The Effect of Positivity Constraints on Polarized Parton Densities

The impact of positivity constraints on the polarized parton densities has been studied. Special attention has been paid to the role of positivity constraints in determining the polarized strange quark and gluon densities, which are not well determined from the present data on inclusive polarized DIS. Spurred on by the famous European Muon Collaboration (EMC) experiment [1] at CERN in 1987, there has been a huge growth of interest in the partonic spin structure of the nucleon, i.e., how the nucleon spin is built up out from the intrinsic spin and orbital angular momentum of its constituents, quarks and gluons. Our present knowledge about the spin structure of the nucleon comes from polarized inclusive and semi-inclusive DIS experiments at SLAC, CERN, DESY and JLab, polarized proton-proton collisions at RHIC and polarized photoproduction experiments. The determination of the longitudinal polarized parton densities in QCD is one of the important aspects of this knowledge. Many analyses [2, 3] of the world data on inclusive polarized DIS have been performed in order to extract them. It was shown that if the convention of a flavor symmetric sea is used1 the polarized valence quarks are well determined, while the polarized strange sea and polarized gluon densities are weakly constrained2. In this talk we will discuss the effect of positivity constraints on the polarized parton densities and will demonstrate their importance in determining the strange and gluon densities, especially at high x. The polarized parton densities have to satisfy the positivity condition, which in LO QCD implies: |∆ fi(x,Q)| ≤ fi(x,Q), |∆ f̄i(x,Q)| ≤ f̄i(x,Q). (1) The constraints (1) are the consequence of a probabilistic interpretation of the parton densities in the naive parton model, which is still valid in LO QCD. Beyond LO the parton densities are not physical quantities and the positivity constraints on the polarized parton densities are more complicated. They follow from the positivity condition for the polarized lepton-hadron cross-sections ∆σi in terms of the unpolarized ones (|∆σi| ≤ σi) 1 In the absence of polarized charged current neutrino experiments a flavor decomposition is not possible. 2 About the situation in semi-inclusive DIS see the talk by R. Sassot at this Workshop [4]. 0.01 0.1 1 0.0 0.1 0.2 0.3 0.4 0.5