Uncertainty induced by QCD coupling in the CTEQ global analysis of parton distributions

TL;DR

This paper presents a method to accurately quantify the combined uncertainty in parton distribution functions arising from the QCD coupling strength, enhancing the precision of theoretical predictions at collider experiments.

Contribution

The authors introduce a simple, statistically rigorous method to incorporate the uncertainty of the QCD coupling into PDF uncertainties, validated with a series of specialized PDF sets.

Findings

The method accurately reproduces the combined uncertainty in PDFs and cross sections.

Application to CTEQ6.6AS PDFs demonstrates the impact on collider predictions.

The approach simplifies uncertainty estimation in high-energy physics analyses.

Abstract

We examine the dependence of parton distribution functions (PDFs) on the value of the QCD coupling strength $\alpha_{s}(M_{Z})$. We explain a simple method that is rigorously valid in the quadratic approximation normally applied in PDF fitting, and fully reproduces the correlated dependence of theoretical cross sections on $\alpha_s$ and PDF parameters. This method is based on a statistical relation that allows one to add the uncertainty produced by $\alpha_s$, computed with some special PDF sets, in quadrature with the PDF uncertainty obtained for the fixed $\alpha_s$ value (such as the CTEQ6.6 PDF set). A series of four CTEQ6.6AS PDFs realizing this approach, for $\alpha_s$ values in the interval $0.116 \leq \alpha_{s}(M_{Z}) \leq 0.120$, is presented. Using these PDFs, the combined $\alpha_{s}$ and PDF uncertainty is assessed for theoretical predictions at the Fermilab Tevatron and Large Hadron Collider.