Parameterisation of σ_{1/2}-σ_{3/2} for Q^2 \geq 0 and non-resonance contribution to the GDH sum rule

A description of the virtual photon absorption cross section difference \sigma_{1/2}-\sigma_{3/2} for the proton and the neutron is obtained with a parameterisation based on a Regge type approach. The parameterisation is obtained from global fits to the cross section data derived from the spin asymmetries measured in DIS of longitudinally polarised leptons from polarised ^1H, ^3He and ^2H targets in the range 0.3 GeV^2 < Q^2 < 70 GeV^2 and 4 GeV^2 < W^2 < 300 GeV^2. The fits give a reliable description of the data and provide predictions for the photo-production through a smooth Q^2-transition. The contribution above the resonance region to the Gerasimov-Drell-Hearn sum rule for real and virtual photons has been evaluated. For the real photons this contribution accounts for a large fraction of the discrepancy between the sum rule expectations and the single pion photo-production analysis estimate