Complete NLO BFKL impact factors for quarkonium hadroproduction in NRQCD: the case of ${}^1S_0^{[1]}$, ${}^1S_0^{[8]}$, and ${}^3S_1^{[8]}$ states

TL;DR

This paper provides the first complete next-to-leading-order impact factors for quarkonium hadroproduction within the BFKL formalism, enabling more precise theoretical predictions for forward-backward quarkonium production at colliders.

Contribution

It delivers the first full NLO calculation of impact factors for specific quarkonium states in the BFKL framework, including real-emission contributions and divergence cancellations.

Findings

Soft divergences cancel between real and virtual emissions.

Collinear singularities are compatible with factorisation at one loop.

This work enables next-to-leading-logarithmic precision studies in quarkonium production.

Abstract

We present the first complete next-to-leading-order calculation of the impact factors for hadroproduction of the ${}^1S_0^{[1]}$, ${}^1S_0^{[8]}$, and ${}^3S_1^{[8]}$ NRQCD states within the BFKL formalism. We complete the recent virtual-correction computation presented in JHEP 12 (2024) 129 by that of the real-emission contributions. We observe the cancellation of the soft divergences between these real- and virtual-emission contributions and we note that the surviving collinear singularities are compatible with factorisation up to one loop for a novel class of processes where BFKL resummation can be applied. Our work indeed represents the first complete NLO quarkonium impact factor in the BFKL framework and paves the way to first next-to-leading-logarithmic-precision studies for hadroproduction of forward-backward quarkonium associated production at hadron colliders.