One-loop impact factors for heavy quarkonium production: $S$-wave case

With the aim to extend the study of inclusive heavy quarkonium production at forward rapidities with the resummation of high partonic center-of-momentum-energy logarithms beyond Leading Logarithmic Approximation (LLA), the explicit analytic results for one-loop corrections to the following impact factors had been obtained: $\gamma R \to Q\bar{Q}\left[^1S_0^{[8]} \right]$, $g R \to Q\bar{Q}\left[^1S_0^{[1]} \right]$, $gR\to Q\bar{Q}\left[ ^1S_0^{[8]} \right]$ and $gR\to Q\bar{Q}\left[ ^3S_1^{[8]}\right]$, with $R$ being the Reggeized gluon and $Q$ is the heavy quark. The computation is done in the framework of Lipatov's gauge-invariant EFT for Multi-Regge processes in QCD with the tilted-Wilson-line regularisation for rapidity divergences. As expected, only single-logarithmic rapidity divergence proportional to the one-loop Regge trajectory of a gluon remains in the final result for impact-factors. Numerical comparison with Regge limits ($s/(-t) \gg 1$) of one-loop QCD amplitudes, described in the paper, provides a strong cross-check of obtained results. The relations of obtained results with other regularisation schemes for rapidity divergences used in low-$x$ physics, such as BFKL scheme, High-Energy Factorisation (HEF) scheme and shockwave scheme, are given.