标题： 关于Drell-Levy-Yan关系到$O(α_s^2)$ 显示英文标题

标题： On the Drell-Levy-Yan Relation to $O(α_s^2)$

摘要： 我们研究Drell、Levy和Yan（DLY）建立的关联关系的有效性，该关系将深度非弹性散射（DIS）函数与e^+e^-湮灭中的单粒子碎片化函数联系起来，分别定义在类空（q^2<0）和类时（q^2>0）区域。 这里的q表示在深度非弹性散射过程或湮灭过程中交换的虚光子的动量。 将最初仅在标度部分子模型中推导出的DLY关系扩展到QCD的所有阶次，会导致描述DIS结构函数和碎片化函数各自q^2依赖性的两个演化核之间的联系。 与此相关，我们推导了空间和时间类分裂函数在下一阶（NLO）以及非极化和极化散射的系数函数在下一下一阶（NNLO）的转换关系。 结果表明，描述结构函数F_2(x,Q^2), F_L(x,Q^2)其中Q^2=|q^2|或者$F_2(x,Q^2), \partial F_2(x,Q^2)/\partial \ln(Q^2)$以及相应碎片化函数的组合单态演化演化核在下一阶（NLO）范围内满足DLY关系。 我们还对Gribov和Lipatov提出的关系进行了评论。 显示英文摘要

摘要： We study the validity of a relation by Drell, Levy and Yan (DLY) connecting the deep inelastic structure (DIS) functions and the single-particle fragmentation functions in e^+e^- annihilation which are defined in the spacelike (q^2<0) and timelike (q^2>0) regions respectively. Here q denotes the momentum of the virtual photon exchanged in the deep inelastic scattering process or the annihilation process. An extension of the DLY-relation, which originally was only derived in the scaling parton model, to all orders in QCD leads to a connection between the two evolution kernels determining the q^2-dependence of the DIS structure functions and the fragmentation functions respectively. In relation to this we derive the transformation relations between the space-and time-like splitting functions up to next-to-leading order (NLO) and the coefficient functions up to NNLO both for unpolarized and polarized scattering. It is shown that the evolution kernels describing the combined singlet evolution for the structure functions F_2(x,Q^2), F_L(x,Q^2) where Q^2=|q^2| or $F_2(x,Q^2), \partial F_2(x,Q^2)/\partial \ln(Q^2)$ and the corresponding fragmentation functions satisfy the DLY relation up to next-to-leading order. We also comment on a relation proposed by Gribov and Lipatov.