Double logarithms,ln2(1/x),and the NLO Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution for the nonsinglet component of the nucleon spin structure functiong1

Abstract

Theoretical predictions show that at low values of Bjorken x the spin structure function ${g}_{1}$ is influenced by large logarithmic corrections ${\mathrm{ln}}^{2}(1/x),$ which may be predominant in this region. These corrections are also partially contained in the next leading order (NLO) part of the standard Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution. Here we calculate the nonsinglet component of the nucleon structure function, ${g}_{1}^{\mathrm{NS}}{=g}_{1}^{p}\ensuremath{-}{g}_{1}^{n},$ and its first moment, using a unified evolution equation. This equation incorporates the terms describing the NLO DGLAP evolution and the terms contributing to the ${\mathrm{ln}}^{2}(1/x)$ resummation. In order to avoid double counting in the overlapping regions of the phase space, a unique way of including the NLO terms into the unified evolution equation is proposed. The scheme-independent results obtained from this unified evolution are compared to the NLO fit to experimental data, GRSV2000. An analysis of the first moments of ${g}_{1}^{\mathrm{NS}}$ shows that the unified evolution including the ${\mathrm{ln}}^{2}(1/x)$ resummation goes beyond the NLO DGLAP analysis. Corrections generated by double logarithms at low x influence the ${Q}^{2}$ dependence of the first moments strongly.