Issues in the Determination of Parton Distribution Functions

TL;DR

This paper discusses the challenges and principles involved in accurately determining and estimating errors in parton distribution functions derived from experimental data, emphasizing the importance of comprehensive error analysis.

Contribution

It highlights the need for systematic error estimation in parton distribution fits and clarifies the principles necessary for such analysis, which are often overlooked.

Findings

Standard principles for error analysis are applicable but complex with many data points.

Careful logical consideration is required for large data sets.

Current fits often lack detailed error estimates.

Abstract

The CTEQ and MRS parton distributions involve a substantial number (~30) of parameters that are fit to a large number (~900) of data. Typically, these groups produce fits that represent a good fit to the data, but there is no substantial attempt to determine the errors associated with the fits. Determination of errors would involve consideration of the experimental statistical and systematic errors and also the errors in the theoretical formulas that relate the measured cross sections to parton distributions. We discuss the principles that would be needed in such an error analysis. These principles are standard. However, certain aspects of the principles appear counter-intuitive in the case of a large number of data. Accordingly, we strive to devote careful attention to the logic behind the methods.