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

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