Canonical statistical hadronization with local baryon conservation for higher-order cumulants

We study higher-order cumulants of the conserved baryon number at the LHC within the canonical ensemble with local baryon conservation. We generalize the density correlations approach of [Phys. Rev. C 110, L061902 (2024)] to incorporate the effect of Gaussian local conservation in spatial rapidity space in cumulants up to 6th order. Gaussian local conservation improves upon the commonly employed $V_c$ approach, yielding comparable predictions at midrapidity, but marked differences for larger rapidity acceptances. Our coordinate-space results are in exact agreement with the diffusion master equation approach for all cumulant ratios up to $\kappa_6/\kappa_2$. Using the blast-wave model to apply kinematic cuts, we obtain predictions for net-proton cumulants in O--O and Pb--Pb collisions at the LHC that establish an ideal hadron gas baseline. We find that local baryon conservation alone can drive $\kappa_6/\kappa_2$ to small or even negative values in restricted acceptance, a behavior often associated with chiral criticality. The conservation baseline must therefore be carefully accounted for when interpreting upcoming LHC measurements.