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

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.

13 pages, 5 figures, the structure function values corresponding to physical basis DGLAP evolution are included in the ancillary files. v2: version is published in Eur. Phys. J. C v3: source code available at [https://gitlab.com/mirjatevio/physicalbasis_nlo], no changes in the article text