Inequalities between quark densities

Abstract

We propose an inequality between the longitudinally polarized density and the transversity of a quark in a nucleon. This inequality, whose validity is limited to very small scales, is based on considerations about Lorentz transformations and on commonly accepted models. Therefore it may be used as a consistecy check with other models. It turns out to agree with most model preedictions. Moreover it allows to establish, thanks to the positivity constraint, another inequality between the longitudinally polarized and the unpolarized valence quark density. We show that this latter inequality may be extended to any Q^2, consistently with commonly used factorization schemes and with some nonperturbative evolution models. This inequality finds nontrivial applications to the valence "d"-quark densities and is compared with data analyses, with model predictions and with parametrizations of quark densities.