Uncover the correlation between jet energy correlators and multiplicity fluctuations

The energy-energy correlator (EEC) and multiplicity are two fundamental observables probing complementary aspects of QCD jets: the former characterizes the angular structure of energy flows in a scale-dependent manner, while the latter is sensitive to the entire history of particle production. In this \emph{Letter}, we uncover a nontrivial correlation between them by studying the EEC as a function of jet internal multiplicity. We introduce the multiplicity-conditioned EEC jet function (MCJF) and perform a factorization calculation to next-to-leading order accuracy. It is found that, for jet samples selected at a given normalized multiplicity $\nu = N_{\rm ch}/\langle N_{\rm ch} \rangle$, the EEC in the angular region $\Lambda_{\rm QCD}/p_{T,\rm jet}\ll\chi\ll R$ acquires a $\nu$-dependent anomalous dimension. Thus the $\nu$-conditioned EEC provides a direct and robust probe to the multiplicity generating function in the perturbative regime. In addition, understanding $\nu$ dependence of the EEC is also crucial for isolating possible multiplicity-dependent bias effects in the EEC measurements in nuclear environment.