Unwinding the rare <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math> 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Ω</a:mi></a:math> baryons. Our methodology combines diquarklike proxy model inputs for both charm-quark and gluon channels, calculated at the initial energy scales, with a Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution that ensures a consistent treatment of heavy-quark thresholds, following directly from the heavy-flavor nonrelativistic evolution scheme. We complement our work with a phenomenological study of next-to-leading logarithm/next-to-leading order plus resummed <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="normal">Ω</d:mi><d:mrow><d:mn>3</d:mn><d:mi>c</d:mi></d:mrow></d:msub></d:math> plus jet distributions using (sym) 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.