Measurements of the charge-dependent two-particle angular correlation function in proton-lead (pPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_\mathrm{NN}}$ = 8.16 TeV and lead-lead (PbPb) collisions at $\sqrt{s_\mathrm{NN}}$ = 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 ($\Delta \eta$) and relative azimuthal angle ($\Delta \phi$), for various multiplicity and transverse momentum ($p_\mathrm{T}$) intervals. A multiplicity dependence of the balance function is observed in $\Delta \eta$ and $\Delta \phi$ for both systems. The width of the balance functions decreases toward high-multiplicity collisions in the momentum region $\lt$ 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 suggest that the balance functions become narrower at higher energies, which is consistent with the idea of delayed hadronization and the effect of radial flow.
$\Delta\eta$ projection of balance function in low $p_{T}$ in 0-10% centrality
$\Delta\eta$ projection of balance function in low $p_{T}$ in 30-40% centrality
$\Delta\eta$ projection of balance function in low $p_{T}$ in 70-80% centrality
We report on two-particle charge-dependent correlations in pp, p-Pb, and Pb-Pb collisions as a function of the pseudorapidity and azimuthal angle difference, $\mathrm{\Delta}\eta$ and $\mathrm{\Delta}\varphi$ respectively. These correlations are studied using the balance function that probes the charge creation time and the development of collectivity in the produced system. The dependence of the balance function on the event multiplicity as well as on the trigger and associated particle transverse momentum ($p_{\mathrm{T}}$) in pp, p-Pb, and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 7$, 5.02, and 2.76 TeV, respectively, are presented. In the low transverse momentum region, for $0.2 < p_{\mathrm{T}} < 2.0$ GeV/$c$, the balance function becomes narrower in both $\mathrm{\Delta}\eta$ and $\mathrm{\Delta}\varphi$ directions in all three systems for events with higher multiplicity. The experimental findings favor models that either incorporate some collective behavior (e.g. AMPT) or different mechanisms that lead to effects that resemble collective behavior (e.g. PYTHIA8 with color reconnection). For higher values of transverse momenta the balance function becomes even narrower but exhibits no multiplicity dependence, indicating that the observed narrowing with increasing multiplicity at low $p_{\mathrm{T}}$ is a feature of bulk particle production.
Balance function in $\Delta\eta$ 0_5%.
Balance function in $\Delta\eta$ 30_40%.
Balance function in $\Delta\eta$ 70_80%.
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