Tetraquark-Jet Systems at the High-Luminosity LHC

Abstract: 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 ($T_{4Q}$) 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.