Proton spin structure function, g1, with the unified evolution equations including NLO DGLAP terms and double logarithms, ln(1/x)

Abstract

Theoretical predictions show that at low values of the Bjorken parameter x the spin structure function, g1, is influenced by large logarithmic corrections, $\ln^2(1/x)$ , which may be predominant in this region. These corrections are also partially contained in the NLO part of the standard DGLAP evolution. Here we calculate the nucleon structure function, g1, and the gluon distribution, $\Delta g$ , using the unified evolution equations written for the singlet and the non-singlet parton distributions. These equations include (i) the terms which describe the NLO DGLAP evolution and (ii) the ladder and non-ladder terms which contribute to the resummation of $\ln^2(1/x)$ . Subtractions of singularities from the evolution kernels are performed so as to avoid double counting the double logarithmic contributions coming from the NLO DGLAP and the ladder and non-ladder terms. The sensitivity of the results to the factorization scheme applied is tested by introducing the DGLAP terms into the evolution equations at two different factorization schemes.