Jet Quenching in the Smallest Hadronic Collision Systems

This paper presents pQCD predictions demonstrating that high-momentum particle suppression scales with system size down to very light ion collisions like ${}^{3}\mathrm{He}+{}^{3}\mathrm{He}$, identifying these small systems as ideal for observing QGP-induced energy loss while concluding that such mechanisms cannot explain the large elliptic flow observed in $p+\mathrm{Pb}$ collisions.

The Gist

Imagine you are a chef trying to understand how a giant, super-hot soup (called a Quark-Gluon Plasma or QGP) affects the ingredients you throw into it. In the world of particle physics, this "soup" is created when heavy atoms smash into each other at nearly the speed of light.

For years, scientists have known that when they smash huge atoms like Gold or Lead together, the "ingredients" (high-speed particles called jets) get slowed down and lose energy as they travel through this hot soup. This slowing down is called Jet Quenching. It's like throwing a bowling ball into a vat of thick molasses; the ball slows down significantly.

However, a mystery has emerged: When scientists smash smaller atoms (like Hydrogen or Helium) into heavy ones, they see signs that a soup might have formed (the ingredients swirl in a specific pattern), but the bowling balls don't seem to slow down at all. They pass right through as if the soup wasn't there.

This paper is a recipe for solving that mystery by testing even smaller "ingredients" and explaining why the bowling balls behave differently in different sized bowls.

The Big Idea: Testing the "Goldilocks" Zones

The authors of this paper are like scientists testing different sizes of pots to see when the soup starts to form and when it starts to slow things down.

1. The Big Pots (Lead + Lead): We know the soup exists here. The bowling balls slow down a lot.
2. The Medium Pots (Oxygen + Oxygen): Recent experiments suggest the soup exists here too, and the balls slow down.
3. The Tiny Pots (Proton + Lead): Here is the puzzle. The soup seems to swirl, but the balls don't slow down. Why?

The authors propose that to solve this, we need to look at very specific, tiny collisions that haven't been tried much yet: smashing Helium-3, Lithium-6, and Boron-10 atoms together.

The "Goldilocks" Analogy

Think of the different atomic collisions as different sizes of rooms:

• Huge Rooms (Lead): Too big, too messy. It's hard to tell exactly how much the soup is slowing things down because there are so many variables.
• Tiny Rooms (Proton + Lead): Too small and weird. The "walls" of the room (the atomic structure) are so different on each side that it creates confusing signals. The authors suggest that in these rooms, the "bowling ball" (the jet) and the "room swirl" (the soup flow) are out of sync. It's like trying to dance with a partner who is facing the opposite direction; you can't move together, so you don't feel the connection.
• The "Goldilocks" Rooms (Helium-3 and Lithium-6): These are the perfect size! They are small enough to be simple, but big enough to form a real soup. The authors predict that in these specific collisions, the "bowling balls" will finally show clear signs of slowing down. If we see this, it will be the "smoking gun" proof that even the tiniest drops of this hot soup can exist.

The "Decorrelation" Mystery

The paper also explains a confusing observation in Proton + Lead collisions. Scientists saw that the particles were swirling (a sign of a soup), but they also saw that the high-speed particles weren't slowing down.

The authors use a dance floor analogy to explain this:

• Imagine a dance floor where the music (the "soft" particles) is spinning one way, and the lead dancers (the "hard" jets) are spinning another way.
• In a big ballroom (Lead + Lead), everyone spins in the same direction. The lead dancers feel the crowd pushing them, so they slow down.
• In the tiny Proton + Lead room, the lead dancers are spinning in the opposite direction of the crowd. Because they are out of sync, the crowd's push cancels out. To an observer, it looks like the dancers aren't being slowed down at all, even though the soup is there.

The paper predicts that if we look at the new "Goldilocks" collisions (Helium and Lithium), the dancers will finally be in sync, and we will see the slowing down clearly.

The Takeaway

This paper is a roadmap for the future of particle physics. It tells us:

1. Stop looking at the weird, tiny Proton + Lead collisions to prove the soup exists; they are too confusing because the "dancers" are out of sync.
2. Start smashing Helium-3 and Lithium-6 atoms together. These are the cleanest, simplest environments to prove that even the smallest drops of the universe's hottest soup can form and slow down particles.
3. The "Soup" is real everywhere. If we find the right size of collision, we will see that the hot soup forms even in the tiniest systems, solving the mystery of why the big atoms slow down but the small ones seemed to pass through untouched.

In short: The soup is everywhere, but sometimes the ingredients are just dancing to a different beat. We just need to find the right party size to see them dance in sync.

Technical Summary

1. Problem Statement

The formation of Quark-Gluon Plasma (QGP) is well-established in large heavy-ion collisions (Au+Au at RHIC, Pb+Pb at LHC) through signatures like jet quenching, strangeness enhancement, and elliptic flow ($v_2$). However, recent observations in high-multiplicity small systems (p/d/$^3$He + A and p+p) present a paradox:

• Soft Sector: These systems exhibit collective behavior (large low-$p_T$ $v_2$, strangeness enhancement).
• Hard Sector: Unlike large systems, they have not shown significant jet quenching (nuclear modification factor $R_{AB} \approx 1$ in p+Pb), despite theoretical expectations that path-length dependent energy loss should occur.
• Recent Developments: The 2025 LHC runs with Oxygen (O+O) and Neon (Ne+Ne) provided evidence for collectivity in both soft and hard sectors, reigniting the question: What is the smallest system capable of forming a QGP, and why is jet quenching absent in p/d/$^3$He + A?

