Resummation of large logarithms in gamma*pi(0)->gamma
Resummation of large logarithms in gamma*pi(0)->gamma
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DOI：
10.1088/1126-6708/2007/06/039
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发表时间：
2007-04
影响因子：
5.4
通讯作者：
F. Feng;Jian-ping Ma;Qi Wang
中科院分区：
文献类型：
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作者：
F. Feng;Jian-ping Ma;Qi Wang
在对跃迁形式因子的共线分解中，gamma*pi(0) -> gamma的困难部分包含双对数项，如In(2)x，其中x为从0到1的部分的动量分数。对恢复进行简单的求幂会得到发散的结果。我们研究这些In(2)x项的恢复。我们表明，In(2)x项部分来自光锥波函数（LCWF），部分来自形状因子。我们引入一个喷射因子来分解形状因子中的In(2)x项。为了处理来自光锥波函数的In(2)x项，我们引入了一个非标准光锥波函数（NLCWF），该函数的测量链在光锥方向上。在两个波函数之间发现了一个有趣的关系。利用引入的NLCWF和射流因子，可以对形状因子进行重构，得到不含In(2)x项的新硬件。除了重整化尺度p外，引入的NLCWF和射流因子还有额外的尺度来表征它们的x-行为。利用额外尺度和关系的演化，我们可以进行微扰恢复，即在恢复公式中LCWF是唯一的非摄动对象。我们对一些模型的研究结果表明，恢复后的数值预测与未恢复时的数值预测有显著差异，恢复后的数值预测可以很好地描述实验数据。
In the collinear factorization of the form factor for the transition gamma*pi(0) -> gamma the hard part contains double log terms as In(2)x with x as the momentum fraction of partons from 0 to 1. A simple exponentiation for resummation leads to divergent results. We study the resummation of these In(2)x terms. We show that the In(2)x terms come partly from the light-cone wave function(LCWF) and partly from the form factor. We introduce a jet factor to factorize the In(2)x term in the form factor. To handel the In(2)x terms from the LCWF we introduce a nonstandard light-cone wave function(NLCWF) with the gauge links off the light-cone direction. An interesting relation between two wave function is found. With the introduced NLCWF and the jet factor we can re-factorize the form factor and obtain a new hard part which does not contain terms with In(2)x. Beside the renormalization scale p the introduced NLCWF and jet factor have extra scales to characterize their x-behaviors. Using the evolutions of the extra scales and the relation we can do the resummation perturbatively in sense that the LCWF is the only nonpertubative object in the resumed formula. Our results with some models of LCWF show that there is a significant difference between numerical predictions with the resummation and that without the resummation, and the resummed predictions can describe the experimental data.