Energy-energy correlators inside single inclusive jets in heavy-ion collisions with CoLBT-hydro model

Source: arXiv:2605.28788 · Published 2026-05-27 · By Zhong Yang, Raghav Kunnawalkam Elayavalli, Xin-Nian Wang

TL;DR

This paper addresses the challenge of interpreting energy-energy correlators (EEC) inside single inclusive jets in heavy-ion collisions, specifically in a quark-gluon plasma (QGP) environment, where evolving jets interact with a complex, fluctuating background. The authors improve upon the previous CoLBT-hydro simulation framework by introducing a medium momentum scale (QM = 2.0 GeV) that separates vacuum parton shower evolution from in-medium shower evolution, allowing more physically consistent treatment of jet modification due to medium effects. They validate the improved model by reproducing recent CMS experimental measurements of in-jet EEC in 0–10% central Pb+Pb collisions at 5.02 TeV. Additionally, they implement the CMS mixed-event background-subtraction method directly within their simulation, showing it yields results consistent with idealized theoretical subtraction methods, thereby supporting the experimental procedure.

Through detailed analysis, the authors demonstrate that medium-induced soft hadron production from jet-induced hydro response dominates large-angle EEC enhancement while the small-angle region is shaped by competing effects of energy loss and jet pT selection bias. Comparing leading and sub-leading jets ranked by pT reveals a path-length dependence of medium modification effects, with sub-leading jets showing stronger modification due to longer medium traversal. Finally, they propose and demonstrate that the variation of leading-jet EEC with dijet rapidity gap encodes information on the jet-induced diffusion wake, a subtle jet-medium interaction feature, opening a new experimentally accessible avenue to probe QGP transport properties.

Key findings

• Introducing a medium scale QM = 2.0 GeV in CoLBT-hydro allows separating vacuum and in-medium parton shower stages, enabling improved modeling of jet-medium interactions.
• CoLBT-hydro simulation quantitatively reproduces CMS measurements of in-jet EEC ratios Pb+Pb/p+p at √sNN=5.02 TeV for charged hadron pT cuts of 1 and 2 GeV/c (Fig.1).
• Large-angle enhancement in EEC is dominated by jet-induced hydro response, especially the positive particle ('wake front') contribution, while diffusion wake (negative contribution) inside the jet cone is negligible (Fig.2).
• Implementing CMS mixed-event background subtraction in simulation yields nearly identical EEC ratios to idealized theoretical subtraction across most angular scales, validating experimental procedure (Fig.3).
• Sub-leading jets show systematically larger wide-angle enhancement in EEC ratios compared to leading jets, reflecting longer in-medium path length and stronger medium interaction (Fig.4).
• Leading-jet EEC ratios depend on dijet rapidity gap: jets with smaller rapidity gap show enhanced modification at small angular scales consistent with jet-induced diffusion wake effects (Fig.5).
• Increasing charged particle pT cut from 1 to 2 GeV/c suppresses soft particle contributions and reduces large-angle EEC enhancement from medium response.
• The proposed EEC observable encodes the jet-induced diffusion wake in modifications of the jet pT and small-angle correlators dominated by hard particles, making experimental study cleaner.

Threat model

n/a — This is a theoretical and phenomenological study of jet physics in heavy-ion collisions, not a security paper. No adversarial threat or attack scenario is considered.

Methodology — deep read

1. Threat Model & Assumptions: The paper assumes jets produced in heavy-ion collisions at LHC energies traverse a quark-gluon plasma medium, undergoing energy loss and modification primarily due to interactions with the QGP. The adversary (medium) affects jet shower evolution, momentum broadening, and induces medium response; no direct manipulations or eavesdropping scenarios apply since this is a physics modeling study.

2. Data and Simulation Setup: Simulations are performed for 0-10% central Pb+Pb collisions at √sNN = 5.02 TeV using the updated CoLBT-hydro model. The dataset includes full event-by-event hydrodynamic evolution with jet transport. Jets are reconstructed with anti-kT algorithm (R=0.4, and R=1.0 in some studies) using charged hadrons with pT cuts of 1 and 2 GeV/c. Jet pseudorapidity selection is |η_jet| < 1.6.

