On the high-energy instability of quarkonium production

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 $\propto {\alpha }_s^n{\ln }^{n-1}(\widehat{s}\mathrm{/}{M}^2)$ at high partonic center of mass energies $\widehat{s}\gg M^2$. 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: $Q\bar{Q}\left[{}^1{S}_0^{[8]}\right]$ and $Q\bar{Q}\left[{}^1{S}_0^{[1]}\right]$. These results are necessary for the extension of our resummation formalism beyond DLA.