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.

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

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• Triply Heavy $\Omega$ Baryons with JETHAD: A High-Energy Viewpoint
• Tetraquark-Jet Systems at the High-Luminosity LHC
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• All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective
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