Uncover the correlation between jet energy correlators and multiplicity fluctuations

Abstract

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 $ν= N_{\rm ch}/\langle N_{\rm ch} \rangle$, the EEC in the angular region $Λ_{\rm QCD}/p_{T,\rm jet}\llχ\ll R$ acquires a $ν$-dependent anomalous dimension. Thus the $ν$-conditioned EEC provides a direct and robust probe to the multiplicity generating function in the perturbative regime. In addition, understanding $ν$ dependence of the EEC is also crucial for isolating possible multiplicity-dependent bias effects in the EEC measurements in nuclear environment.

Figures (4)

• Figure 1: Standard EEC for jets with $p_T > 500$ GeV and $R = 0.4$. LO+LL predictions (bands) are compared to Pythia8 simulations (markers). The bands represent the perturbative uncertainty from varying the matching scale between $\zeta_{\chi}$ and $2\zeta_{\chi}$. Results are shown for inclusive (red), quark (orange), and gluon (blue) jets.
• Figure 2: Multiplicity-conditioned EEC for jets with $p_T > 500$ GeV and $R = 0.4$, compared with Pythia8 simulations for different multiplicity classes $\nu = N_{\text{ch}}/\langle N_{\text{ch}} \rangle$. $\sigma_{\text{jet}}^{\nu}$ is the cross section for jet with normalized multiplicity $\nu$. Bands show LO+LL predictions with the matching scale varied between $\zeta_{\chi}$ and $2\zeta_{\chi}$, markers denote Pythia8 results.
• Figure 3: Exponent of the multiplicity-conditioned EEC in the asymptotic region as a function of $\nu = N_{\text{ch}} / \langle N_{\text{ch}} \rangle$ for jets with $p_T > 500$ GeV and $R = 0.4$. Pythia8 results are shown as symbols; LO+LL predictions as bands.
• Figure 4: Ratios of the standard gluon‑jet EEC obtained with different multiplicity distributions $P_g(N_{\text{ch}})$, modeled using a skew‑normal ansatz. Variations in the mean (blue dotted), width (yellow dashed), and skewness (red dash‑dotted) are shown relative to a Gaussian reference (black solid).