Next-to-leading order evolution of structure functions without PDFs

TL;DR

This paper develops a method to directly evolve observable structure functions in deep inelastic scattering at next-to-leading order, bypassing the need for parton distribution functions, thus reducing scheme dependence and improving experimental confrontation.

Contribution

It introduces a novel approach to solve DGLAP equations directly for physical structure functions, avoiding reliance on PDFs and their associated ambiguities.

Findings

Numerical solutions show consistent evolution of structure functions.

Comparison indicates advantages over traditional PDF-based evolution.

Method reduces scheme and factorization scale dependence.

Abstract

We formulate and numerically solve the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi~(DGLAP) evolution equations at next-to-leading order in perturbation theory directly for a basis of 6 physical, observable structure functions in deeply inelastic scattering. By expressing the evolution in the physical basis one evades the factorization scale and scheme dependence. Working in terms of observable quantities, rather than parametrizing and fitting unobservable parton distribution functions (PDFs), provides an unambiguous way to confront predictions of perturbative Quantum Chromodynamics with experimental measurements. We compare numerical results for the DGLAP evolution for structure functions in the physical basis to the conventional evolution with PDFs.