scales. We discuss the details pertinent to a proper numerical implementation of the resummed results comprising an iterative solution to the time-like evolution equations, the matching to known fixed-order expressions, and the choice of the contour in the Mellin inverse transformation. First extractions of parton-to-pion fragmentation functions from semi-inclusive annihilation data are performed at different logarithmic orders of the resummations in order to estimate their phenomenological relevance. To this end, we compare our results to corresponding fits up to fixed, next-to-next-to-leading order accuracy and study the residual dependence on the factorization scale in each case.

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