Density correlations under global and local charge conservation

This work presents a formalism to compute spatial n-point correlations of a conserved charge density in a large thermal system in the canonical ensemble, with explicit results presented up to 4th order. The resulting correlators contain local and balancing terms expressed through the grand-canonical susceptibilities for any equation of state. The new formalism is used to introduce a Gaussian local baryon number conservation in (spatial) rapidity in heavy-ion collisions at LHC conditions through a modulation of the balancing term. Connection to the widely used conservation volume Vc = k dV/dy approach is established, indicating that the latter is appropriate for observables within $k/2$ units around midrapidity with k ≈ √2π σy with σy being the Gaussian rapidity width of local baryon conservation. Analysis of the experimental data of the ALICE Collaboration on net proton cumulants in central Pb-Pb collisions at √sNN = 5.02 TeV constraints the range of local baryon conservation to σy = 0.78+0.19-0.16 units, equivalent to Vc = (1.95+0.48-0.39) dV/dy in the conservation volume approach.