Letter
Open Access

How well does nonrelativistic QCD factorization work at next-to-leading order?

Nora Brambilla ^1,2,3, Mathias Butenschoen⁴, and Xiang-Peng Wang ^5,1,*

¹Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Strasse 1, 85748 Garching, Germany
²Technical University of Munich, Institute for Advanced Study, Lichtenbergstrasse 2a, 85748 Garching, Germany
³Technical University of Munich, Munich Data Science Institute, Walther-von-Dyck-Strasse 10, 85748 Garching, Germany
⁴II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
⁵Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, Hubei 430079, China

^*Contact author: xpwang@ccnu.edu.cn

Phys. Rev. D 112, L011902 – Published 15 July, 2025

DOI: https://doi.org/10.1103/8xqs-45pz

Abstract

We perform a thorough investigation of the universality of the long-distance matrix elements (LDMEs) of nonrelativistic QCD factorization based on a next-to-leading order (NLO) fit of $J / ψ$ color octet LDMEs to high transverse momentum $p_{T}$ $J / ψ$ and $η_{c}$ production data at the LHC. We thereby apply a novel fit-and-predict procedure to systematically take into account scale variations, and predict various observables never studied in this context before. In particular, the LDMEs can well describe $J / ψ$ hadroproduction up to the highest measured values of $p_{T}$ , as well as $ϒ (n S)$ production via potential nonrelativistic QCD based relations. Furthermore, $J / ψ$ production in $γ γ$ and $γ p$ collisions is surprisingly reproduced down to $p_{T} = 1 GeV$ , as long as the region of large inelasticity $z$ is excluded, which may be of significance in future quarkonium studies, in particular at the EIC and the high-luminosity LHC. In addition, our summary reveals an interesting pattern as to which observables still evade a consistent description.

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How well does nonrelativistic QCD factorization work at next-to-leading order?

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