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arXiv 0909.5176hep-ph
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部分子分布拟合中的参数化依赖和Delta卡方检验

Parametrization dependence and Delta Chi-squared in parton distribution fitting

Jon Pumplin

摘要:

部分子分布函数(PDF),这是从高能对撞机的数据的解释必不可少的,通过将它们表示为包含许多参数的函数形式测量。这些参数是通过拟合各种实验数据来确定的。通过最小化拟合质量的标准$χ^2$度量来获得最佳拟合PDF集。在Hessian方法中,通过将$χ^2$在其最小值的$Δχ^2$范围内的所有拟合视为可接受,估计不确定度范围。通过各种参数估计,用于此目的的适当$Δχ^2$值约为50 - 100,置信限为90%。本文解决了长期存在的悖论,为什么经验值是如此之大,比$Δχ^2=2.7$为90%的信心,将预期的基础上,标准高斯统计。

英文摘要:

Parton distributions functions (PDFs), which are essential to the interpretation of data from high energy colliders, are measured by representing them as functional forms containing many parameters. Those parameters are determined by fitting a wide variety of experimental data. The best-fit PDF set is obtained by minimizing the standard $χ^2$ measure of fit quality. The uncertainty range is estimated in the Hessian method by regarding as acceptable, all fits for which $χ^2$ lies within $Δχ^2$ of its minimum. The appropriate value of $Δχ^2$ for this purpose has been estimated by a variety of arguments to be approximately 50 - 100 for a 90% confidence limit. This paper resolves the long-standing paradox of why that empirical value is so much larger than the $Δχ^2=2.7$ for 90% confidence that would be expected on the basis of standard Gaussian statistics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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