Multimodal Fragmentation of All-Heavy Pentaquarks: Uncertainty-Aware Predictions for Hadron Colliders

Abstract

We present an uncertainty-aware description of leading-power fragmentation for all-charm pentaquark states ($S$-wave $|cccc\bar{c}\rangle$) at hadron colliders. We construct a multimodal set of collinear fragmentation functions, PQ5Q1.1, incorporating both perturbative and nonperturbative uncertainties. Perturbative effects are estimated via missing higher-order variations (F-MHOUs), while the nonperturbative wave function is modeled through controlled modifications of its transverse-momentum structure (F-NPWF), consistently combined within a replica-like framework. The initial-scale input for constituent charm fragmentation is refined to describe both compact multiquark and diquark-driven production mechanisms. We employ the (sym)JETHAD interface to study NLL/NLO$^+$ semi-inclusive pentaquark-plus-jet production at the HL-LHC and future FCC. The bottom sector is left to future dedicated studies due to its enhanced sensitivity to nonperturbative modeling. Our results provide a flexible framework for uncertainty-controlled predictions, bridging exotic-hadron structure, heavy-flavor fragmentation, and high-energy QCD.