Evolution of structure functions at NLO without PDFs

TL;DR

This paper develops a method to directly evolve DIS structure functions at NLO without relying on PDFs, simplifying the analysis and avoiding scheme dependence, with potential applications to LHC data analysis.

Contribution

It introduces a physical basis approach to NLO evolution of structure functions directly in terms of $F_2$ and $F_L$, bypassing the need for PDFs.

Findings

Derives NLO evolution equations for structure functions in the physical basis.

Shows the approach is free from factorization scheme and scale ambiguities.

Discusses application to global LHC cross section analysis.

Abstract

We formulate the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution of the Deep Inelastic Scattering (DIS) structure functions $F_2$ and $F_{\rm L}$ at next to leading order in $\alpha_s$ (NLO) directly in terms of the structure functions rather than parton distributions (PDFs). We call this the physical basis approach. In practice, we first express the NLO quark singlet and gluon PDFs in terms of the structure functions $F_2$ and $F_{\rm L}$ in momentum space. Employing these expressions in the DGLAP evolution, we arrive at the evolution equations for $F_2$ and $F_{\rm L}$ in the physical basis. We demonstrate how one is free from defining a factorization scale and scheme when using the physical basis evolution equations. We also discuss the process of applying the NLO physical basis to global analysis of LHC cross sections.