arXiv 1007.40052010-07hep-phhep-th

小q_T下的Drell-Yan产生、横向部分子分布和共线异常

Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly

Thomas Becher, Matthias Neubert

备注：: 32 pages, 2 figures; version to appear in Eur. Phys. J. C
发表信息：: Eur.Phys.J.C71:1665,2011
DOI：: 10.1140/epjc/s10052-011-1665-7

摘要：

利用有效场论的方法，直接在q_T空间中导出了小横动量下Drell-Yan截面的全阶精确表达式，并对所有大截面进行了数值计算.明确给出了NNLL阶重定所需的反常维数和匹配系数。讨论了我们的结果与Collins-Soper-Sterman公式之间的精确关系，并作为副产品得到了以前未知的三圈系数A^（3）.在小横动量下的截面的朴素因式分解被共线异常打破，这阻止了依赖于x_T的部分子分布函数的过程独立定义。一个因式分解定理推导出的两个这样的功能，其中的依赖硬动量转移分离出来的产品。余项分解为纵动量变量和x_T^2的两个函数的乘积，导出了其重整化群演化的封闭形式并求解。在O（alpha_s）处计算了这些函数在小x_T处与标准部分子分布的匹配，而它们的反常维数对三个循环是已知的。

英文摘要：

Using methods from effective field theory, an exact all-order expression for the Drell-Yan cross section at small transverse momentum is derived directly in q_T space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins-Soper-Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A^(3) is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of x_T-dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and x_T^2, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small x_T onto standard parton distributions is calculated at O(alpha_s), while their anomalous dimensions are known to three loops.

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