Sensitivity of Jet Observables to Molière Scattering Off Quasiparticles in Quark-Gluon Plasma

This paper presents a full calculation of Molière scattering between jet partons and QGP quasiparticles implemented within the Hybrid Model, demonstrating that photon-tagged jets serve as a sensitive probe for detecting distinctive experimental signatures of these hard scatterings through their impact on jet substructure observables like the Soft Drop angle and jet girth.

The Gist

Here is an explanation of the paper, translated from high-energy physics jargon into everyday language using analogies.

The Big Picture: The "Liquid" vs. The "Granular"

Imagine the Quark-Gluon Plasma (QGP)—the super-hot soup created when heavy atoms collide—as a giant, swirling liquid.

• The Old View: For a long time, scientists thought this liquid was perfectly smooth, like water. If you threw a pebble (a high-energy particle) into it, the pebble would just slow down smoothly, creating ripples (wakes) as it went.
• The New Reality: This paper argues that if you look at this liquid with a super-powerful microscope (using very high-energy particles), it's not smooth at all. It's actually made of tiny, individual grains, like sand.

The scientists in this paper wanted to answer a big question: Can we see the "sand grains" inside the "liquid"?

The Experiment: Throwing a Jet into the Soup

To test this, they use Jets.

• The Jet: Imagine a high-speed bullet train (a jet of particles) shooting through the liquid.
• The Interaction: Usually, the train just pushes the liquid aside, creating a wake behind it (like a boat). This is the "strongly coupled" part—the liquid moves as a whole.
• The Twist (Molière Scattering): Sometimes, the train hits a single grain of sand head-on. This is a Molière scattering. Instead of just pushing the liquid, the train smashes into a specific particle, knocking it sideways at a sharp angle.

The Analogy:

• Smooth Liquid: Driving a car through deep fog. You slow down, and the fog swirls around you.
• Molière Scattering: Driving through a hailstorm. Most of the time, the hail is just a blur, but occasionally, you get hit by a single, large hailstone that knocks your car sideways.

What Did They Do? (The Hybrid Model)

The scientists built a computer simulation called the Hybrid Model. Think of this model as a video game engine that simulates how these particle trains behave in the plasma.

1. The "Soft" Part: They already knew how to simulate the car slowing down in the fog (the liquid behavior).
2. The "Hard" Part: In this new paper, they added the rules for the hailstones. They calculated the math for how often a jet hits a "grain of sand" and how hard it gets knocked off course.
3. The Result: They ran the simulation to see what happens to the shape of the jet when these "hailstone hits" occur.

The Detective Work: Finding the "Hailstones"

The problem is that the "fog" (the liquid wake) is so thick and the "hail" (the scattering) is so rare that it's hard to tell them apart.

• The Selection Bias: If you just look at all the jets that survive the trip, you are mostly seeing the ones that didn't hit anything hard. They are the "lucky" jets that stayed straight. This hides the evidence of the collisions.
• The Solution (Photon Tagging): To fix this, the scientists decided to look at Photon-Tagged Jets.
  • The Photon: Imagine a flash of light (a photon) that flies out of the collision. Light doesn't get stuck in the fog; it flies straight out at full speed.
  • The Match: If you see a flash of light and a jet coming out in opposite directions, you know exactly how much energy the jet should have had.
  • The Test: If the jet is missing energy, it's because it hit the fog. But if the jet is wide and spread out (has a large "girth" or "splitting angle"), it suggests it hit a hailstone and got knocked sideways, rather than just slowing down.

The Key Findings

1. Broadening: When Molière scatterings happen, the jet doesn't just slow down; it gets wider. The particles inside the jet spread out more than they would in a smooth liquid.
2. The "Knob" Strategy: The paper shows that by changing two "knobs" in the experiment, we can isolate the effect:
   • Knob 1 (Jet Size): Use smaller jets to ignore the "fog" (wakes) and focus on the "hail" (scattering).
   • Knob 2 (Energy Selection): Look at jets that are significantly slower than the light flash. This removes the bias of only looking at the "lucky" straight jets.
3. The Smoking Gun: They found that if you look at the right kind of jets (small, tagged with light, and slower than the light), the data shows the jets are wider in heavy-ion collisions than in normal collisions. This widening is the fingerprint of the jet hitting the "sand grains" (quasiparticles) inside the plasma.

Why Does This Matter?

This is a huge deal for physics.

