Parametrization dependence and Delta Chi-squared in parton distribution fitting

TL;DR

This paper investigates why the empirically chosen Delta Chi-squared value for parton distribution function uncertainties is much larger than the Gaussian expectation, addressing a longstanding paradox in high energy physics data fitting.

Contribution

It provides an explanation for the discrepancy between the empirical Delta Chi-squared and the Gaussian statistical expectation in PDF fitting.

Findings

Empirical Delta Chi-squared is around 50-100 for 90% confidence.

The paper explains the reasons behind the larger-than-expected Delta Chi-squared value.

Addresses a long-standing paradox in the interpretation of PDF uncertainties.

Abstract

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 $\chi^2$ measure of fit quality. The uncertainty range is estimated in the Hessian method by regarding as acceptable, all fits for which $\chi^2$ lies within $\Delta\chi^2$ of its minimum. The appropriate value of $\Delta\chi^2$ 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 $\Delta\chi^2=2.7$ for 90% confidence that would be expected on the basis of standard Gaussian statistics.