Curing the high-energy perturbative instability of vector-quarkonium-photoproduction cross sections at order with high-energy factorisation

Jean-Philippe Lansberg; Maxim Nefedov; Melih A. Ozcelik

doi:10.1140/epjc/s10052-024-12588-x

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 351
https://doi.org/10.1140/epjc/s10052-024-12588-x

Regular Article - Theoretical Physics

Curing the high-energy perturbative instability of vector-quarkonium-photoproduction cross sections at order $α α_{s}^{3}$ $\alpha \alpha _s^3$ with high-energy factorisation

Jean-Philippe Lansberg¹, Maxim Nefedov¹^,2^b and Melih A. Ozcelik¹

¹ Université Paris-Saclay, CNRS IJCLab, 91405, Orsay, France
² National Centre for Nuclear Research (NCBJ), Pasteura 7, 02-093, Warsaw, Poland

^b Maxim.Nefedov@ijclab.in2p3.fr

Received: 8 December 2023
Accepted: 18 February 2024
Published online: 3 April 2024

Abstract

We cure the perturbative instability of the total-inclusive-photoproduction cross sections of vector S-wave quarkonia observed at high photon-proton-collision energies ( $\sqrt{s_{γ p}}$ $\sqrt{s_{\gamma p}}$ ) in Next-to-Leading Order (NLO) Collinear-Factorisation (CF) computations. This is achieved using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA), which is a subset of the Leading-Logarithmic Approximation (LLA) of HEF which resums higher-order QCD corrections proportional to $α_{s}^{n} {ln}^{n - 1} (\hat{s} / M^{2})$ $\alpha _s^n \ln ^{n-1} ({\hat{s}}{/}M^2)$ in the Regge limit $\hat{s} ≫ M^{2}$ ${\hat{s}}\gg M^2$ with $M^{2}$ $$M^2$$ being the quarkonium mass and $\hat{s}$ ${\hat{s}}$ is the squared partonic-center-of-mass energy. Such a DLA is strictly consistent with the NLO and NNLO DGLAP evolutions of the parton distribution functions. By improving the treatment of the large- $\hat{s}$ ${\hat{s}}$ asymptotics of the CF coefficient function, the resummation cures the unphysical results of the NLO CF calculation. The matching is directly performed in $\hat{s}$ ${\hat{s}}$ space using the Inverse-Error Weighting matching procedure which avoids any possible double counting. The obtained cross sections are in good agreement with data. In addition, the scale-variation uncertainty of the matched result is significantly reduced compared to the LO results. Our calculations also yield closed-form analytic limits for $\hat{s} ≫ M^{2}$ ${\hat{s}}\gg M^2$ of the NLO partonic CF and numerical limits for contributions to those at NNLO scaling like $α_{s}^{2} ln (\hat{s} / M^{2})$ $\alpha _s^2 \ln ({\hat{s}}/M^2)$ .

© The Author(s) 2024

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/.