Density correlations under global and local charge conservation

This work presents a formalism to compute spatial <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>n</a:mi></a:math>-point correlations of a conserved charge density in a large thermal system in the canonical ensemble, with explicit results presented up to fourth 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 CERN Large Hadron Collider conditions through a modulation of the balancing term. Connection to the conservation volume <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>V</b:mi><b:mi>c</b:mi></b:msub></b:math> approach is established, indicating that the latter is appropriate for observables within a limited range around midrapidity. Quantitative analysis of the experimental data of the ALICE Collaboration on net proton cumulants in central Pb-Pb collisions at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msqrt><c:msub><c:mi>s</c:mi><c:mrow><c:mi>N</c:mi><c:mi>N</c:mi></c:mrow></c:msub></c:msqrt><c:mo>=</c:mo><c:mn>5.02</c:mn></c:mrow></c:math> TeV shows significant evidence for local baryon conservation. Published by the American Physical Society 2024