 Parton distribution function

A parton distribution function specifies a hadron's partonic content as a function of longitudinal momentum fraction and a stated parton factorization scale. In the leading collinear parton model, $f_i(x)dx$ has a number-density interpretation for partons of species $i$ with fractions in $dx$. It is not generally normalized to one.

For a proton, the integrals of the valence differences count two net up quarks and one net down quark. A momentum-weighted sum over all quark, antiquark and gluon species gives total momentum fraction one. These are different sum rules. Beyond the simplest approximation, the definition depends on factorization scheme and renormalized field correlations; a naive positive classical probability interpretation is not universal. The functions enter factorized cross sections and evolve with resolution, rather than being predictions of a free-quark model.^[ref]