I present the first implementation in MadGraph5_aMC@NLO of leading-order (LO) cross sections for $S$-wave quarkonium, leptonium and $B_c$-meson bound-state production in Non-Relativistic QCD and Non-Relativistic QED. In these proceedings, I specifically report on the extension of MadGraph5_aMC@NLO to quarkonium states, the simplest bound states in QCD, and describe the capabilities of our new tool for quarkonium production in a wide variety of collider environments.
I present a comprehensive benchmarking of our LO tool against Helac-Onia, followed by a demonstration of its expanded capabilities, enabling studies complementing and extending state-of-the-art phenomenology. This work provides the community with an all-encompassing tool for quarkonium-production studies in QCD, delivering reliable, efficient and fast automated computations and lays the foundation for our future NLO extensions.