Living on the edge: radius effects in the angular substructure of heavy-ion jets

TL;DR

This paper addresses the challenge of edge effects in angular jet substructure measurements within heavy-ion collisions by focusing on the two-point energy correlator (EEC). It develops a factorization-based analytical framework and a simple phenomenological model that predicts edge distortions scale linearly with the mean axis decorrelation $\langle \phi \rangle$ and with even powers of $R_L/R$, yielding a multiplicative correction $E(\langle \phi \rangle, R_L/R) = 1 - \langle \phi \rangle K(R_L/R)$. Monte Carlo studies across p-p and Pb-Pb using Pythia8, Herwig7, CoLBT, and JEWEL reveal that, in p-p, leading edge corrections scale as $(R_L/R)^4$, while Pb-Pb, especially with recoils, exhibits a larger $(R_L/R)^2$ component, with Pb-Pb/p-p ratios substantially reducing but not eliminating edge effects. The work provides a practical framework to quantify and mitigate edge-induced distortions, enabling more robust theory-data comparisons and guiding future improvements in heavy-ion event generators via benchmarking of the $\langle \phi \rangle$ distribution. Overall, the study offers a significant step toward disentangling genuine QGP-induced modifications from reconstruction artifacts in jet angular substructure observables.

Abstract

Jet substructure observables serve as essential tools for probing the quark-gluon plasma produced in relativistic heavy-ion collisions. Their interpretation, however, is often complicated by edge effects, which arise when correlated particles fall outside the reconstructed jet radius, introducing distortions that obscure the underlying QCD dynamics. In this work, we present a comprehensive phenomenological study of edge effects in soft-insensitive angular observables, taking the two-point energy correlator (EEC) as a representative example. We argue that these distortions scale linearly with the average angular separation between the winner-take-all and $E$-scheme axes $\langle φ\rangle$, and validate this behavior across proton-proton (p-p) simulations with Pythia8 and Herwig7, as well as lead-lead (Pb-Pb) simulations using JEWEL and CoLBT. In p-p collisions, edge effects are strongly suppressed, scaling as $(R_L/R)^4$, whereas medium-modified jets can exhibit larger distortions, with contributions scaling as $(R_L/R)^2$ and $(R_L/R)^4$. Taking Pb-Pb/p-p ratios of the EEC substantially reduces, but does not completely eliminate, these distortions, highlighting the need of accounting for edge effects in the interpretation of heavy-ion jet substructure measurements. Since edge effects are largely governed by the $\langle φ\rangle$ distribution, studying this distribution provides a new handle for benchmarking and constraining the modeling of edge effects in heavy-ion event generators.

Figures (15)

• Figure 1: Top: two-point energy correlator for anti-$k_T$ jets with $120 < p_T < 140$ GeV, computed using the same event sample in $\sqrt{s}=5.02$ TeV p-p collisions, for jet radii $R = 0.2$ (black triangles), $R = 0.4$ (blue circles), and $R = 0.8$ (pink squares). Middle: Ratio between the EEC for $R = 0.2$ and $R = 0.4$. Bottom: Ratio between the EEC for $R = 0.4$ and $R = 0.8$.
• Figure 2: Top: Two-point energy correlator for anti-$k_T$ jets with $120 < p_T < 140$ GeV, computed using the same sample of events with the CoLBT in $\sqrt{s_{\rm NN}} = 5.02$ TeV 0-10$\%$ Pb-Pb collisions, for jet radii $R = 0.4$ (blue circles), and $R = 0.8$ (pink squares). Bottom: ratio between the EEC for $R = 0.4$ and $R = 0.8$.
• Figure 3: Top: ratio of the EEC computed within anti-$k_T$ jets of radius $R = 0.4$ to that obtained with $R = 0.8$, using the same sample of events generated with Pythia8 in $\sqrt{s} = 5.02$ TeV p-p collisions, shown for three different jet $p_T$ bins. Bottom: same as top, but using Herwig7.
• Figure 4: Top: ratio of the EEC computed within jets with radius $R = 0.4$ to that obtained with $R = 0.8$, using the same sample of jets generated with the CoLBT in $\sqrt{s_{\rm NN}} = 5.02$ TeV 0-10$\%$ Pb-Pb collisions, shown for three different jet $p_T$ bins. Bottom: same as top, but using JEWEL with recoils.
• Figure 5: Top: edge effects defined as in \ref{['eq:edge_effects']} for the highest five $R_L$ bins shown as a function of the average $E$-scheme WTA-axes difference $\langle \phi \rangle$ for Pythia8 in $\sqrt{s} = 5.02$ TeV p-p collisions. Bottom: same as top but for Herwig7. Linear fits to both Pythia8 and Herwig7 are included. The corresponding fit parameters, including their errors, are listed in Table \ref{['tab:fits_binbybin_pp']} of Appendix \ref{['appA']}.