Why ${\alpha }_s$ Cannot be Determined from Hadronic Processes without Simultaneously Determining the Parton Distributions

Abstract

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.

Comments: 13 pages, 6 figures; final version, to be published in EPJC. Concluding section expanded and clarified