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

@article{Forte2020Why\_,
  title={Why \$\$\alpha \_s\$\$ cannot be determined from hadronic processes without simultaneously determining the parton distributions},
  author={Stefano Forte and Zahari Kassabov},
  journal={The European Physical Journal C},
  year={2020}
}
We 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… 
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