A Breath of Fresh Air for Molière: Detecting Molière Scattering using Jet Substructure Observables in Oxygen Collisions

This paper proposes that jet substructure observables, specifically the Soft Drop splitting angle and energy-energy correlators, in ultra-relativistic oxygen-oxygen collisions can uniquely detect rare, large-angle Molière scatterings between jet partons and quark-gluon plasma quasiparticles, offering a model-independent method to probe the medium's short-distance structure.

The Gist

Imagine you are trying to understand the texture of a thick, sticky soup. If you drop a marble into it, the marble slows down, splashes, and leaves a trail. But what if you wanted to know if the soup is made of tiny, individual grains of rice (quasiparticles) or if it's just a smooth, continuous goo?

This paper is about using high-energy physics to answer that question, but instead of soup, the scientists are studying Quark-Gluon Plasma (QGP)—a super-hot, ultra-dense liquid created when atomic nuclei smash together.

Here is the story of their discovery, broken down into simple concepts:

1. The Setup: The "Oxygen" Experiment

Usually, scientists smash huge lead (Pb) nuclei together to create a massive, long-lasting drop of this plasma. It's like dropping a bowling ball into a swimming pool; the splash is huge, and the water (plasma) swallows the ball whole.

In this paper, the researchers suggest using Oxygen (O) nuclei instead. Oxygen is much smaller than lead. Smashing two oxygen atoms together is like dropping a marble into a teacup.

• Why do this? Because the "teacup" is so small, the marble (a high-energy particle jet) doesn't get completely swallowed by the "thick soup" (strong energy loss). This allows us to see the subtle, individual bumps and grains (quasiparticles) inside the soup that usually get hidden in the big splashes of lead collisions.

2. The Mystery: The "Molière" Bump

The scientists are looking for a specific type of interaction called Molière scattering.

• The Analogy: Imagine running through a crowded dance floor.
  • Scenario A (The Soup): You run through, and the crowd moves with you, slowing you down smoothly. This is "strong coupling."
  • Scenario B (The Grains): You run through, and you occasionally bump hard into specific dancers, knocking them sideways and getting knocked sideways yourself. This is Molière scattering. It's a rare, hard "bump" rather than a smooth drag.

The paper argues that to explain recent data from the CMS experiment (which measured how many particles survive the crash), scientists must include these hard "bumps" in their math. Without them, the model doesn't fit the data.

3. The Detective Work: Looking at the "Jet's Hair"

When a high-energy particle (a jet) flies through the plasma, it leaves a trail. The scientists want to look at the internal structure of that trail to see if it got "bumped." They use two special tools:

Tool A: The "Soft Drop" (The Haircut)

Jets are messy; they have a core and a fuzzy halo of soft particles. The "Soft Drop" algorithm is like a barber who shaves off all the fuzzy, soft hair to reveal the main structure underneath.

• The Finding: When Molière scattering happens, the jet gets a "bad haircut." The main branches of the jet get pushed further apart (wider angle).
• The Result: In Oxygen collisions, the scientists found that jets with these "bumps" have a significantly wider split angle compared to normal collisions. It's like seeing a tree branch that was snapped and pushed wide open by a sudden gust of wind.

Tool B: The "Energy-Energy Correlator" (The Echo)

This tool measures how energy is distributed at different angles within the jet.

• The Finding: If the jet parton hits a quasiparticle, it deflects. This creates a specific "echo" or pattern in the energy distribution.
• The "Bump": The scientists found a distinct "hump" or peak in their data at a specific angle.
  • The Metaphor: Imagine throwing a stone into a pond. The ripples spread out. If the stone hits a hidden rock (a quasiparticle), the ripples change shape in a very specific way. The "hump" in their graph is that specific shape change.
  • The Cool Part: The size of this "hump" changes depending on how fast the stone was thrown. Faster stones (higher energy) hit the rocks at sharper angles, making the hump move. This confirms they are seeing real physical deflections, not just random noise.

