Higher-order strongly intensive observables for forward-backward multiplicity correlations

Forward-backward multiplicity correlations probe the longitudinal structure of particle production, but fluctuations in the number of emitting sources complicate their interpretation. Strongly intensive observables remove the contribution of source-number fluctuations at second order. Here we extend the construction to all cumulant orders. For independent identical sources whose emission law does not depend on the source count, we build a normalized hierarchy of strongly intensive observables with $n$ new algebraically independent quantities at order $n$. Every observable is normalized to unity for statistically independent particles, vanishes when both window multiplicities are fixed, and remains finite at equal positive window means. We give explicit expressions through fourth order and an all-order recursion. Analytical particle production models and PYTHIA calculations for $pp$ collisions at $\sqrt{s}=0.9$ and 13 TeV demonstrate the sensitivity to window geometry, event selection, and connected multiparticle correlations. Fits constrained by the mean multiplicities and second-order observables provide conditional higher-order benchmarks. Deviations of these benchmarks from the PYTHIA results test the assumed correlation hierarchy, subject to the quality of the lower-order fit. Preliminary ALICE measurements at $\sqrt{s}=13$ TeV are used to illustrate the corresponding model-dependent scenarios.