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Exploiting $ν$-dependence of projected energy correlators in HICs

We extend the recently derived factorization formula for energy-energy correlators to study the analytic structure of general $ν$-point projected energy correlators in heavy ion collisions. The $ν$-point projected energy correlators (or, $ν$-correlators) are an analytically continued family of the integer $N$-point projected energy correlators, which probe correlations between $N$ final-state particles. By tracking the largest separation ($χ$) between the $N$ particles, in vacuum, their structure is closely related to the DGLAP splitting functions and exhibits a classical scaling behavior $\sim 1/χ$ which is modified by resummation through the anomalous dimensions. We show that, in a thermal medium, the $ν$-correlators display non-trivial angular scaling already at the leading order in perturbation theory. We find that for non-integer values, particularly $ν<1$, medium-induced jet function is enhanced compared to $ν>1$. This is particularly manifested in the ratios of $ν$-correlators with respect to the two-point energy correlator which encode an intrinsic angular information for $ν<1$ when compared to large $ν$ values. Moreover, for small-$ν$ values, the $ν$-correlators appear to saturate at $ν=0.01$. We further confirm our leading-order numerical computations against simulated events from JEWEL for the parton level production cross-section. Finally, we qualitatively discuss the effect of BFKL resummation for various values of $ν$.