Unwinding the rare $\Omega$ sector: Fragmentation of fully charmed baryons from HL-LHC to FCC

By adopting a hadron-structure-oriented approach, we present and discuss the release of the novel OMG3Q1.0 set of collinear fragmentation functions for fully charmed, rare $\Omega$ baryons. Our methodology combines diquark-like proxy model inputs for both charm-quark and gluon channels, calculated at the initial energy scales, with a DGLAP evolution that ensures a consistent treatment of heavy-quark thresholds, following directly from the HF-NRevo scheme. We complement our work with a phenomenological study of NLL/NLO$^+$ resummed $\Omega_{3c}$ plus jet distributions using (sym)JETHAD at the HL-LHC and the future FCC. Unraveling the production mechanisms of rare, yet-unobserved hadrons, as provided by the OMG3Q1.0 functions, stands as a key asset for deepening our understanding of QCD at future high-energy hadron colliders.