Unified description of the non-singlet spin dependent structure function g1 incorporating Altarelli-Parisi evolution and the double logarithmic ln2(1/x) effects at low x

A unified equation for the non-singlet spin dependent structure function g1ns(x,Q2)=g1p(x,Q2)−g1n(x,Q2) which incorporates the complete leading order Altarelli-Parisi evolution at finite x and double logarithmic ln2(1/x) effects at x→0 is formulated. This equation is solved assuming simple phenomenological parametrisation of the non-perturbative part of the structure function. Reasonable agreement is obtained with the recent data obtained by the Spin Muon Collaboration. Predictions for the small x behaviour of g1ns(x,Q2) in the kinematical range which may be relevant for the possible HERA measurements are given. The contribution to the Bjorken sum coming from the region of very small values of x is quantified. Extrapolation of g1(x,Q2) to the region of small x and small Q2 is also discussed.