System-size dependence of charged-particle suppression in ultrarelativistic nucleus-nucleus collisions

This study presents the first measurement of charged-particle nuclear modification factors in neon-neon collisions and systematically compares them with oxygen-oxygen, xenon-xenon, and lead-lead data to demonstrate that charged-particle suppression scales with nuclear size and is well-described by energy loss models rather than initial-state nuclear effects.

The Gist

Imagine you are throwing a handful of marbles through a crowded room. If the room is empty, the marbles fly straight through. But if the room is packed with people, the marbles will bump into them, slow down, lose energy, and maybe even stop.

This is essentially what the CMS Collaboration at CERN (the European Organization for Nuclear Research) did in this new paper, but instead of marbles and people, they used subatomic particles and a super-hot, dense soup of energy called Quark-Gluon Plasma (QGP).

Here is the breakdown of their discovery in simple terms:

1. The Big Experiment: Smashing Nuclei Together

Scientists smash heavy atoms (like Lead, Xenon, Oxygen, and Neon) together at nearly the speed of light. When they collide, they create a tiny, fleeting drop of the QGP—a state of matter that existed just after the Big Bang. It's so hot and dense that it acts like a thick, sticky fluid.

2. The Mystery: How Big Does the "Room" Need to Be?

When high-energy particles (partons) try to fly through this QGP, they lose energy. This is called "jet quenching."

• The Question: Does the amount of energy lost depend on how big the "room" (the colliding nuclei) is?
• The Problem: Scientists knew that in huge collisions (like Lead-Lead), particles lose a lot of energy. But they weren't sure if this happened in smaller collisions (like Oxygen-Oxygen) or if there was a specific "tipping point" where the QGP stops forming.

3. The New Discovery: The "Neon" Test

To solve this, the team looked at four different sizes of atomic collisions, ranging from small to huge:

• Oxygen (O) – The smallest.
• Neon (Ne) – This is the new discovery! They measured Neon-Neon collisions for the first time. Think of Neon as the "Goldilocks" size: bigger than Oxygen, but smaller than Xenon.
• Xenon (Xe) – Medium-large.
• Lead (Pb) – The giant.

They measured how many high-speed particles survived the crash in each system. This is called the Nuclear Modification Factor ($R_{AA}$).

• If $R_{AA} = 1$, the particles didn't lose any energy (like running through an empty room).
• If $R_{AA} < 1$, the particles got slowed down (like running through a crowd).

4. The Results: A Smooth Slide, Not a Cliff

The team found something fascinating:

• The Trend: As the size of the nucleus increased (from Oxygen to Lead), the suppression of particles got stronger.
• The Shape: The graph of energy loss wasn't a straight line; it had a "dip" around a certain speed, then rose up again.
• The Neon Surprise: The Neon data fit perfectly in the middle. It showed that energy loss happens even in these tiny systems, and it scales smoothly with the size of the nucleus. There is no sudden "on/off" switch; it's a smooth gradient.

Analogy Time:
Imagine you are walking through different crowds:

• Oxygen: A small group of friends. You bump into a few people and slow down a little.
• Neon: A busy coffee shop. You bump into more people and slow down more.
• Lead: A packed concert mosh pit. You can barely move; you lose almost all your speed.

The paper confirms that the "crowd density" (system size) directly controls how much you slow down, even in the smallest crowds (Neon).

5. The Theory Check: Did the Models Get It Right?

Scientists have computer models to predict how particles should behave.

• The "Old" Models: Some models only looked at the initial state of the atoms (like checking the size of the room before the party starts). These models failed to explain the data. They couldn't explain why particles lost so much energy.
• The "New" Models: Models that included the idea of particles losing energy while moving through the hot soup (the QGP) matched the data perfectly.

Why Does This Matter?

This study is a big deal because it proves that even in very small collisions (like Neon-Neon), a hot, dense medium is formed that slows down particles.

It tells us that the transition from "no medium" to "full medium" is smooth. It helps physicists understand exactly how the "fire" of the Big Bang behaves in different sizes of containers. It's like finally understanding exactly how much friction a car tire has on wet pavement, whether you are driving a go-kart or a semi-truck.

In a nutshell: The CMS team smashed different sized atoms, measured how much the particles slowed down, and found that the bigger the atom, the more the particles slowed down, following a smooth, predictable pattern that only makes sense if a "hot soup" is formed in even the smallest collisions.

Technical Summary

1. Problem Statement

In ultrarelativistic heavy-ion collisions, high-energy partons traverse the Quark-Gluon Plasma (QGP) and lose energy, leading to a suppression of high transverse momentum ($p_T$) particle yields compared to proton-proton ($pp$) collisions. This phenomenon is quantified by the nuclear modification factor, $R_{AA}$.

While the existence of this suppression is well-established in large systems like Lead-Lead (PbPb), the system-size dependence of parton energy loss remains experimentally unconstrained. Previous studies relied heavily on centrality-selected observables within a single nuclear system (e.g., varying centrality in PbPb). However, centrality selection introduces geometric biases and selection effects, particularly in peripheral collisions, making it difficult to isolate the pure effect of system size (nuclear radius) on energy loss. There is a need for a model-independent characterization of how energy loss scales with the size of the colliding nuclei ($A$) across different nuclear species.

