Jet peak shapes based on two-particle angular correlations in lead-lead collisions at $\sqrt{{s_{\mathrm{NN}}}}$ = 5.02 TeV

Using CMS data from lead-lead and proton-proton collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, this study investigates the longitudinal invariance and shape evolution of jet-induced peaks in two-particle angular correlations, revealing that the peaks broaden significantly in pseudorapidity and exhibit increased longitudinal asymmetry as collision centrality and particle pseudorapidity increase.

The Gist

Imagine you are at a massive, chaotic concert where thousands of people are packed into a stadium. Suddenly, the lights go out, and a massive explosion happens in the center. In the world of particle physics, this is what happens when scientists smash two heavy lead atoms together at nearly the speed of light.

This explosion creates a tiny, super-hot soup of energy called the Quark-Gluon Plasma (QGP). It's so hot and dense that the usual rules of matter break down, and particles that are normally stuck together (like protons) melt into a free-flowing fluid.

The paper you're asking about is like a forensic investigation into what happens to a specific "bullet" fired through this soup. Here is the story, broken down simply:

1. The Setup: The "Trigger" and the "Echo"

In these collisions, sometimes a high-energy particle (a "trigger") gets knocked loose and shoots out. As it flies, it drags a trail of other particles behind it, forming a Jet. Think of this jet like a speedboat cutting through water; it leaves a wake behind it.

Scientists use a clever trick to study this. They pick one fast-moving particle (the "trigger") and look at all the other particles flying near it. They measure two things:

• The Angle (Left/Right): How far to the side are the other particles?
• The Distance (Forward/Backward): How far ahead or behind are they?

In a normal vacuum (like empty space), these particles would form a tight, symmetrical cone around the trigger, like a perfect arrowhead.

2. The Experiment: The "Mud" vs. The "Air"

The researchers compared two scenarios:

• The "Air" (Proton-Proton collisions): Two tiny protons smash together. There is no "soup" here, just empty space. The jet looks like a perfect, tight arrowhead.
• The "Mud" (Lead-Lead collisions): Two heavy lead nuclei smash together, creating that giant Quark-Gluon Plasma soup.

3. The Discovery: The Jet Gets "Squished" and "Stretched"

When the jet flies through the "Mud" (the heavy lead collisions), something interesting happens to its shape.

• The "Mud" Effect: The jet doesn't stay tight. It gets wider. Imagine throwing a stone into a calm pond; the ripples are tight. Now imagine throwing that same stone into thick mud; the splash spreads out more.
• The Asymmetry (The Tug-of-War): This is the most surprising part. In the heavy collisions, the jet doesn't just get wider; it gets lopsided.
  • If the trigger particle is moving toward the "front" of the stadium (forward direction), the trail of particles behind it gets stretched out in that same direction.
  • It's like if you were running through a crowd, and instead of people just scattering around you, the crowd seemed to be pushing you forward, stretching your wake out in front of you.

4. The Analogy: The "Crowded Dance Floor"

Imagine a crowded dance floor (the Quark-Gluon Plasma).

• In the empty room (Protons): If you spin around, your arms (the jet particles) stay in a perfect circle.
• On the crowded floor (Lead): If you try to spin, the crowd bumps into you.
  • The paper found that the crowd doesn't just bump you randomly. Because the crowd is expanding outward (like a balloon inflating), it pushes your arms in a specific way.
  • If you are near the edge of the crowd, the expansion pushes your "wake" further out in the direction you are facing. The jet peak gets stretched along the direction of the crowd's expansion.

5. Why Does This Matter?

This stretching tells the scientists two huge things:

1. The Medium is Alive: The "soup" isn't just a static wall; it's a flowing, expanding fluid. The jet is interacting with the flow of the universe's earliest moments.
2. Breaking the Rules: In physics, we often expect things to look the same no matter how fast you are moving (this is called "longitudinal invariance"). But this paper shows that at the very edges of the collision, this rule breaks. The "soup" changes the shape of the jet depending on where you are looking.

The Bottom Line

The CMS team at CERN took a snapshot of these collisions and realized that when high-speed particles fly through the super-hot "soup" created by heavy atoms, they don't just slow down—they get stretched and skewed by the expanding fluid.

It's like watching a kite fly through a gusty wind; you can't just see the kite, you have to look at how the wind distorts the kite's tail to understand the wind itself. This paper helps us understand the "wind" of the early universe.

Technical Summary

1. Problem Statement

In ultrarelativistic heavy-ion collisions, a deconfined state of matter known as the Quark-Gluon Plasma (QGP) is formed. High-energy partons produced in the initial hard scattering traverse this medium, losing energy via "jet quenching." While jet quenching is well-established, the specific mechanisms of how the medium modifies the internal structure of jets—particularly their longitudinal dynamics and particle density distributions—remain an area of active investigation.

Previous studies have largely focused on fully reconstructed jets at high transverse momentum ($p_T$). However, two-particle angular correlations offer a complementary approach to study jet properties over a broader range of energies and early-stage dynamics. A key theoretical question addressed in this work is the longitudinal invariance of jet yields near midrapidity. While boost invariance is expected near midrapidity, it may break down at forward rapidities due to the longitudinal expansion of the medium and evolving parton densities. This paper investigates how the shape of the "near-side" jet peak in two-particle correlations evolves with collision centrality, particle momentum, and pseudorapidity ($\eta$).

2. Methodology

The analysis utilizes data collected by the CMS detector at the LHC.

