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 $0.116\le {\alpha }_s(M_Z)\le 0.120$, 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.

• Received 7 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.054021