DGLAP的规范变换群：求和规则、分类与求解
Scheme transformations as the gauge group of DGLAP: sum rules, classification and solution
浏览论文内容
中文总结 AI 辅助
本文以规范变换视角研究DGLAP演化，分类保持对称性与求和规则的方案变换，并利用规范自由度将演化方程化简为二阶线性方程，从而精确求解并估计高阶修正。
中文摘要 AI 辅助
部分子密度依赖于重整化方案，任意两个方案之间通过一个保持演化方程DGLAP形式的变换相联系。在Mellin空间中，这样的变换对演化核的作用类似于规范变换，我们在整个讨论中均采用这一观点。对于非极化密度，我们首先探讨哪些变换同时保持演化核的电荷共轭与味对称性以及动量与价数求和规则。对称性将变换约化为少数几个块，求和规则仅约束两个Mellin矩，在此留下一个自由度，即夸克单态与胶子之间的动量分配，并固定价数。所得分类是完备的，因为以渐近自由作为边界条件，方案的改变由其作用于演化核所决定。在此群内，保持正定性的变换构成一个半群，同样的论证也适用于极化密度。仅不满足求和规则的变换也不会丢失，因为由求和规则本身确定的归一化可修复之，我们利用这一点在不放弃求和规则的前提下，将共线密度定义为横动量依赖密度的积分。随后我们利用同一规范自由度来求解演化。将演化核规范掉，可将任意阶的DGLAP方程约化为单个二阶线性方程加上一个求积，并以精确满足求和规则的方式组织对缺失高阶项的估计。
英文摘要
A parton density depends on the renormalization scheme, and any two schemes are connected by a transformation that preserves the DGLAP form of the evolution. In Mellin space such a transformation acts on the evolution kernels as a gauge transformation, and we take this point of view throughout the discussion. For the unpolarized densities we first ask which transformations also preserve the charge-conjugation and flavor symmetries of the evolution kernels and the momentum and valence number sum rules. The symmetries reduce the transformation to a few blocks, and the sum rules constrain only two Mellin moments, where they leave a single freedom, the split of momentum between the quark singlet and the gluon, and freeze the valence numbers. The resulting classification is complete, because with asymptotic freedom as a boundary condition a change of scheme is determined by its action on the kernels. Inside this group, the transformations that preserve positivity form a semigroup, and the same argument covers the polarized densities. A transformation that fails only the sum rules is not lost either, since a normalization that the sum rules themselves determine repairs it, and we use this to define collinear densities as integrals of transverse-momentum-dependent densities without giving up the sum rules. We then use the same gauge freedom to solve the evolution. Gauging the kernel away reduces DGLAP at any order to a single second-order linear equation plus a quadrature, and it organizes the estimate of missing higher orders in a way that respects the sum rules exactly.
发表机构
- Stony Brook University（石溪大学）
机构由 AI 辅助整理，请以论文原文为准。
