Unveiling QCD Criticality with Cross-Rapidity Net-Baryon Cumulants
Fluctuations of conserved charges are a primary tool in the search for the QCD critical endpoint, but their beam-energy dependence is complicated by global baryon-number conservation, whose influence changes as the experimental acceptance covers different fractions of the collision system. We propose using correlations of net-baryon fluctuations between two separated rapidity windows to exploit the distinct signatures of conservation and critical dynamics. Global conservation produces a negative cross-window correlation, whereas a common long-wavelength critical fluctuation produces a positive one. We show that, within a canonical independent-source framework, the conservation-induced background and the critical signal enter additively at leading order, allowing the leading conservation term to be estimated and subtracted. The resulting yield-scaled correlator follows the nonmonotonic enhancement of an Ising-mapped equilibrium correlation length along a freeze-out trajectory passing near a hypothetical critical endpoint, while wider rapidity windows reduce the response through thermal smearing. Cross-rapidity cumulants therefore provide a rapidity-differential strategy for reducing the leading conservation background and sharpening fluctuation-based searches for QCD criticality in beam-energy-scan experiments.