Tetraquark-Jet Systems at the High-Luminosity LHC

We investigate the high-energy production of tetraquark-jet systems at the LHC and its forthcoming high-luminosity upgrade. In this review, we examine the leading–power fragmentation of fully heavy tetraquarks (T4Q) in hadronic collisions, highlighting their relevance as novel probes of multiquark dynamics in QCD. Our analysis relies on the hadron–structure–oriented TQ4Q1.1 fragmentation functions, built within a nonrelativistic QCD framework that incorporates both gluon- and heavy-quark-initiated channels. Threshold-consistent DGLAP evolution is performed through the HF-NRevo scheme, enabling a unified treatment of mass thresholds and scale variations. We also provide a systematic discussion of uncertainties arising from color-composite long-distance matrix elements (LDMEs) and from perturbative hard- and fragmentation-scale inputs (H- and F-MHOUs). Phenomenological predictions are obtained using the (sym)Jethad framework at NLL/NLO+ accuracy for semi-inclusive tetraquark-jet production at the LHC and beyond. This review connects the emerging spectroscopy of fully heavy exotics with modern fragmentation-based approaches to hadron structure and high-energy QCD.