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Observing Transverse Momentum Broadening from TEECs in Heavy Ion Collisions

This paper investigates transverse energy-energy correlators (TEECs) in heavy-ion collisions by combining NLL' resummation with first-order medium modifications to demonstrate that while classical momentum broadening lowers the back-to-back peak, radiative corrections and medium response significantly enhance angular decorrelations and spread deposited energy across the azimuth.

Original author: João Barata, Hai Tao Li, Andrey V. Sadofyev, João M. Silva

Published 2026-11-09

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CC BY 4.0

Original author: João Barata, Hai Tao Li, Andrey V. Sadofyev, João M. Silva

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

In the most violent collisions imaginable, where atomic nuclei are smashed together at nearly the speed of light, a state of matter known as the quark-gluon plasma is born. This substance is not a gas or a liquid in any ordinary sense, but a seething, dense soup of the fundamental building blocks of matter—quarks and gluons—that usually remain locked inside protons and neutrons. For a fleeting instant, this plasma exists at temperatures trillions of degrees hotter than the center of the sun, mimicking the conditions of the universe just microseconds after the Big Bang. To understand how this exotic matter behaves, physicists act as cosmic detectives, firing high-energy particles through the plasma and watching how they emerge. When a particle travels through this dense medium, it does not move in a straight line; it bumps into the surrounding particles, losing energy and scattering sideways. By measuring exactly how these particles scatter and how their energy spreads out, scientists can map the invisible properties of the plasma itself, revealing how it resists motion and how it reacts to being disturbed.

A recent study by João Barata, Hai Tao Li, Andrey V. Sadofyev, and João M. Silva focuses on a specific way to measure this scattering. They looked at events where two high-energy jets of particles are created moving in opposite directions, a configuration known as back-to-back. In a perfect vacuum, these two jets would travel in a straight line, exactly 180 degrees apart. However, when they pass through the quark-gluon plasma, the medium pushes them slightly off course. The researchers used a sophisticated tool called a transverse energy-energy correlator to track the flow of energy around these jets. This method does not require identifying every single particle in the final explosion; instead, it measures the total energy flowing in different directions, creating a map of how the energy is distributed around the original path of the jets. By analyzing this map, the team could distinguish between two different ways the plasma affects the jets: a simple sideways push and a more complex process where the jets radiate new particles.

The team constructed a detailed theoretical model to simulate what happens when a pair of particles, created in a clean, high-energy collision, travels through a uniform layer of this plasma. They separated the effects into two categories. The first is a classical effect, similar to a ball rolling through thick mud and getting nudged sideways by random bumps. This "momentum broadening" causes the jets to spread out slightly, lowering the sharp peak of energy that would otherwise be seen directly opposite the first jet. The second effect is radiative, where the interaction with the plasma forces the jets to emit additional particles, much like a car kicking up a spray of water as it speeds through a puddle. The researchers found that while the simple sideways push does change the shape of the energy distribution, the radiative effect is far more powerful. It significantly suppresses the peak of energy at the back-to-back angle and pushes a much larger amount of energy into wider angles, creating a much broader spread than the simple push alone would cause.

To make their model complete, the researchers also accounted for the reaction of the plasma itself. When a jet plows through the medium, it leaves a wake, depositing energy into the surrounding soup. This deposited energy does not stay in one spot; it spreads out over the entire circle around the collision point. The team calculated that this "medium response" adds a slow, steady background of energy that is small right at the back-to-back peak but grows larger as you look further away from it. This means that the total picture of what happens to a jet in a heavy-ion collision is a combination of the jet being pushed sideways, the jet radiating new particles, and the plasma itself swelling with the energy the jet left behind.

The results of this study provide a clearer way to interpret data from heavy-ion collision experiments. The researchers showed that if scientists only look at the simple sideways push, they will miss the most dramatic changes caused by the plasma. The radiative corrections, which were often neglected in previous studies of this specific back-to-back configuration, turn out to be essential for understanding the data. Without accounting for these radiative effects, the theoretical predictions would not match the experimental reality. The study confirms that the transverse energy-energy correlator is a sensitive probe that can distinguish between these different physical mechanisms. By separating the simple broadening from the complex radiation and the medium's response, the team has provided a more precise toolkit for physicists to measure the microscopic properties of the quark-gluon plasma, helping to reveal how this primordial state of matter truly behaves under extreme conditions.

