Event-by-event fluctuations of mean transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13 TeV with PYTHIA8 and HERWIG7 models

Abstract: Estimations of event-by-event mean transverse momentum ($\langle p_{\rm T} \rangle$) fluctuations are reported in terms of the integral correlator, $\langle \Delta p_{\rm T} \Delta p_{\rm T}\rangle$, and the skewness of event-wise $\langle p_{\rm T} \rangle$ distribution in proton$-$proton (pp) collisions at $\sqrt{s}=13$ TeV with the Monte Carlo event generators PYTHIA8 and HERWIG7. The final-state charged particles with transverse momentum ($p_{\rm T}$) and pseudorapidity ($\eta$) ranges $0.15 \leq p_{\rm T}\leq 2.0$ GeV/$c$ and $|\eta| \leq 0.8$ were considered for the investigation. The correlator, $\langle \Delta p_{\rm T} \Delta p_{\rm T}\rangle$, is observed to follow distinct decreasing trends with average charged particle multiplicity ($\langle N_{\rm ch} \rangle$) for the models. Furthermore, both models yield positive finite skewness in low-multiplicity events. Fluctuations are additionally studied using the transverse spherocity estimator ($S_{\rm 0}$) to understand the relative contributions of hard scattering (jets) and other soft processes to the observed fluctuations. Comparing model predictions for $\langle p_{\rm T} \rangle$ fluctuations provides valuable insight into the sensitivity of these fluctuations to hadronization and parton shower models. This is essential for a reliable interpretation of the fluctuation dynamics in pp collisions. Moreover, such comparisons would help to establish a crucial baseline for identifying and studying non-trivial fluctuations in heavy-ion collisions.