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

Abstract

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

minor changes for publication