Abstract; Measurements of the charge-dependent two-particle angular correlation function in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of $$ sqrt{s_{textrm{NN}}} $$; ; ; s; NN; ; ; = 8.16 TeV and lead-lead (PbPb) collisions at $$ sqrt{s_{textrm{NN}}} $$; ; ; s; NN; ; ; = 5.02 TeV are reported. The pPb and PbPb data sets correspond to integrated luminosities of 186 nb−1 and 0.607 nb−1, respectively, and were collected using the CMS detector at the CERN LHC. The charge-dependent correlations are characterized by balance functions of same- and opposite-sign particle pairs. The balance functions, which contain information about the creation time of charged particle pairs and the development of collectivity, are studied as functions of relative pseudorapidity (∆η) and relative azimuthal angle (∆ϕ), for various multiplicity and transverse momentum (pT) intervals. A multiplicity dependence of the balance function is observed in ∆η and ∆ϕ for both systems. The width of the balance functions decreases towards high-multiplicity collisions in the momentum region < 2 GeV, for pPb and PbPb results. Integrals of the balance functions are presented in both systems, and a mild dependence of the charge-balancing fractions on multiplicity is observed. No multiplicity dependence is observed at higher transverse momentum. The data are compared with hydjet, hijing, and ampt generator predictions, none of which capture completely the multiplicity dependence seen in the data. The comparison of results with different center-of-mass energies suggests that the balance functions become narrower at higher energies, which is consistent with the idea of delayed hadronization and the effect of radial flow.
