Pentaquark-Jet Systems at the High-Luminosity LHC
All-heavy pentaquarks provide a unique laboratory for exploring the interplay between exotic-hadron structure, heavy-quark dynamics, and perturbative Quantum Chromodynamics (QCD). In this review, we present the completed release of the uncertainty-aware collinear fragmentation-function family PQ5Q1.1, covering both all-charm (P5c) and all-bottom (P5b) states. The extension to the bottom sector follows the resolution of theoretical and numerical issues affecting heavy-bottom fragmentation and completes the public LHAPDF6 release of the PQ5Q1.1 family. The PQ5Q1.1 functions are constructed within a multimodal framework that accounts for both compact multiquark formation and diquark–antiquark–diquark production mechanisms. A replica-based strategy is adopted to quantify perturbative and nonperturbative uncertainties through missing-higher-order variations (F-MHOUs) and controlled modifications of the hadronic wave-function structure (F-NPWF). For phenomenological applications, we employ the data-validated (sym)JETHAD framework to investigate semi-inclusive pentaquark-plus-jet production at NLL/NLO+ accuracy at the High-Luminosity Large Hadron Collider. We present predictions for differential distributions, assessing the impact of fragmentation dynamics, uncertainty propagation, and hadron-structure effects across the charm and bottom sectors. By combining precision fragmentation tools with collider-oriented observables, this review establishes a unified framework connecting heavy-pentaquark spectroscopy, hadronization mechanisms, and high-energy QCD phenomenology.