• Asymptotic Freedom: It proves that even though the QGP acts like a liquid on a large scale, at the smallest scales, it behaves like a gas of individual particles. This confirms a fundamental rule of the universe called "Asymptotic Freedom."
• New Microscope: It gives us a new way to "see" the microscopic structure of the universe's first moments (the Big Bang soup) using particle colliders.

In Summary:
The scientists built a better simulation to show that the "liquid" of the early universe is actually made of tiny particles. By looking at high-speed particle jets that get knocked sideways by these particles (and using light flashes to keep score), they found the first clear signs that we can "see" the individual grains of sand inside the cosmic soup.

Technical Summary

Here is a detailed technical summary of the paper "Sensitivity of Jet Observables to Moli`ere Scattering Off Quasiparticles in Quark-Gluon Plasma."

1. Problem Statement

The Quark-Gluon Plasma (QGP) created in heavy-ion collisions behaves as a strongly coupled liquid at macroscopic scales (length scales $\gtrsim 1/T$), exhibiting hydrodynamic flow with low viscosity. However, Quantum Chromodynamics (QCD) dictates asymptotic freedom at short length scales, implying the existence of quark- and gluon-like quasiparticles.

The central problem addressed is how to experimentally probe this microscopic, particulate structure of the QGP. While standard jet quenching models (like the Hybrid Model) successfully describe soft, strongly coupled interactions (energy loss, transverse momentum broadening, and hydrodynamic wakes), they lack a consistent framework for rare, hard, perturbative 2$\to$2 elastic scatterings (Moli`ere scatterings) between high-energy jet partons and thermal quasiparticles. Detecting these rare large-angle scatterings is crucial for distinguishing the "liquid" vs. "particulate" nature of the QGP.

2. Methodology

The authors extend the Hybrid Model of jet quenching to incorporate perturbative Moli`ere scatterings alongside the existing non-perturbative, strongly coupled dynamics.

A. Theoretical Framework

• Moli`ere Scattering Calculation: The authors review and adapt perturbative QCD calculations (based on Ref. [39]) for 2$\to$2 elastic scattering ($cd \to ab$). Unlike previous works that tracked only the scattered jet parton, this framework explicitly tracks both outgoing partons (the deflected jet parton and the recoiling thermal parton).
• Phase Space Constraints: To ensure the validity of the perturbative treatment and avoid double-counting with the strongly coupled soft sector, the authors impose kinematic cuts on the Mandelstam variables:
  $$|t|, |u| > a m_D^2$$
  where $m_D$ is the Debye mass and $a=10$ is a conservative threshold parameter. This excludes soft, collinear divergences.
• Kinematic Sampling: The authors derive probability distributions for the final-state kinematics (momenta and angles) of the scattered partons. They introduce a set of dimensionless variables ($x, \tilde{k}_{min}^\chi, \tilde{k}, \phi$) to facilitate efficient Monte Carlo sampling of the phase space. Analytic integration is performed over two of the four dimensions to reduce computational cost.

B. Implementation in the Hybrid Model

• Hybrid Dynamics: The model treats jet evolution as a sequence of time steps. At each step, a parton propagates through a hydrodynamic background.
  • Soft Sector: Continuous energy loss and Gaussian transverse momentum broadening (parameterized by $\kappa_{sc}$ and $K$) are applied, representing strong coupling.
  • Hard Sector: At each step, a probability is calculated for a Moli`ere scattering to occur. If it occurs, the scattering type (e.g., $qq \to qq$, $qg \to qg$) and kinematics are sampled.
• Post-Scattering Evolution: Both outgoing partons are treated as active jet constituents. They lose energy, generate wakes, and may undergo further scatterings.
• Conservation Laws: The model accounts for the removal of a thermal quasiparticle from the medium (creating a "hole" or negative particle contribution) and the subsequent hadronization of all surviving partons using a colorless hadronization prescription (JETSCAPE) to handle color flow disruption.

C. Parameters

The study fixes the following parameters based on consistency with data and theoretical constraints:

• Strong coupling constant: $g_s = 2.25$ ($\alpha_s \approx 0.4$).
• Threshold parameter: $a = 10$.
• Soft broadening parameter: $K = 15$ (chosen to ensure a smooth transition between the Gaussian soft tail and the hard Moli`ere tail).
• Energy loss parameter: $\kappa_{sc} = 0.37$ (tuned to match inclusive jet/hadron suppression $R_{AA}$ when Moli`ere scattering is included).