4. Why This Matters

For a long time, physicists have suspected that even though the Quark-Gluon Plasma acts like a thick liquid, it must be made of tiny, individual particles (quarks and gluons) because of the laws of quantum mechanics. But seeing them is incredibly hard because the liquid is so "sticky."

This paper provides a roadmap for how to see them:

1. Use Oxygen collisions (small teacups) to reduce the "noise" of the thick liquid.
2. Look for wider splits in the jet's structure (the haircut).
3. Look for specific "humps" in the energy patterns (the echoes).

The Bottom Line

The authors are saying: "We have a new, clear way to see the individual grains of sand inside the soup." If future experiments at the Large Hadron Collider (LHC) find these specific patterns in Oxygen collisions, it will be the first direct, model-independent proof that energetic particles can bounce off the tiny quasiparticles inside the Quark-Gluon Plasma. It's like finally seeing the individual dancers on the dance floor, rather than just seeing the blur of the crowd.

Technical Summary

1. Problem Statement

The Quark-Gluon Plasma (QGP) created in ultra-relativistic heavy-ion collisions behaves as a strongly coupled liquid at macroscopic scales. However, at short distances (high momentum transfer), Quantum Chromodynamics (QCD) dictates the presence of weakly coupled, quasiparticle-like degrees of freedom (quarks and gluons).

• The Challenge: While jets traversing the QGP lose energy, distinguishing between energy loss mechanisms is difficult. Strongly coupled energy loss (hydrodynamic wake excitation) dominates in large systems like Lead-Lead (PbPb) collisions, masking rare, perturbative, large-angle elastic scatterings known as Moli`ere scatterings ($2 \to 2$ processes).
• The Opportunity: Oxygen-Oxygen (OO) collisions produce smaller QGP droplets than PbPb collisions. This reduces the path length ($L$) and the contribution of strongly coupled energy loss (which scales as $L^3$), while the contribution from weakly coupled Moliere scatterings scales linearly with $L$. This makes OO collisions an ideal "breath of fresh air" to isolate and detect Moliere scattering.
• The Gap: Previous models failed to reproduce recent CMS charged-particle suppression data in OO collisions without explicitly including Moli`ere scattering. Furthermore, no theoretical study had yet analyzed how these scatterings modify the internal jet substructure in OO collisions.

2. Methodology

The authors utilize the Hybrid Strong/Weak Coupling Model (Hybrid Model) to simulate jet propagation through the QGP.

• Simulation Framework:
  • Parton Shower: Generated using Pythia 8 with EPPS21 nuclear parton distribution functions (nPDFs).
  • Strong Coupling Energy Loss: Modeled via a holographic formula ($dE/dx$) where the interaction strength is governed by a dimensionless parameter $\kappa_{sc}$.
  • Hydrodynamic Background: Uses state-of-the-art event-by-event hydrodynamic profiles (unlike previous event-averaged models) to account for fluctuations in small OO droplets.
  • Jet Wakes: Soft hadrons excited by the jet are generated using the Cooper-Frye prescription applied to the stress-energy tensor perturbation.
  • Moli`ere Scattering: Implemented as a perturbative $2 \to 2$ scattering process between jet partons and thermalized medium quasiparticles. It enforces large momentum transfer ($|t|, |u| > a m_D^2$) and includes transverse momentum kicks.
• Parameter Tuning: The parameter $\kappa_{sc}$ was re-fitted to PbPb data using the new event-by-event hydrodynamics and EPPS21 nPDFs.
  • Without Moli`ere: $\kappa_{sc} = 0.37$.
  • With Moli`ere: $\kappa_{sc} = 0.335$.
  • Note: These values differ from prior studies due to the updated hydrodynamic profiles and nPDFs.
• Observables:
  1. Charged Hadron Suppression ($R_{AA}$): To validate the model against CMS data.
  2. Soft Drop Splitting Angle ($R_g$): A groomed observable identifying the first hard splitting in a jet, designed to remove soft wake contributions.
  3. Energy-Energy Correlators (EEC): A two-point correlation function measuring angular correlations between energy deposits, sensitive to both hard splittings and soft wakes.

