Exotic and Rare Hadrons Across Flavor Sectors: Fragmentation, Symmetries, and Collider Phenomenology

Exotic and rare hadrons, including tetraquarks, pentaquarks, and multiply heavy baryons, provide a unique laboratory for exploring the symmetries and dynamical mechanisms underlying hadron formation in QCD. Recent observations at the LHC, including the discovery of a family of all-charm tetraquark candidates and the establishment of doubly charmed baryons, have renewed interest in understanding the production mechanisms of multiquark and heavy-flavor states across different flavor sectors. Their production probes the interplay between perturbative and nonperturbative dynamics, offering new insights into the emergence of complex bound states beyond the conventional quark model. We present a unified fragmentation-based framework for the description of heavy and exotic hadron production, developed within the Heavy-Flavor Non-Relativistic evolution (HF-NRevo) scheme. This approach enables the consistent construction and evolution of fragmentation functions across energy scales while incorporating a systematic treatment of theoretical uncertainties. The framework reveals common structures and symmetry patterns linking quarkonia, tetraquarks, pentaquarks, and triply heavy baryons, thereby providing a coherent description of a broad class of hadronic systems. Publicly available fragmentation-function sets implemented in LHAPDF are discussed together with representative phenomenological applications at present and future colliders. Particular attention is devoted to the role of intrinsic heavy-quark components and to their impact on selected production channels. These studies establish a predictive and uncertainty-aware framework for heavy-flavor and multiquark phenomenology, highlighting how symmetry principles can guide the exploration of hadron structure, multiquark dynamics, and the production of rare states in high-energy collisions.