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

Martin M. Block, Loyal Durand, Phuoc Ha, and Douglas W. McKay

Phys. Rev. D 84, 094010 – Published 9 November 2011

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 $e p$ scattering as recently combined by the H1 and ZEUS groups. We use initial distributions $F_{2}^{γ p} (x, Q_{0}^{2})$ 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 $F_{2}^{γ p} (x, Q_{0}^{2})$ 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 $F_{2}^{γ p} (x, Q^{2})$ with the HERA data that the assumption of leading-order DGLAP evolution is inconsistent with those data.