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

TL;DR

This work develops a factorization framework for $PE^{[\nu]}(\chi)$ in heavy-ion collisions, extending prior two-point results to general $\nu$-point projected energy correlators. It demonstrates that a thermal medium induces nontrivial angular scaling at leading order and that correlators with $\nu<1$ are enhanced relative to $\nu>1$, providing intrinsic angular information. The authors compute the medium-induced jet function $J^{[\nu]}(\omega,\chi,L)$ at leading order in double Glauber insertions, derive its analytic structure across two phase-space regions, and validate the findings against JEWEL simulations, indicating robustness of the qualitative trends. They also discuss potential BFKL-like resummation for rapidity scales and highlight the necessity of higher-order and dense-medium studies to fully connect $\nu$-dependence to medium evolution and anomalous dimensions in QCD jets.

Abstract

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 $ν$.

Figures (9)

• Figure 1: Variation of the jet function as a function of $L$ for various values of $\nu$ at fixed $\chi = 0.01$. The solid lines show the results obtained from the full numerical computation of the jet function and dotted lines represent the approximation $L \to \infty$. The medium parameters are $T=0.4$ GeV, $L=5$ fm and $m_D=0.8$ GeV.
• Figure 2: Variation of the jet function as a function of angle $\chi$ for various values of $\nu$. The medium parameters are $T=0.4$ GeV, $L=5$ fm and $m_D=0.8$ GeV.
• Figure 3: Variation of jet function as a function $\nu$ for various values of $\chi$. Here again the medium parameters are $L=5$ fm, $T=0.4$ GeV.
• Figure 4: Variation of ratios of $\nu$-point energy correlators with that of $\nu=2$ as a function of angle $\chi$. Medium parameters are same as the one used in Figure \ref{['fig:nuratio']}.
• Figure 5: Variation of ratios of resummed and leading order jet functions as a function of angle $\chi$ for various values of $\nu$ and $\omega=100$ GeV.