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

Abstract

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 ($J^{PC}=0^{++}$), axial vector ($J^{PC}=1^{+-}$), and tensor ($J^{PC}=2^{++}$). 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 (HF-NRevo) 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 (sym)JETHAD, 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.

Comments: Six NLO collinear FF sets for fully heavy tetraquarks (TQ4Q1.1), covering scalar, axial, and tensor states. Includes MHOU replicas, LDME variations, and DGLAP evolution, released in LHAPDF format at https://github.com/FGCeliberto/Collinear_FFs/. Supplemental Mathematica notebook with all short-distance coefficients