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

TL;DR

This paper derives explicit solutions to the leading-order DGLAP equations using Laplace transforms and applies them to HERA deep inelastic scattering data, revealing inconsistencies with the LO evolution assumption.

Contribution

The paper provides a novel explicit solution to the LO DGLAP equations and demonstrates its application to real experimental data, highlighting limitations of the LO approximation.

Findings

LO DGLAP evolution is inconsistent with HERA data

Explicit solutions enable detailed analysis of structure functions

Comparison shows need for higher-order corrections

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 $F_2^{\gamma p}(x,Q_0^2)$ and $G(x,Q_0^2)$ fixed by a global fit to the HERA data. From $F_2^{\gamma p}(x,Q_0^2)$ we obtain the singlet quark distribution $F_s(x,Q_0^2)$---using small non-singlet quark distributions taken from either the CTEQ6L or the MSTW2008LO analyses---evolve 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 $F_2^{\gamma p}(x,Q^2)$ with the HERA data, that the assumption of leading-order DGLAP evolution is inconsistent with those data.