3. Key Contributions

• Model Validation in OO Collisions: The paper demonstrates that the Hybrid Model only reproduces recent CMS measurements of charged-particle suppression in OO collisions when Moli`ere scatterings are included. Without them, the model underestimates the suppression.
• First Substructure Analysis in OO: This is the first theoretical study of how Moli`ere scattering modifies jet substructure specifically in OO collisions, moving beyond inclusive suppression metrics.
• Disentangling Mechanisms: The authors propose specific kinematic cuts (e.g., track $p_T$ cuts) and observable ratios (OO/pp) that can distinguish Moli`ere scattering effects from jet-induced wakes and selection biases.

4. Key Results

A. Charged Hadron Suppression ($R_{AA}$)

• Calculations including only initial-state effects (nPDFs) fail to describe CMS data.
• Adding strong coupling energy loss and wakes yields modest suppression but still fails to match data.
• Crucial Finding: Agreement with CMS data is achieved only when Moli`ere scatterings are included, confirming their necessity in describing OO collisions.

B. Soft Drop Angle ($R_g$) Modifications

• Mechanism: Moli`ere scattering imparts large momentum kicks, broadening the angular separation of resolved splittings within a jet.
• Result: In OO collisions, the inclusion of Moli`ere scattering leads to a significant enhancement (ratio > 1) of jets with large splitting angles ($R_g \gtrsim 0.2$) relative to pp collisions.
• Significance: Unlike in PbPb collisions, where selection bias (jets losing energy and shifting to lower $p_T$) suppresses large $R_g$, the smaller size of OO droplets minimizes this bias. Thus, an OO/pp ratio of $R_g$ exceeding unity at large angles is a distinctive, model-independent signature of Moli`ere scattering.

C. Energy-Energy Correlators (EEC)

• General Effect: Moli`ere scatterings and wakes both enhance large-angle correlations ($R_L$) within jets.
• Isolating Moli`ere: By imposing a track cut of $p_T > 2$ GeV, the soft hadrons from jet wakes are effectively removed.
  • In this regime, an OO/pp EEC ratio exceeding unity in the range $0.2 \lesssim R_L < R_{jet}$ is a direct signature of Moli`ere scattering.
• The "Bump" Feature: For jets with $R_{jet} = 0.8$, the OO/pp EEC ratio exhibits a local maximum (bump) at a specific angle $R_L \approx 0.5$.
  • Physical Interpretation: This bump corresponds to the typical deflection angle of a parton after a Moli`ere scattering.
  • $p_T$ Dependence: As jet $p_T$ increases, the position of this bump shifts to smaller angles (consistent with perturbative QCD expectations where higher energy partons scatter at smaller angles). This dependence provides a quantitative measure of the scattering kinematics.

5. Significance and Future Outlook

• Microscopic Probe: These results demonstrate that jet substructure in OO collisions offers a unique window into the quasiparticle degrees of freedom of the QGP, which are otherwise obscured by strong coupling effects in larger systems.
• Experimental Roadmap: The paper provides a clear roadmap for experimentalists (CMS, ATLAS, ALICE) to detect Moli`ere scattering:
  1. Measure the OO/pp ratio of $R_g$ for $R_g \gtrsim 0.2$.
  2. Measure the OO/pp ratio of EECs with a $p_T > 2$ GeV track cut.
  3. Look for the characteristic "bump" in the EEC ratio for $R_{jet} \sim 0.8$ and verify its shift with jet $p_T$.
• Model Independence: The proposed signatures (enhancement of large-angle correlations and the specific angular bump) are robust against model variations, offering a definitive test of the existence of weakly coupled quasiparticles in the QGP.
• Broader Impact: Successful detection would allow for a Bayesian quantification of QGP parameters (like $\kappa_{sc}$ and coupling constants) and could potentially reveal differences in the coupling strength of QGP produced at RHIC vs. LHC energies.