Rapidity scan approach for net-baryon cumulants with a statistical thermal model

Utilizing rapidity-dependent measurements to map the QCD phase diagram provides a complementary approach to traditional beam-energy-dependent measurements around midrapidity. The changing nature of thermodynamic properties of QCD matter along the beam axis in heavy-ion collisions at low collision energies both motivates and poses challenges for this method. In this study, we derive the analytical cumulant-generating function for subsystems within distinct rapidity windows, while accounting for global net-baryon charge conservation of the full system. Rapidity-dependent net-baryon cumulants are then calculated for a system exhibiting inhomogeneity along the beam axis, and their sensitivity to finite acceptances through changing rapidity bin widths is explored. We highlight the nontrivial behaviors exhibited by these cumulants, underscoring their importance in establishing a noncritical baseline for interpreting net-proton cumulants in the search for the QCD critical point. Finally, we discuss the implications of the rapidity scan for mapping the QCD phase diagram within the current context.