Technical Summary: Observing Transverse Momentum Broadening from TEECs in Heavy Ion Collisions

Problem Statement
High-energy partons traversing the quark-gluon plasma (QGP) produced in heavy-ion collisions undergo multiple interactions, acquiring transverse momentum and radiating additional partons. These processes modify the angular distribution of the final-state energy flow, offering a probe of the medium's microscopic properties. While significant progress has been made in understanding medium modifications of jet substructure and energy correlators in collinear configurations, back-to-back topologies present a distinct setting for theoretical computation and experimental testing via angular decorrelations. However, these distributions are not exclusively sensitive to medium effects; they receive substantial contributions from perturbative and non-perturbative vacuum QCD processes. Consequently, developing a clear understanding of back-to-back configurations requires controlled observables that allow for the assessment of the relative size of different physical effects. The Transverse Energy-Energy Correlator (TEEC) is proposed as such an observable, measuring azimuthal correlations between final-state hadronic transverse energy flows without requiring the assignment of particles to individual jets.

Methodology
The authors study the TEEC in the back-to-back limit ( $\tau \to 0$ ) for a color-singlet quark-antiquark pair produced in a hard process and propagating through a homogeneous background medium. To isolate final-state effects, the authors adopt a simplified scenario of an $e^+e^-$ collision occurring in the presence of a bulk background state, effectively removing initial-state nuclear effects.

The theoretical framework relies on the following methodological pillars:

Factorization and Resummation: Starting from the vacuum Transverse Momentum Dependent (TMD) factorization formula, the authors retain the vacuum factorized structure while incorporating medium effects through modifications to the functions entering the back-to-back TMD formula. The vacuum distribution is calculated at Next-to-Leading Logarithmic prime (NLL $'$ ) accuracy, combining resummation of large logarithms associated with small angular decorrelations with fixed-order calculations.
Medium-Modified Jet Functions: The medium effects are isolated within the jet functions. The authors distinguish between two primary mechanisms:
- Classical Momentum Broadening: Modeled as a modification to the jet function at zeroth order in the strong coupling ( $\alpha_s^0$ ), described by a dipole function in the harmonic-oscillator approximation. This accounts for the broadening of the parent parton's trajectory without resolved radiation.
- Medium-Induced Radiative Corrections: Calculated at first order in the strong coupling ( $\mathcal{O}(\alpha_s)$ ) using the BDMPS-Z formalism. The authors evaluate the in-medium $q \to qg$ cross section, separating the contribution into time regions: "in-in" (splitting and propagation entirely within the medium), "in-out" (splitting within the medium, propagation outside), and "out-out" (splitting outside the medium). The "out-out" region is identified as vacuum splitting following broadening and is subtracted to isolate the genuine medium-induced radiative correction.
Analytic Evaluation: The authors perform an analytic evaluation of the medium-induced radiative correction. They decompose the four-point correlator into factorizable and non-factorizable contributions, utilizing large $N_c$ approximations and harmonic-oscillator potentials. The calculation involves careful handling of infrared and ultraviolet divergences, including the introduction of a regulator for the relative momentum integration and the use of plus-prescriptions to handle soft singularities.
Medium Response: The authors include the non-perturbative contribution associated with the medium's response to the dijet system. This is modeled as a mean energy flow sourced by each jet, spreading deposited energy over the whole azimuth.

Key Contributions and Results

Separation of Effects: The paper provides a formalism that separates classical momentum broadening from medium-induced radiative corrections within the TEEC framework.
Impact of Broadening: Numerical studies indicate that classical momentum broadening primarily lowers the back-to-back peak of the TEEC distribution while leaving the distribution elsewhere nearly unchanged.
Impact of Radiative Corrections: Radiative corrections significantly suppress the back-to-back peak further and enhance larger angular decorrelations. The authors find that these corrections are essential for a quantitative interpretation of the peak, a component neglected in previous studies of the back-to-back limit in heavy-ion collisions.
Medium Response: The inclusion of the medium response (modeled as a mean energy flow) results in a contribution that varies slowly across the back-to-back region. It is small at the peak but grows toward larger angles, providing a slowly varying background that differs in angular dependence from the perturbative contribution.
Analytic Formulas: The work derives explicit analytic expressions for the medium-induced radiative correction, including factorizable and non-factorizable parts, and the in-out interference terms, evaluated in the large $N_c$ harmonic-oscillator limit.

Significance
The paper demonstrates that the TEEC is sensitive to distinct components of in-medium evolution, specifically distinguishing between classical momentum broadening and radiative corrections. The results highlight that a quantitative interpretation of the back-to-back peak requires control over medium-induced radiative corrections, which were previously neglected. By providing a framework that combines NLL $'$ vacuum resummation with first-order medium corrections and a model for medium response, the study offers guidance for experimental studies aiming to disentangle these effects. The work establishes that the angular dependence of the medium response differs from that of the perturbative contribution, allowing their relative importance to be assessed as a function of angular decorrelation.

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