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

References in corpus (20)

• LHAPDF6: parton density access in the LHC precision era
• New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC
• Precise Measurement of Dimuon Production Cross-Sections in muon neutrino Fe and muon antineutrino Fe Deep Inelastic Scattering at the Tevatron
• The Large Hadron-Electron Collider at the HL-LHC
• The Structure of the Proton in the LHC Precision Era
• Precise Measurement of Neutrino and Anti-neutrino Differential Cross Sections
• The Longitudinal Structure Function at the Third Order
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• Parton Distributions in Nucleons and Nuclei
• Meaningful characterisation of perturbative theoretical uncertainties
• Hadron structure in high-energy collisions
• Approximate N${}^3$LO Parton Distribution Functions with Theoretical Uncertainties: MSHT20aN${}^3$LO PDFs
• On the Drell-Levy-Yan Relation to $O({\alpha }_s^2)$
• An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations
• Deep inelastic cross-section measurements at large y with the ZEUS detector at HERA
• How well can we guess theoretical uncertainties?
• On the Consistent Use of Scale Variations in PDF Fits and Predictions
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• An FONLL prescription with coexisting flavor number PDFs
• Evolution of structure functions in momentum space

Cited by in corpus (1)

• Factorisation schemes for proton PDFs