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

TL;DR

This paper develops a comprehensive theoretical framework for the production and fragmentation of fully heavy tetraquarks, incorporating advanced QCD techniques and uncertainty analysis, to aid experimental searches at high-energy colliders.

Contribution

It introduces a novel set of fragmentation functions for heavy tetraquarks, combining NRQCD, DGLAP evolution, and uncertainty quantification, with phenomenological predictions for collider experiments.

Findings

First systematic treatment of uncertainties in tetraquark fragmentation

Predictions for tetraquark production cross sections at HL-LHC and FCC

Inclusion of angular multiplicities as probes of QCD dynamics

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.