The paper aims to resolve this by predicting jet quenching signatures in even lighter ion collisions and analyzing the relationship between hard and soft event planes.

2. Methodology

The authors utilize a perturbative Quantum Chromodynamics (pQCD) based energy loss model to simulate high-momentum particle production. Key methodological components include:

• Energy Loss Mechanism: The model calculates both collisional and radiative energy loss of partons traversing a 2+1D viscous hydrodynamic medium.
• Fluctuations: It incorporates event-by-event and path-by-path fluctuations.
• Small-System Corrections: Crucially, the model includes specific corrections for small system sizes regarding both radiative and collisional energy loss.
• Baseline Calculations: A baseline for the nuclear modification factor ($R_{AA}$) is established using Next-to-Leading Order (NLO) pQCD computations modified by nuclear Parton Distribution Functions (nPDFs), without energy loss.
• Parameter Fixing: The sole free parameter, the strong coupling constant ($\alpha_s$), is fixed by fitting data from Pb+Pb and Au+Au collisions.
• Observables:
  • $R_{AB}$: Nuclear modification factor defined as $\langle N_{coll} \rangle^{-1} Y_{AA} / Y_{pp}$.
  • $v_2$: The second Fourier coefficient of the azimuthal distribution. The paper distinguishes between the intrinsic hard elliptic flow ($v_2^{hard}$) and the experimentally measured scalar product method ($v_2\{SP\}$), which depends on the correlation between the hard event plane ($\psi_{hard}$) and the soft event plane ($\psi_{soft}$).

3. Key Contributions

• First Predictions for Ultra-Light Ions: The paper provides the first theoretical predictions for jet quenching in collisions involving $^{10}$B + $^{10}$B, $^6$Li + $^6$Li, $^4$He + $^4$He, and $^3$He + $^3$He.
• Scaling Law Identification: The authors identify a scaling relationship for suppression in symmetric systems: $R_{AB} \propto (\sqrt{AB})^{1/3}$.
• Decoupling of $v_2$ Components: The study explicitly separates the intrinsic energy-loss-induced anisotropy ($v_2^{hard}$) from the measured anisotropy ($v_2\{SP\}$), explaining why $v_2\{SP\}$ can be near zero even when energy loss is present.
• Identification of "Goldilocks" Systems: The paper identifies $^6$Li and $^3$He as ideal candidates for future experiments due to minimal nPDF uncertainties and clean suppression signals.

4. Key Results

A. Nuclear Modification Factor ($R_{AB}$)

• Symmetric Systems: The model predicts a non-trivial suppression in symmetric systems ranging from $^{208}$Pb+$^{208}$Pb down to $^3$He+$^3$He. The suppression scales approximately linearly with $(\sqrt{AB})^{1/3}$.
• Asymmetric Systems: The model predicts suppression in asymmetric systems (A+B), but this trend disagrees strongly with existing p+Pb data (where $R_{AB} \approx 1$). The authors attribute this discrepancy to theoretical and experimental complications specific to asymmetric systems, particularly non-trivial hard-soft correlations not fully captured in the current model.
• Clean Baselines: $^6$Li+$^6$Li and $^3$He+$^3$He are predicted to have anomalously small nPDF uncertainties, making them the "cleanest" environments to isolate QGP-induced energy loss from initial-state effects.

B. Elliptic Flow ($v_2$) and Event Plane Correlations

• Intrinsic vs. Measured Flow: The model predicts that while the intrinsic hard elliptic flow ($v_2^{hard}$) is small but non-zero in all small systems (indicating energy loss is occurring), the experimentally measured $v_2\{SP\}$ is approximately zero.
• Mechanism of Suppression: This occurs due to decorrelation between the hard event plane ($\psi_{hard}$) and the soft event plane ($\psi_{soft}$).
  • In Pb+Pb, $\psi_{hard}$ and $\psi_{soft}$ are strongly correlated, yielding $v_2\{SP\} > 0$.
  • In Ne+Ne and O+O, they are uncorrelated.
  • In p+Pb, they show slight anti-correlation, driving $v_2\{SP\}$ toward zero or negative values.
• Implication for p+Pb: The large $v_2 > 0$ measured in p+Pb is not caused by final-state partonic energy loss (jet quenching). Instead, the authors argue it likely stems from missing physics (e.g., initial-state correlations) or experimental biases.

5. Significance and Outlook

• Resolving the Small-System Puzzle: The paper suggests that the absence of observed jet quenching in p+Pb is not evidence against QGP formation but rather a consequence of event plane decorrelation masking the signal in $v_2\{SP\}$ measurements.
• Experimental Roadmap: The authors advocate for symmetric small-system collisions (specifically $^3$He+$^3$He and $^6$Li+$^6$Li) at the LHC. These systems offer the best opportunity to observe jet quenching with minimal theoretical ambiguity.
• Future Directions:
  • High-$p_T$ $v_2$ measurements in O+O and Ne+Ne to test the prediction $v_2\{SP\} \approx 0$.
  • Electroweak $v_2$ measurements in p+Pb to disentangle initial-state effects.
  • Development of theoretical frameworks that simultaneously describe hard and soft particle production and their correlations.

In conclusion, the paper argues that jet quenching is a generic prediction of energy loss models even in the smallest systems, but its experimental signature is obscured in asymmetric collisions by event plane decorrelation. Symmetric light-ion collisions are proposed as the definitive test for the existence of the smallest QGP droplets.