Why αs cannot be determined from hadronic processes without simultaneously determining the parton distributions

We show that any determination of the strong coupling alpha s 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. 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 contours in the joint space of alpha s and the PDF parameters.