Longitudinal boost invariance of the charge balance function in hadron-hadron and nucleus-nucleus collisions

Using Monte Carlo generators of the PYTHIA model for hadron-hadron collisions and a multiphase transport (AMPT) model for nucleus-nucleus collisions, the longitudinal boost invariance of charge balance function and its transverse-momentum dependence are carefully studied. It shows that the charge balance function is boost invariant in both $p+p$ and $\mathrm{Au}+\mathrm{Au}$ collisions in these two models, consistent with experimental data. The balance function properly scaled by the width of the pseudorapidity window is independent of the position or the size of the window and is corresponding to the balance function of the whole pseudorapidity range. This longitudinal property of balance function also holds for particles in small transverse-momentum ranges in the PYTHIA and the AMPT default models, but is violated in the AMPT with string melting. The physical origin of the results is discussed.