Hadronic rescattering effects on net-proton cumulants from functional renormalization group calculations

Abstract: Net-proton cumulants in the Beam Energy Scan region of heavy-ion collisions are widely used to probe critical fluctuations associated with the conjectured critical endpoint of Quantum Chromodynamics (QCD). Most existing studies, however, concentrate on the initial-state or phase-transition contributions, while the impact of hadronic rescattering on these observables has not been fully quantified. To address this gap, we construct event-by-event proton and antiproton distributions from functional renormalization group (fRG) cumulants using the maximum entropy principle, and propagate the resulting particles through the hadronic transport model SMASH in a simplified spherical evolution setup. We systematically investigate how the hadronic cascade modifies net-proton cumulants at collision energies $\sqrt{s_{NN}}=3.0$, 3.9, 4.9, 7.2, and 7.7~GeV. In the canonical-ensemble framework, which enforces exact net-baryon number conservation, the higher-order cumulant signal---in particular the ratio $C_4/C_2$ at $\sqrt{s_{NN}}=4.9$~GeV---is strongly reduced during the early stage of the cascade; the suppression of $C_4/C_2$ reaches approximately $20\%$. The non-monotonic energy dependence inherited from the fRG input survives the hadronic evolution, but its magnitude is substantially modified. These results demonstrate that hadronic rescattering provides a non-negligible background effect that must be accounted for when extracting QCD critical-point signals from experimental data.