Ablinger J, Blümlein J, Klein S, Schneider C, Wißbrock F
Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040, Linz, Austria.
Deutsches Elektronen Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen, Germany.
Nucl Phys B. 2011 Mar 1;844(1):26-54. doi: 10.1016/j.nuclphysb.2010.10.021.
The contributions [Formula: see text] to the [Formula: see text] massive operator matrix elements describing the heavy flavor Wilson coefficients in the limit [Formula: see text] are computed for the structure function [Formula: see text] and transversity for general values of the Mellin variable . Here, for two matrix elements, [Formula: see text] and [Formula: see text], the complete result is obtained. A first independent computation of the contributions to the 3-loop anomalous dimensions [Formula: see text], [Formula: see text], and [Formula: see text] is given. In the computation advanced summation technologies for nested sums over products of hypergeometric terms with harmonic sums have been used. For intermediary results generalized harmonic sums occur, while the final results can be expressed by nested harmonic sums only.
针对结构函数(F_2(x,Q^2))和广义 Mellin 变量值下的横向性，计算了在(N_c\to\infty)极限下描述重味 Wilson 系数的(O(\alpha_s^n))大质量算符矩阵元的贡献(C_{ij}^{(n)})。这里，对于两个矩阵元(C_{qq}^{(n)})和(C_{qg}^{(n)})，得到了完整结果。给出了对三圈反常维度(\gamma_{qq}^{(3)})、(\gamma_{qg}^{(3)})和(\gamma_{gq}^{(3)})贡献的首次独立计算。在计算中，使用了针对超几何项与调和和乘积的嵌套和的高级求和技术。对于中间结果，出现了广义调和和，而最终结果仅能用嵌套调和和表示。