3. Algorithm & Architecture: CoLBT-hydro combines Linear Boltzmann Transport (LBT) for hard parton interactions with 3+1D viscous hydrodynamics (CLVisc) for medium evolution and response. A new intermediate scale QM=2.0 GeV splits vacuum shower evolution in PYTHIA8 at higher scales and in-medium transport at lower scales, with vacuum evolution resumed after jet exits medium down to hadronization scale Q0=0.5 GeV. Hydro response is extracted by running simulations with and without jets to isolate jet-induced medium excitation.

The EEC observable is calculated by correlating transverse momenta pairs of charged hadrons inside jets, binned by angular distance R_L between hadron pairs relative to the winner-take-all jet axis. The normalization accounts for all pairs weighted by pT,i*pT,j. To handle background, both an idealized theoretical subtraction (difference of hydro outputs) and a CMS-style mixed-event background subtraction procedure matching event multiplicity are applied.

4. Training & Simulation Regime: Not applicable in typical ML sense; instead, the event-by-event hydrodynamic and jet transport simulations are performed using large-scale HPC resources (NERSC, etc.). Specific simulation parameters like CM energy, centrality, jet pT bins, angular bin widths, and particle pT cuts are defined. Comparison with experimental data from CMS enables validation.

5. Evaluation & Validation Protocols: The primary metric is the ratio of the EEC distribution inside jets in Pb+Pb collisions over that in p+p collisions, compared at various angular bins. Both small and large angular scales are studied. Different background subtraction techniques are compared to assess robustness. Leading vs sub-leading jet EECs are compared to investigate path-length dependence. The dijet rapidity gap dependence of leading-jet EEC ratios probes jet-induced diffusion wake signals. Results are compared directly to CMS measurements wherever available. Figures 1–5 illustrate key comparisons.

6. Reproducibility: The CoLBT-hydro framework is built upon publicly known tools like PYTHIA8 and FASTJET. The hydrodynamic model is from CLVisc. While code release status is not stated explicitly, the model components are referenced to prior publications. CMS experimental data is publicly available. Exact random seeds and hyperparameters for simulations are not detailed in the paper extract.

Concrete End-to-End Example: A jet with reconstructed pT between 120-140 GeV/c and radius R=0.4 is selected. Its constituents are reclustered with WTA axis. Charged hadrons with pT > 1 GeV/c within R=0.4 around jet axis are collected. The EEC is computed by correlating transverse momenta of all hadron pairs binned by their pairwise angular distance R_L. The Pb+Pb and p+p EEC distributions are computed separately; their ratio shows deviations due to medium modifications. Background contributions are subtracted ideally via simulation difference in hydro with/without jets, and alternatively via CMS mixed-event method within simulated events. Agreement validates experimental procedure. The resulting ratio reproduces CMS data (Fig.1). Further slicing by leading vs sub-leading jets, and by dijet rapidity gap, reveals path length and diffusion wake effects (Figs. 4, 5).

Technical innovations

• Introduction of a medium momentum scale QM=2.0 GeV to delineate vacuum and in-medium parton shower evolution stages, enabling more self-consistent multi-stage jet evolution modeling.
• Implementation of the CMS mixed-event background subtraction procedure directly within the CoLBT-hydro model simulation to verify its accuracy against idealized theoretical subtraction.
• Decomposition method to isolate jet-induced hydro response contributions (positive wake front vs negative diffusion wake) to the in-jet EEC observable, clarifying their distinct angular effects.
• Use of pT-ranked leading and sub-leading jets within events to probe the in-medium path-length dependence of jet modification effects in EEC.
• Proposal and demonstration that the dijet rapidity gap dependence of leading-jet EEC ratios serves as a clean, experimentally accessible signal of jet-induced diffusion wake, encoded in hard-particle modifications.

