We extend the study of exotic matter formation via the set of collinear, variable-flavor-number-scheme fragmentation functions for fully charmed or bottomed tetraquarks in three quantum configurations; scalar ( J P C = 0 + + ), axial vector ( J P C = 1 + − ), and tensor ( J P C = 2 + + ). We adopt single-parton fragmentation at leading power and implement a nonrelativistic quantum chromodynamics (NRQCD) factorization scheme tailored to tetraquark Fock-state configurations. Short-distance inputs at the initial scale are modeled using updated calculations for both gluon- and heavy-quark-initiated channels. A threshold-consistent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution is then applied via the novel heavy-flavor nonrelativistic-evolution () hybrid scheme. We provide the first systematic treatment of uncertainties from nonperturbative color-composite long-distance matrix elements (LDMEs), as well as from perturbative hard-scattering (H-MHOUs) and fragmentation-scale inputs (F-MHOUs), assessed separately and in combination. To support phenomenology, we compute NLL / NLO + cross sections for tetraquark-jet systems at the HL-LHC and FCC within the hybrid collinear and high-energy factorization (HyF) as implemented in , incorporating angular multiplicities as key observables sensitive to high-energy QCD dynamics. We also provide expected event yields based on realistic luminosity scenarios, offering a concrete benchmark for experimental searches. This work connects the investigation of exotic hadrons with state-of-the-art precision QCD.
Francesco Giovanni Celiberto (Thu,) studied this question.