https://doi.org/10.1140/epjc/s10052-022-10793-0
Regular Article - Theoretical Physics
Revisiting evolution equations for generalised parton distributions
1
IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
2
Department of Integrated Sciences and Center for Advanced Studies in Physics, Mathematics and Computation, University of Huelva, 21071, Huelva, Spain
Received:
7
June
2022
Accepted:
9
September
2022
Published online:
8
October
2022
We revisit the evolution of generalised parton distributions (GPDs) in momentum space. We formulate the evolution kernels at one loop in perturbative quantum chromodynamics (pQCD) in a form that is suitable for numerical implementation and that allows for an accurate study of their properties. This leads to the first open-source implementation of GPD evolution equations able to cover the entire kinematic region and allowing for heavy-quark-threshold crossings. The numerical implementation of the GPD evolution equations is publicly accessible through the APFEL++ evolution library and is available within the PARTONS framework. Our formulation makes use of the operator definition of GPDs in light-cone gauge renormalised in the 
scheme. For the sake of clarity, we recompute the evolution kernels at one loop in pQCD, confirming previous calculations. We obtain general conditions on the evolution kernels derived from the GPD sum rules and show that our formulation obeys these conditions. We analytically show that our calculation reproduces the DGLAP and the ERBL equations in the appropriate limits and that it guarantees the continuity of GPDs. We numerically check that the evolved GPDs fulfil DGLAP and ERBL limits, continuity, and polynomiality. We benchmark our numerical implementation against analytical evolution in conformal space. Finally, we perform a numerical comparison to an existing implementation of GPD evolution, finding general good agreement on the kinematic region accessible to the latter. This work provides a pedagogical description of GPD evolution equations which benefits from a renewed interest as future colliders, such as the electron-ion colliders in the United States and in China, are being designed. It also paves the way for the extension of GPD evolution codes to higher accuracies in pQCD desirable for precision phenomenology at these facilities.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
