Ball Richard D, Nocera Emanuele R, Rojo Juan
The Higgs Centre for Theoretical Physics, University of Edinburgh, JCMB, KB, Mayfield Rd., Edinburgh, EH9 3JZ Scotland.
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP UK.
Eur Phys J C Part Fields. 2016;76(7):383. doi: 10.1140/epjc/s10052-016-4240-4. Epub 2016 Jul 8.
It has been argued from the earliest days of quantum chromodynamics that at asymptotically small values of the parton distribution functions (PDFs) of the proton behave as [Formula: see text], where the values of [Formula: see text] can be deduced from Regge theory, while at asymptotically large values of the PDFs behave as [Formula: see text], where the values of [Formula: see text] can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents [Formula: see text] and [Formula: see text] from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio [Formula: see text] at large , and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.
从量子色动力学的早期就有人认为，在渐近小的 值下，质子的部分子分布函数（PDFs）表现为[公式：见正文]，其中[公式：见正文]的值可以从雷杰理论推导出来，而在渐近大的 值下，PDFs表现为[公式：见正文]，其中[公式：见正文]的值可以从布罗德斯基 - 法拉尔夸克计数规则推导出来。我们通过从部分子分布的各种全局拟合中提取指数[公式：见正文]和[公式：见正文]，分析它们的标度依赖性，并将它们的值与朴素预期进行比较，来批判性地检验这些说法。我们发现，对于价分布，雷杰理论和计数规则至少在不确定性范围内得到了证实，而对于海夸克和胶子，结果则不太确定。我们还比较了各种PDF拟合对于大 的结构函数比[公式：见正文]的结果，并告诫要警惕由于过度约束的参数化而导致的不切实际的不确定性估计。
