Why $$\alpha _s$$ cannot be determined from hadronic processes without simultaneously determining the parton distributions

AbstractWe show that any determination of the strong coupling $$\alpha _s$$αs from a process which depends on parton distributions, such as hadronic processes or deep-inelastic scattering, generally does not lead to a correct result unless the parton distributions (PDFs) are determined simultaneously along with $$\alpha _s$$αs. We establish the result by first showing an explicit example, and then arguing that the example is representative of a generic situation which we explain using models for the shape of equal $$\chi ^2$$χ2 contours in the joint space of $$\alpha _s$$αs and the PDF parameters.