UNBIASED SPIN-DEPENDENT PARTON DISTRIBUTION FUNCTIONS

We present the first unbiased determination of spin-dependent, or polarized, parton distribution functions of the proton. A statistically sound representation of the corresponding uncertainties is achieved by means of the NNPDF methodology, formerly developed for unpolarized distributions and generalized to the polarized here for the first time. The features of the procedure, based on robust statistical tools - Monte Carlo sampling for error propagation, neural networks for PDF parametrization, genetic algorithm for their minimization and possibly reweighting for including new data samples without refitting - and their implementation are illustrated in detail. Sets of polarized parton distributions are obtained at next-to-leding order accuracy in perturbative quantum chromodynamics, based on both fixed-target inclusive deeply-inelastic scattering and the most recent polarized hadron collider data. A quantitative appraisal on the potential role of future measurements at an Electron-Ion Collider is also presented. We study the stability of our results upon the variation of several theoretical and methodological assumptions and we present a detailed investigation of the first moments of our polarized parton distributions, compared to other recent analyses. We find that the uncertainty on the gluon distribution from available data was substantially underestimated in previous determinations; in particular, we emphasize that a large contribution to the gluon may arise from the unmeasured small-x region, against the common belief that this is actually rather small. We demonstrate that an Electron-Ion Collider would provide evidence of a possible large gluon contribution to the nucleon spin, though with a sizable residual uncertainty.