Exploring differential two-particle correlations in $\gamma p$ and low-multiplicity pp collisions using PYTHIA8

A study of two-particle differential number ($B$) and transverse momentum ($P_{2}^\mathrm{CD}$) balance functions in photon-proton ($\gamma p$) and proton-proton (pp) collisions at $\sqrt{s}=$ 5.36 TeV is presented. The analysis focuses on inclusive charged hadrons within the pseudorapidity coverage $|\eta|<2.4$ and the transverse momentum interval $0.3 < p_\mathrm{T} < 3.0$ GeV and examines their correlations in terms of relative pseudorapidity ($\Delta\eta$) and relative azimuthal angle ($\Delta\phi$). The correlation functions are evaluated for same- and opposite-sign pairs, and their combinations are used to extract charge-dependent (CD) and charge-independent (CI) components. The evolution of the near-side peak of the CD correlations is investigated in terms of $\Delta\eta$ and $\Delta\phi$ as a function of charged-particle multiplicity ($N_\mathrm{ch}$) for $\gamma p$ collisions and compared to pp collisions at a similar multiplicity range. A clear multiplicity dependence of the balance function width is obtained. The width is found systematically lower in $\gamma p$ events than in pp collisions. This study provides valuable information on particle correlations and production mechanisms in low-$N_\mathrm{ch}$ regimes for upcoming measurements in small systems.