Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study

We extend the study of exotic matter formation via the { TQ4Q1.1} set of collinear, variable-flavor-number-scheme fragmentation functions for fully charmed or bottomed tetraquarks in three quantum configurations: scalar (JPC = 0⁺⁺), axial vector (JPC = 1⁺⁻), and tensor (JPC = 2⁺⁺). We adopt single-parton fragmentation at leading power and implement a nonrelativistic QCD 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 DGLAP evolution is then applied via HFNRevo. We provide the first systematic treatment of uncertainties propagated from the color-composite long-distance matrix elements that govern the nonperturbative hadronization of tetraquarks. To support phenomenology, we compute NLL/NLO⁺ cross sections for tetraquark-jet systems at the HL-LHC and FCC using (sym)JETHAD, incorporating angular multiplicities as key observables sensitive to high-energy QCD dynamics. This work connects the investigation of exotic hadrons with state-of-the-art precision QCD.