Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross section data. We review definitions of the PDFs and their relations to high-energy cross sections. We focus on the PDFs in protons, but also discuss PDFs in nuclei. We review in some detail the standard statistical treatment needed to fit the PDFs to data using the Hessian method. We discuss tests that can be used to critically examine whether the needed assumptions are indeed valid. We also present some ideas of what one can do in the case that the tests indicate that the assumptions fail.

中文翻译：

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高能碰撞中的强子结构

Parton分布函数（PDF）描述了由夸克和胶子组成的强子的结构。需要它们来预测高能碰撞中的短距离过程，并通过拟合横截面数据来确定它们。我们回顾了PDF的定义及其与高能截面的关系。我们关注质子的PDF，但也讨论原子核的PDF。我们将详细介绍使用Hessian方法将PDF拟合到数据所需的标准统计处理。我们讨论了可用于严格检查所需假设是否确实有效的测试。我们还提出了一些关于在测试表明假设失败的情况下可以做什么的想法。