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

TL;DR

This paper derives explicit one-loop impact factors for S-wave heavy quarkonium production within Lipatov's EFT, extending high-energy resummation beyond LLA and providing cross-checked results with various schemes.

Contribution

It presents the first analytic one-loop impact factors for specific heavy quarkonium production channels in Lipatov's EFT, including regularization scheme comparisons.

Findings

Only single-logarithmic rapidity divergence remains after regularization.

Numerical results agree with Regge limit QCD amplitudes.

Relations with other rapidity divergence schemes are established.

Abstract

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.