2. Methodology

The CMS Collaboration performed a systematic cross-system comparison using data from four distinct nucleus-nucleus collision systems at the CERN Large Hadron Collider (LHC):

• Oxygen-Oxygen (OO): $A=16$, $\sqrt{s_{NN}} = 5.36$ TeV.
• Neon-Neon (NeNe): $A=20$, $\sqrt{s_{NN}} = 5.36$ TeV (First measurement).
• Xenon-Xenon (XeXe): $A=129$, $\sqrt{s_{NN}} = 5.44$ TeV (0–80% centrality).
• Lead-Lead (PbPb): $A=208$, $\sqrt{s_{NN}} = 5.02$ TeV (Minimum bias).

Key Technical Steps:

• Data Collection: The NeNe data were collected in 2025 with an integrated luminosity of $0.76 \pm 0.04 \text{ nb}^{-1}$.
• Event Selection: Minimum bias events were selected using energy deposits in the Hadron Forward (HF) calorimeters ($3.0 < |\eta| < 5.2$) coincident with colliding bunches.
• Particle Reconstruction: Primary charged particles ($c\tau > 1$ cm) were reconstructed in the silicon tracker within the pseudorapidity range $|\eta| < 1$.
• Normalization: The $R_{AA}$ was calculated using a nucleon-number normalization ($1/A^2$) rather than a model-dependent Glauber overlap estimate, defined as:
  $$R_{AA} = \frac{1}{A^2} \left( \frac{d\sigma_{AA}/dp_T}{d\sigma_{pp}/dp_T} \right)$$
• Standardization: To ensure a fair comparison, all $R_{AA}$ measurements were re-binned into identical $p_T$ intervals matching the coarsest binning (XeXe). The PbPb and $pp$ reference spectra were merged using $p_T$-weighted averages to preserve spectral shapes.
• Systematic Uncertainties: Evaluated via variations in tracking efficiency, particle species composition (using ALICE $pp$ data scaled by charged-particle density), luminosity, and momentum resolution.

3. Key Contributions

• First NeNe Measurement: This paper presents the first measurement of the charged-particle $R_{AA}$ in Neon-Neon collisions, filling a critical gap in system size between Oxygen (OO) and Xenon (XeXe).
• Model-Independent System Size Scaling: By comparing minimum bias collisions across four different nuclear species ($A=16, 20, 129, 208$) using $A^{1/3}$ (proportional to nuclear radius) as the scaling variable, the study avoids the biases inherent in centrality selection.
• Unified Comparison: The analysis recasts existing CMS measurements (OO, XeXe, PbPb) into a common framework, allowing for a direct evaluation of the evolution of suppression with system size.

4. Results

• Qualitative Trends: All four systems exhibit similar qualitative shapes for $R_{AA}(p_T)$:
  • A downward slope at low $p_T$.
  • A local minimum around $5\text{--}7$ GeV.
  • An upward slope at higher $p_T$.
• Magnitude Ordering: The magnitude of suppression is strictly ordered by the nucleon number $A$. As $A$ increases, $R_{AA}$ decreases.
  • NeNe vs. OO: NeNe shows stronger suppression than OO below $p_T \approx 20$ GeV, suggesting a smooth transition in suppression magnitude with system size.
  • High $p_T$ Behavior: At high $p_T$, the systems converge to comparable values, though luminosity uncertainties currently limit a definitive statement on the relative magnitude at the highest $p_T$.
• Dependence on $A^{1/3}$: When plotted against $A^{1/3}$, the $R_{AA}$ values show a monotonic decrease as system size increases. This confirms that the nuclear radius is a primary driver of the suppression magnitude.
• Theoretical Comparison:
  • Initial-State Effects Only: Models incorporating only nuclear parton distribution functions (nPDFs, e.g., EPPS21, nNNPDF3.0) fail to reproduce the observed trends. They predict only modest suppression with weak $A$ dependence, significantly underestimating the data.
  • Energy Loss Models: Models incorporating parton energy loss (e.g., DGLV+SPLC, CUJET/CIBJET, Bayesian inference, LCPI) successfully reproduce the monotonic evolution of $R_{AA}$ with increasing $A$. These models generally agree with the data within uncertainties for $p_T > 9.6$ GeV.

5. Significance

• Constraining QGP Formation: The results provide strong evidence that parton energy loss mechanisms are active even in small collision systems (NeNe and OO). The monotonic dependence on system size supports the existence of a deconfined medium whose properties scale with the nuclear radius.
• Theoretical Guidance: The data rules out scenarios where suppression is driven solely by initial-state effects. It provides stringent constraints for theoretical models regarding the path-length dependence of energy loss and the scaling of the jet transport coefficient ($\hat{q}$) in small systems.
• Future Physics Programs: The study offers guidance for selecting ion species in future LHC runs, demonstrating that light-ion collisions (like NeNe) are powerful probes for studying the onset of QGP formation and the transition from cold nuclear matter effects to hot medium effects.

In summary, this work establishes a clear, model-independent link between the size of the colliding nuclear system and the magnitude of high-$p_T$ particle suppression, confirming that energy loss scales with the nuclear radius and validating the presence of medium-induced effects in small collision systems.