3. Key Contributions

1. First Full Implementation: This is the first study to fully embed perturbative 2$\to$2 Moli`ere scatterings into a realistic, multi-scale jet quenching model (Hybrid Model) that also includes hydrodynamic wakes and strong-coupling energy loss.
2. Dual-Parton Tracking: The framework explicitly evolves both the scattered jet parton and the recoiling medium parton, acknowledging that both contribute to the final jet substructure and the hydrodynamic wake.
3. Observable Identification: The paper systematically identifies which jet observables are sensitive to Moli`ere scattering versus those dominated by selection bias or jet wakes.
4. Photon-Tagged Jet Strategy: The authors propose using photon-tagged jets with specific kinematic selections ($x_J = p_{jet}^T / p_\gamma^T$) to mitigate the "survivor bias" inherent in inclusive jet measurements, thereby isolating the effects of hard scattering.

4. Results

The authors analyzed various observables in PbPb collisions ($\sqrt{s_{NN}} = 5.02$ TeV) comparing four scenarios: (1) No Moliere/No Wake, (2) No Moliere/With Wake, (3) With Moliere/No Wake, and (4) With Moliere/With Wake.

• Inclusive Jets (Ungroomed):
  • Jet Shape & Fragmentation: Moliere scattering broadens the jet shape and softens the fragmentation function. However, these effects are **dwarfed** by the narrowing caused by selection bias (jets that lose less energy are selected) and the broadening from jet wakes. These observables are not suitable for isolating Moliere scattering.
• Groomed Observables (Soft Drop):
  • Soft Drop Angle ($R_g$): Moliere scattering broadens the $R_g$ distribution. In inclusive jets, selection bias suppresses large $R_g$, partially masking the Moliere effect.
  • Leading $k_T$: Similar to $R_g$, Moli`ere scattering enhances large $k_T$ splittings, but selection bias remains a confounding factor.
• Jets Within Jets (Subjets):
  • Moli`ere scattering increases the number of subjets ($n_{SubJ}$) and the angular separation between them. However, selection bias again suppresses these multi-prong structures in inclusive samples.
• Photon-Tagged Jets (The Key Finding):
  • Mitigating Bias: Selecting events based on the photon energy ($p_\gamma^T$) rather than the jet energy reduces the bias toward unquenched jets.
  • $R_g$ and Girth ($g$):
    • For narrow jets ($R=0.2$) with a loose selection ($x_J > 0.2$), the broadening induced by Moli`ere scattering overcomes the narrowing from selection bias. The PbPb/$pp$ ratio of $R_g$ and girth approaches or exceeds unity at large angles.
    • For wide jets ($R=0.6$), jet wakes dominate the broadening at large angles, masking the Moli`ere signal unless the selection is very restrictive ($x_J > 0.8$).
  • Experimental Validation: The authors compare their results to recent CMS measurements of $R_g$ and girth in photon-tagged jets. They note that CMS data for $x_J > 0.4$ shows ratios close to unity, and a specific data point for girth ($0.08 < g < 0.1$) is significantly above unity, consistent with the Moli`ere scattering prediction.

5. Significance and Outlook

• Microscopic Structure of QGP: The detection of Moli`ere scatterings would provide direct evidence that energetic partons resolve the quasiparticle nature of the QGP, confirming the emergence of a strongly coupled liquid from an asymptotically free gauge theory.
• Experimental Roadmap: The paper provides a clear strategy for experimentalists:
  1. Use photon-tagged jets to reduce selection bias.
  2. Focus on narrow jets ($R=0.2$) to minimize wake contamination.
  3. Include jets with lower $x_J$ (e.g., $x_J > 0.2$) to capture the full spectrum of energy loss and maximize the Moli`ere signal.
  4. Measure groomed splitting angles ($R_g$) and jet girth ($g$).
• Future Directions: The authors suggest that Oxygen-Oxygen (OO) collisions may be an ideal arena for this search. The smaller system size reduces the path length $L$, suppressing the $O(L^3)$ strongly coupled energy loss (and its associated bias) more effectively than the $O(L)$ collisional Moli`ere scattering, thereby enhancing the relative signal.

In conclusion, this work establishes a rigorous theoretical framework for identifying the "smoking gun" of hard scattering in the QGP, moving beyond inclusive suppression measurements to differential substructure observables that can probe the microscopic degrees of freedom of the quark-gluon plasma.