Probing Forward-Backward Multiplicity Correlations and Fluctuations Using the Strongly Intensive Observable $\Sigma$ in Pb-Pb Collisions at SPS Energies with UrQMD

Abstract

The strongly intensive observable $\Sigma$, constructed from charged-pion multiplicities in separated forward (F) and backward (B) pseudorapidity intervals $\Delta \eta$, is studied within the UrQMD transport model for Pb--Pb collisions at SPS energies. The dependence of $\Sigma$ on $\Delta \eta$ is investigated as a function of collision energy, centrality, and acceptance to probe the longitudinal structure of multiplicity fluctuations and correlations. For $\sqrt{s_{NN}}>6$ GeV, $\Sigma$ exhibits a non-monotonic dependence on $\Delta \eta$, increasing from values near unity at small separation, reaching a maximum at intermediate $\Delta \eta$, and decreasing towards unity at larger separation. Decomposition into scaled variance and covariance terms shows that this behavior arises from their different $\Delta \eta$ dependences. Calculations with resonance decays switched off show that resonances dominate short-range correlations, while $\Sigma >1$ at larger $\Delta \eta$ indicates fluctuations and correlations extending over broader pseudorapidity intervals. The magnitude of $\Sigma$, together with its fluctuation and covariance components, increases from central to peripheral collisions, with fluctuations dominating over covariance at large $\Delta \eta$. As the collision energy increases, the pseudorapidity interval over which $\Sigma >1$ persists becomes significantly larger, whereas at lower energies, where resonance dynamics dominate particle production, $\Sigma$ is nearly independent of $\Delta \eta$. An acceptance-scaling study reveals deviations from simple binomial scaling in regions of strong correlations. These results demonstrate the sensitivity of $\Sigma$ to the interplay between multiplicity fluctuations and forward--backward correlations in heavy-ion collisions.