The applications of the resummation of the QCD corrections to hard-scattering coefficient functions, enhanced by the logarithms of partonic center of mass energy to the physics of production of heavy quarkonia will be discussed. Two main examples are total inclusive cross sections of hadroporoduction of eta-c meson[1] and photoproduction of J/psi[2]. In both cases, the resummation resolves the problem of perturbative instability of the NLO Collinear Factorisation computation. The application of the formalism to the case of exclusive photoproduction of J/psi, where it cures an similar problem, will be briefly discussed. The status of the computation of loop corrections to the impact-factors of heavy quarkonium production, which are needed to extend the formalism beyond Leading-Logarithmic Approximation, will be presented [3].
[1] J.P. Lansberg, M. Nefedov and M.A. Ozcelik, Matching next-to-leading-order and high-energy-resummed calculations of heavy-quarkonium-hadroproduction cross sections, JHEP 05, 083 (2022) [arXiv:2112.06789 [hep-ph]].
[2] J.P. Lansberg, M.Nefedov and M.A. Ozcelik, Curing the high-energy perturbative instability of vector-quarkonium-photoproduction cross sections at order $\alpha \alpha_s^3$ with high-energy factorisation, [arXiv:2306.02425 [hep-ph]]
[3] M.Nefedov, On the high-energy instability of quarkonium production, [arXiv:2309.09608 [hep-ph]].
