Simulation Studies of  $$\textrm{R}_2(\Delta \eta ,\Delta \phi )$$ and  $$\textrm{P}_2(\Delta \eta ,\Delta \phi )$$ Correlation Functions in pp Collisions with the PYTHIA and HERWIG Models

We presented a study of charge-independent (CI) and charge-dependent (CD) two-particle differential number correlation functions $$\textrm{R}_2$$ and transverse momentum correlation functions $$\textrm{P}_2$$ in pp collisions at $$\sqrt{s} = 2.76$$ TeV with the PYTHIA and HERWIG models. Calculations were presented for unidentified hadrons in three $$p_\textrm{T}$$ ranges $$0.2 < p_\textrm{T} \le 2.0$$ GeV/c, $$2.0 < p_\textrm{T} \le 5.0$$ GeV/c, and $$5.0 < p_\textrm{T} \le 30.0$$ GeV/c. PYTHIA and HERWIG both qualitatively reproduce the near-side peak and away-side ridge correlation features reported by experiments. At low $$p_\textrm{T}$$ , both models produce narrower near-side peaks in $$\textrm{P}_2$$ correlations than in $$\textrm{R}_2$$ as reported by the ALICE collaboration in p–Pb and Pb–Pb collisions. This suggests that the narrower shape of the $$\textrm{P}_2$$ near-side peak is largely determined by the $$p_\textrm{T}$$ dependent angular ordering of hadrons produced in jets. Both PYTHIA and HERWIG predict widths that decrease with increasing $$p_\textrm{T}$$ . Widths extracted for $$\textrm{P}_2$$ correlators are typically significantly narrower than those of the $$\textrm{R}_2$$ counterparts [1].