Heavy-flavor multimodal fragmentation to $S$-wave pentacharms at next-generation hadron colliders

We investigate the leading-power fragmentation of fully charmed pentaquark states ($S$-wave $\mathrm{\mid }c\bar{c}ccc⟩$ pentacharms) at hadron colliders. We introduce a new set of multimodal collinear fragmentation functions, named PQ5Q1.0. They rely on an enhanced calculation of the initial-scale input for the constituent heavy-quark fragmentation channel, making them well suited to describe the short-distance emission of either a compact multicharm state or a dicharm-charm-dicharm configuration. To explore phenomenological implications, we use the (sym)JETHAD multimodular interface to study NLL/NLO${}^{+}$ semi-inclusive production rates for pentacharm-plus-jet systems at the forthcoming HL-LHC and the future FCC. Our analysis represents a further step toward bridging the domains of hadronic structure, precision QCD, and exotic matter.