A rigorous bound on quark distributions in the nucleon

I deduce an inequality between the helicity and the transversity distribution of a quark in a nucleon, at small energy scales. Then I establish, thanks to the positivity constraint, a rigorous bound on longitudinally polarized valence quark densities, which finds nontrivial applications to d-quarks. This, in turn, implies a bound for the distributions of the longitudinally polarized sea, which is probably not SU(3)-symmetric. Some model predictions and parametrizations of quark distributions are examined in the light of these results.