On the high-energy instability of quarkonium production

Abstract: The perturbative instability of NLO collinear factorisation (CF) computations of $p_T$-integrated cross sections of heavy quarkonium production at high hadronic or photon-hadron collision energy is discussed. We resolve this problem via the matching of NLO CF computation with the resummation of higher-order corrections $\propto \alpha_s^n \ln^{n-1}(\hat{s}/M^2)$ at high partonic center of mass energies $\hat{s}\gg M^2$. The resummation is performed in the Doubly-Logarithmic Approximation(DLA) of High-Energy Factorisation(HEF) formalism. We also report the results of the first computation of one-loop corrections to impact-factors involving heavy quark-antiquark pair in the intermediate states considered in the Non-Relativistic QCD (NRQCD) factorisation formalism for quarkonium production: $Q\bar{Q}\left[{}^1S_0^{[8]} \right]$ and $Q\bar{Q}\left[{}^1S_0^{[1]} \right]$. These results are necessary for the extension of our resummation formalism beyond DLA.