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

Abstract: We present the first complete next-to-leading order calculation of the impact factors for hadroproduction of $S$-wave quarkonium states within the BFKL formalism. We present the computation of the real-emission contributions which completes the recent one of one-loop virtual corrections by one of us for the impact factors for the ${}^1S_0^{[1]}$, ${}^1S_0^{[8]}$, and ${}^3S_1^{[8]}$ NRQCD states. We prove the cancellation of soft divergences between real and virtual contributions, and 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.