Internal multiplicity distributions of jets from nonlinear evolution within the jet function framework

Jets selected with high internal charged-particle multiplicity exhibit markedly different substructure patterns compared to inclusive jet samples. Such correlations motivate a systematic study of jet observables as a function of the normalized multiplicity, $\nu =N_{\mathrm{c}\mathrm{h}}\mathrm{/}⟨N_{\mathrm{c}\mathrm{h}}⟩$. In this work, we develop a theoretical framework for the full charged-particle multiplicity distribution of exclusive and inclusive jets, formulated within the jet-function approach. The hard production and jet function are evaluated at NLO+LL${}_R$ accuracy. The internal parton dynamics governing the multiplicity distribution are described by coupled nonlinear branching equations with angular ordering, supplemented by a nonperturbative modeling term that accounts for hadron-level effects. The resulting predictions are validated against $\text{textsc}Pythia8$ simulations and compared with CMS data. We examine the effects of both nonperturbative and perturbative components in shaping the multiplicity distribution, and show that Koba–Nielsen–Olesen (KNO) scaling is notably violated in the region $\nu >2$ in the full solution, with a trend consistent with Monte Carlo results. This framework that numerically solves the nonlinear multiplicity evolution goes beyond DLA-like approximations and reproduces key features seen in event generators, providing a solid foundation for future investigations of multiplicity – conditioned jet substructure within the jet function formalism.