低x下的质子结构函数：分形分布
Proton structure functions at low $x$: the Fractal distributions
AI总结：
本文在次领头阶微扰QCD下抽取小x部分子分布函数，发现海夸克PDF在x<0.01时呈分形自相似行为，并用HERA小x数据验证了基于分形参数化的理论预言与实验一致。
摘要：
本文给出了在微扰QCD次领头阶精度下对极小动量分数x处的部分子分布函数的抽取。我们表明，“海夸克分布函数”在x<0.01时具有固定指数的“分形”或自相似行为。为此，考虑了一种基于“分形”方法的简单部分子分布函数参数化形式，尤其是针对海夸克PDF的参数化。分析中包含了HERA上深度非弹性散射过程中电子-质子和正电子-质子的小x实验数据集，其范围为1.5<Q^2<650（GeV^2）且x<0.01。本分析中的不确定度估计采用标准“Hessian”方法进行。总体而言，考虑χ²/dof的整体值以及理论与数据的比较，结果表明在极小动量分数x处实验数据集与理论预言之间具有良好的一致性。最后，我们给出了利用文献中可用的各种近期质子PDF模型所得到的相关小x观测量预言之间的详细比较。
英文摘要：
In this paper, we present the extraction of the Parton Distribution Functions (PDFs) at small momentum fractions x and at the next-to-leading order (NLO) accuracy in perturbative QCD. We show that the "sea quark distribution functions" have "Fractal" or self-similar behaviour with fixed exponent at $x<0.01$. To this end, a simple parametrization for the Parton Distribution Functions and especially for the sea quarks PDFs based on the "Fractal" approach is considered. The small $x$ experimental datasets on electron-proton ($e^-p$) and positron-proton ($e^+p$) in DIS processes at HERA for the range of $1.5< Q^2 < 650$ ($GeV^2$) and $x<0.01$ are included in this analysis. The estimations of the uncertainty in the present analysis are carried out using the standard "Hessian" method. In total, considering the overall value of $χ^2/{\rm dof}$ and theory/data comparisons, the results indicate nice agreements between the experimental datasets and the theory predictions at small momentum fractions $x$. Finally, we present detailed comparisons between predictions for the relevant small-$x$ observables obtained with various recent models of proton PDFs available in literature.
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