• Datasets:
  • PbPb Collisions: Recorded in 2018 at $\sqrt{s_{NN}} = 5.02$ TeV, with an integrated luminosity of $0.607 \text{ nb}^{-1}$.
  • pp Collisions: Recorded in 2017 at the same energy, with an integrated luminosity of $252 \text{ nb}^{-1}$, serving as a vacuum reference.
• Event Selection:
  • Minimum-bias (MB) events were selected using energy deposits in the Hadron Forward (HF) calorimeters.
  • Events were categorized by centrality (0–10% to 50–80%) based on the fraction of the inelastic cross-section.
  • Primary vertices were required to be within $|v_z| < 15$ cm of the nominal interaction point.
• Track Selection:
  • Charged particles were selected within $|\eta| < 2.4$ and $1 < p_T < 10$ GeV.
  • Strict quality cuts were applied regarding track impact parameters ($|d_z|/\sigma_z < 3$, $|d_{xy}|/\sigma_{xy} < 3$), $p_T$ resolution ($<10\%$), and track fit $\chi^2$.
• Correlation Analysis:
  • Variables: The analysis examines the relative pseudorapidity ($\Delta\eta = \eta_{asso} - \eta_{trig}$) and azimuthal angle ($\Delta\phi = \phi_{asso} - \phi_{trig}$) between a high-$p_T$ "trigger" particle and lower-$p_T$ "associated" particles.
  • Background Subtraction: A mixed-event technique was employed to construct a background distribution ($B$) representing uncorrelated pairs. The signal ($S$) was normalized by $B$ to correct for pair-acceptance effects. Long-range correlations (background) were subtracted using regions where $|\Delta\eta| > 2$.
  • Peak Characterization: The near-side jet peak (centered at $\Delta\eta=0, \Delta\phi=0$) was projected onto the $\Delta\eta$ and $\Delta\phi$ axes. These projections were fitted with a double-Gaussian function to extract the effective width ($\sigma$) of the peak.
  • Asymmetry Measurement: The longitudinal asymmetry was quantified by the ratio of associated yields on the positive and negative sides of the peak: $R = Y_{\Delta\eta > 0} / Y_{\Delta\eta < 0}$. This was studied as a function of the trigger particle's pseudorapidity ($\eta_{trig}$).

3. Key Contributions

• Systematic Study of Jet Peak Broadening: The paper provides a comprehensive measurement of how the longitudinal ($\sigma_{\Delta\eta}$) and transverse ($\sigma_{\Delta\phi}$) widths of the near-side jet peak change with collision centrality and particle $p_T$.
• Longitudinal Invariance Test: It explicitly tests the breakdown of longitudinal boost invariance by measuring the asymmetry of the jet peak shape at forward rapidities ($|\eta_{trig}| > 1.5$).
• Comparison with Models: The results are compared against the HYDJET 1.9 Monte Carlo generator, which combines hydrodynamic expansion with PYTHIA-based hard processes. The study highlights limitations in current models regarding centrality-dependent broadening.

4. Results

• Centrality Dependence of Widths:
  • In PbPb collisions, both $\sigma_{\Delta\eta}$ and $\sigma_{\Delta\phi}$ increase as the collision becomes more central (higher overlap).
  • Longitudinal Broadening Dominance: The broadening in the longitudinal direction ($\sigma_{\Delta\eta}$) is significantly more pronounced than in the transverse direction ($\sigma_{\Delta\phi}$).
  • $p_T$ Dependence: This broadening effect is most significant for lower $p_T$ associated particles (soft fragments). As the $p_T$ of the particles increases, the centrality dependence weakens, and the widths approach the pp baseline values.
• Longitudinal Asymmetry:
  • At midrapidity (low $|\eta_{trig}|$), the jet peak is symmetric ($R \approx 1$).
  • At forward rapidities (high $|\eta_{trig}|$), a significant asymmetry emerges, with the ratio $Y_{\Delta\eta > 0} / Y_{\Delta\eta < 0}$ increasing.
  • This asymmetry is more pronounced in central PbPb collisions compared to peripheral ones or pp collisions.
• Model Comparison:
  • The HYDJET 1.9 model fails to reproduce the observed centrality-dependent broadening of the longitudinal jet peak width, suggesting its internal modeling assumptions (specifically regarding the hard component's boost invariance) are insufficient to describe the medium-induced modifications.

5. Significance

• Medium Modification Mechanisms: The observed longitudinal broadening and asymmetry provide strong evidence that the soft fragments of jets interact with the longitudinally expanding QGP medium. The results support interpretations where the jet's soft components are "pushed" forward by the collective flow of the medium or suffer energy loss that alters the angular distribution.
• Breakdown of Boost Invariance: The increasing asymmetry at forward rapidities indicates a breakdown of longitudinal boost invariance for jet-associated yields, likely due to the interplay between the jet and the evolving parton densities and medium expansion.
• Constraints on Theory: These measurements provide critical constraints for theoretical models of jet-medium interactions. The failure of HYDJET to predict the observed broadening suggests a need for more sophisticated modeling of how hard partons couple to the hydrodynamic flow of the QGP, particularly for soft hadrons.
• Methodological Robustness: The study demonstrates the utility of two-particle correlations as a sensitive probe for jet substructure modifications, offering a simpler background subtraction method and access to a wider kinematic range than fully reconstructed jet analyses.

In conclusion, this work establishes that the shape of jet peaks in heavy-ion collisions is not static but dynamically modified by the QGP, with distinct signatures in the longitudinal direction that depend on collision geometry and particle kinematics.