Why $$\alpha _s$$ cannot be determined from hadronic processes without simultaneously determining the parton distributions
Stefano Forte, Zahari Kassabov
Abstract
Abstract We show that any determination of the strong coupling $$\alpha _s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>α</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> 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 $$\alpha _s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>α</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> . 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 $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>χ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> contours in the joint space of $$\alpha _s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>α</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> and the PDF parameters.