Document Type

Article

Publication Date

2024

DOI

10.1140/epjc/s10052-024-13169-8

Publication Title

The European Physical Journal C

Volume

84

Issue

8

Pages

867 (1-15)

Abstract

The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide approximated results depending on the assumptions and the methodology adopted. These results differ in their sub-leading, neglected terms and ultimately they are associated with different treatments of the theoretical uncertainties. In this work, a novel analytic approach in Mellin space is presented and a new methodology for obtaining closed and exponentiated analytic solutions is devised. Different results for the DGLAP evolution at Next-Leading-Order are compared, discussing advantages and disadvantages for each solution. The generalizations to higher orders are addressed.

Rights

© The Authors 2024.

This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original authors and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Data Availability

Article states: "This manuscript has no associated data. [Author's comment: There are no data associated to this article.]"

Original Publication Citation

Simonelli, A. (2024). Analytic solutions of the DGLAP evolution and theoretical uncertainties. European Physical Journal C, 84(8), 1-15, Article 867. https://doi.org/10.1140/epjc/s10052-024-13169-8

ORCID

0000-0003-2607-9004 (Simonelli)

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