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.
Highlights
We will show that this apparently straightforward and standard procedure may lead to an incorrect determination of αs, and we will argue that this is a generic situation
Any given existing PDF set traces a line in such space: for each value of αs there is a set of best-fit PDF parameters, which corresponds to a point in PDF space
The value of αs corresponding to these configurations may, and in general will, differ substantially from the one obtained using the standard procedure, and in particular it will be closer to the value obtained by simultaneously fitting αs and PDFs to a global dataset
Summary
The value of the strong coupling αs has been routinely determined from a variety of processes which involve hadrons in the initial state, both in electroproduction and hadroproduction. This covers the typical realistic scenarios in which the new data only constrain (or determine) a subset of PDFs: e.g. in the case of the Z pT distribution considered above, the gluon In this latter, common case we will see that the value of αs obtained through the standard procedure leads to an artificially large dispersion of αs values: better-fit points in (PDF, αs) generally lead to αs values which are closer to the global best fit
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