Applications of the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations to the combined HERA data on deep inelastic scattering

Abstract

We recently derived explicit solutions of the leading-order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations for the ${Q}^{2}$ evolution of the singlet structure function ${F}_{s}(x,{Q}^{2})$ and the gluon distribution $G(x,{Q}^{2})$ using very efficient Laplace transform techniques. We apply our results here to a study of the HERA data on deep inelastic $ep$ scattering as recently combined by the H1 and ZEUS groups. We use initial distributions ${F}_{2}^{\ensuremath{\gamma}p}(x,{Q}_{0}^{2})$ and $G(x,{Q}_{0}^{2})$ determined for $x<0.1$ by a global fit to the HERA data, and extended to $x=1$ using the shapes of those distributions determined in the CTEQ6L and MSTW2008LO analyses from fits to other data. Our final results are insensitive at small $x$ to the details of the extension. We obtain the singlet quark distribution ${F}_{s}(x,{Q}_{0}^{2})$ from ${F}_{2}^{\ensuremath{\gamma}p}(x,{Q}_{0}^{2})$ using small nonsinglet quark distributions taken from either the CTEQ6L or the MSTW2008LO analyses, evolve ${F}_{s}$ and $G$ to arbitrary ${Q}^{2}$, and then convert the results to individual quark distributions. Finally, we show directly from a study of systematic trends in a comparison of the evolved ${F}_{2}^{\ensuremath{\gamma}p}(x,{Q}^{2})$ with the HERA data that the assumption of leading-order DGLAP evolution is inconsistent with those data.