On the Sensitivity of the Polarized Parton Densities to Flavour SU(3) Symmetry Breaking

Motivated by the possibility that it may be misleading to assume SU(3) symmetry in the analysis of hyperon β-decays, we study the sensitivity of the polarized parton densities, derived from the world data on inclusive polarized deep inelastic lepton-nucleon scattering, to variation of the value of the nonsinglet axial charge a8 from its SU(3) value of 3F-D. Our most precise knowledge of the internal partonic structure of the nucleon has come from decades of experiments on unpolarized Deep Inelastic Scattering (DIS) of leptons on nucleons. More recently there has been a dramatic improvement in the quality of the data on polarized DIS and consequently an impressive growth in the precision of our knowledge of the polarized parton densities in the nucleon. However, it will be a long time before the polarized data, for the moment limited to neutral current reactions, can match the unpolarized data in volume and accuracy. As a consequence, almost all analyses of the polarized parton densities supplement the DIS (large Q) data with information stemming from low-Q weak interaction reactions. More specifically, it is conventional to use the values of GA/GV from neutron β-decay, and 3F-D from hyperon β-decays to help to pin down the values of the first moments of certain combinations of parton densities: a3 = (∆u+∆ū)(Q )− (∆d+∆d̄)(Q) = GA GV (n → p) ≡ gA , (1) a8 = (∆u+∆ū)(Q ) + (∆d+∆d̄)(Q)− 2(∆s+∆s̄)(Q) = 3F− D , (2) where a3 and a8 are the nonsinglet axial charges corresponding to the 3 rd and 8 components of the axial vector Cabibbo current. In (2) F and D are the SU(3) parameters involved in the matrix elements describing hyperon β-decays. The Bjorken sum rule (1) reflects the isospin SU(2) symmetry, whereas the relation (2) is a consequence of the SU(3) flavour symmetry treatment of the hyperon β-decays. While isospin symmetry is well established, the growing precision of the measurements of magnetic moments and GA/GV ratios in hyperon semi-leptonic decays [1] may be indicating [2]-[4] a non-negligible breakdown of SU(3) flavour symmetry and consequently of Eq. (2). Several attempts have been already made [5, 6] to incorporate some symmetry breaking in the combined analysis of weak interaction data and polarized DIS data. In this note we present a new study on the sensitivity of the polarized parton densities to SU(3) breaking, using the world data on inclusive DIS [7]. A significant improvement of the previous results on this subject has been achieved. Firstly, a consistent NLO QCD treatment of the data has been carried out. Secondly, unlike the previous analyses, the effects of SU(3) symmetry breaking taken into account in our study are model-independent. Further, we present results on the polarized parton densities themselves, not only on their first moments. Finally, we discuss the role of the different factorization schemes.