Datasets

• 0-10% central Pb+Pb collisions at √sNN = 5.02 TeV (simulated with CoLBT-hydro) — event-by-event hydrodynamic and jet transport output
• Proton-proton (p+p) collisions at √s = 5.02 TeV (simulated with PYTHIA8 and analyzed for baseline comparison)
• CMS experimental published data for in-jet EEC measurements in Pb+Pb and p+p at √sNN = 5.02 TeV [Ref. 52]

Baselines vs proposed

• Pb+Pb / p+p EEC ratio with idealized theoretical background subtraction: reproduces CMS measurement with good quantitative agreement for charged hadron pT > 1 GeV/c and pT > 2 GeV/c cuts (Fig.1)
• Pb+Pb / p+p EEC ratio with CMS mixed-event subtraction in simulation: agrees with idealized theoretical subtraction within ≈5% across most RL, with small residuals at large angles (Fig.3)
• Leading jet EEC Pb+Pb / p+p ratio vs sub-leading jet: sub-leading jets show ~10–20% larger enhancement at wide angles due to longer path length (Fig.4)
• Leading-jet EEC Pb+Pb / p+p ratio for dijet pairs with small vs large rapidity gap: difference up to ~10% at small RL indicating diffusion wake effect (Fig. 5)

Limitations

• The hydro-response isolation relies on running paired simulations with and without jets, an idealized theoretical approach not available experimentally.
• The mixed-event background subtraction, while validated, still shows residual deviations at large angles, indicating limitations in background modeling and multiplicity matching.
• No direct treatment or tests of jet quenching in small collision systems or at varied collision energies beyond 5.02 TeV Pb+Pb.
• Simulation parameters and random seeds are not fully detailed, limiting complete numerical reproducibility.
• The analysis focuses on charged hadrons but neutrals and jet flavor dependence remain unexplored here.
• Analysis does not investigate potential model dependence on different hydrodynamic or parton transport implementations beyond CoLBT-hydro.

Open questions / follow-ons

• How do different hydrodynamic models or medium parameters quantitatively affect the predicted in-jet EEC modifications and diffusion wake signals?
• Can the EEC observable be extended to include neutral particles and full jet fragmentation functions for a more complete jet modification picture?
• What is the sensitivity of EEC and its background subtraction to smaller collision systems (p+Pb) or at different collision energies?
• How does the medium-induced modification of heavy-flavor jets influence the in-jet EEC and can it provide complementary constraints on QGP properties?

Why it matters for bot defense

For bot-defense and CAPTCHA practitioners, this paper lies outside direct application but offers an instructive example of background subtraction and signal isolation in extremely noisy and complex environments. The methods used to robustly extract signal correlations (EEC) from overwhelming fluctuating backgrounds using theoretical and experimental subtraction techniques (idealized vs mixed-event) can provide conceptual insights transferable to defending against adversarial noise or automated mimicry in CAPTCHA inputs. The notion of ranking candidates (leading vs sub-leading jets) to probe path-dependent modification effects is conceptually similar to differentiating legitimate from automated traffic based on behavior profiling. Additionally, the decomposition of contributions (signal vs background, positive vs negative wake contributions) is analogous to separating human and bot signals embedded together. Though the physics domain is specialized and qualitative, the multi-stage modeling approach combining physical prior knowledge with data-driven validation may inspire more principled CAPTCHA defense mechanisms for handling adversarially contaminated signals under uncertainty.

Cite

@article{arxiv2605_28788,
  title={ Energy-energy correlators inside single inclusive jets in heavy-ion collisions with CoLBT-hydro model },
  author={ Zhong Yang and Raghav Kunnawalkam Elayavalli and Xin-Nian Wang },
  journal={arXiv preprint arXiv:2605.28788},
  year={ 2026 },
  url={https://arxiv.org/abs/2605.28788}
}

Read the full paper

• arXiv:2605.28788 (abstract)
• arXiv:2605.28788 (PDF)