Observation of impact parameter dependent modifications of nuclear parton distributions in photonuclear Pb+Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV with the ATLAS detector

Using 2018 ATLAS data from ultra-peripheral Pb+Pb collisions at 5.02 TeV, this study provides the first experimental observation that nuclear parton distribution modifications vary with impact parameter, evidenced by a significant difference in $\gamma+A$ jet production cross-sections between collisions with and without forward neutron emission.

The Gist

The Big Picture: A "Ghostly" Collision

Imagine two massive, dense cities (Lead nuclei) zooming toward each other at nearly the speed of light. Usually, when these cities collide, they crash, crumble, and create a chaotic explosion of debris.

But in this experiment, the scientists set up a very specific scenario: Ultra-Peripheral Collisions (UPCs).

Think of this like two giant trucks driving past each other on a highway, so close that their side mirrors almost touch, but they never actually crash. Instead of the trucks hitting, the wind from one truck hits the other. In physics, this "wind" is a flash of light (a photon) emitted by one nucleus that smashes into the other nucleus.

The goal was to see what happens when this "wind" hits the "city" (the nucleus) at different distances from the center.

The Mystery: Are the "Citizens" Different?

Inside the nucleus (the city), there are tiny particles called quarks and gluons (let's call them "citizens"). Scientists have known for a long time that when these citizens are packed tightly together in the center of the nucleus, they behave differently than they do when they are free and alone. They seem to get "lazy" or "suppressed" (a phenomenon called shadowing).

The Big Question: Does this "laziness" happen everywhere in the city, or only in the crowded downtown?

• Hypothesis A: The citizens are all equally lazy, no matter where they live in the nucleus.
• Hypothesis B: The citizens in the crowded center are lazy, but the citizens living on the quiet, sparse outskirts (the "suburbs") are just as energetic and normal as free citizens.

The Experiment: The "Neutron Smoke Signal"

To figure this out, the ATLAS team at CERN used a clever trick involving neutrons (neutral particles) acting like smoke signals.

1. The "Crash" Scenario ($0nXn$): When the photon hits the nucleus hard, it usually excites the nucleus, making it shake violently. This shaking causes it to spit out neutrons. If the detectors see neutrons flying out the front, they know the nucleus was "excited" and likely hit near the center (or the impact was messy).
2. The "Gentle" Scenario ($0n0n$): Sometimes, the photon hits the nucleus very gently, or hits it right on the edge (the outskirts). The nucleus doesn't shake enough to spit out neutrons. If the detectors see zero neutrons, they know this was a very "peripheral" (edge-on) collision where the nucleus stayed calm and intact.

The Analogy: Imagine throwing a rock at a house.

• If you hit the front door hard, the house shakes, windows break, and debris flies out (Neutrons detected).
• If you gently tap the very edge of the roof, the house barely notices, and nothing flies out (No neutrons detected).

The Discovery: The "Edge" is Different

The scientists compared the results of these two scenarios:

• Group A: Collisions where neutrons flew out (Center/Excited hits).
• Group B: Collisions where no neutrons flew out (Edge/Gentle hits).

They measured how often "jets" (sprays of particles created by the collision) were produced in both groups.

The Result:
They found a massive difference!

• In the Center/Excited hits, the "citizens" (partons) were indeed behaving strangely (modified), just as expected.
• In the Edge/Gentle hits, the "citizens" behaved exactly like free citizens. They were not modified at all.

The data showed a 6-sigma significance. In the world of science, this is like flipping a coin and getting "Heads" 6 million times in a row. It is not a fluke; it is a definitive discovery.

Why This Matters

This is the first time scientists have directly proven that where you hit the nucleus matters.

• Before: We thought the whole nucleus was a uniform blob where the rules of physics were the same everywhere.
• Now: We know the nucleus has a "geography." The center is a crowded, modified environment, but the edge is a quiet, normal place where particles act like they are in a vacuum.

The Takeaway

Imagine a crowded dance floor. In the middle, people are jostling, bumping into each other, and moving slowly (modified). But if you stand at the very edge of the room, you can dance freely without anyone bumping into you (unmodified).

This paper proves that the "dance floor" of the atomic nucleus has a distinct edge where the rules of the crowd no longer apply. This helps us understand the structure of matter better and could change how we interpret data from future particle colliders.

In short: The ATLAS team proved that the "edge" of an atomic nucleus is a different world than its "center," and the particles there are free and unmodified.

Technical Summary

1. Problem and Motivation

The study addresses a fundamental question in nuclear physics: Do Nuclear Parton Distribution Functions (nPDFs) depend on the impact parameter ($b_A$) of the collision?

• Context: Standard global fits of nPDFs (e.g., nCTEQ, nNNPDF) typically assume that modifications to parton distributions (such as shadowing at low $x$ or the EMC effect at high $x$) are uniform across the nucleus.
• Theoretical Expectation: Theoretical models suggest that nPDF modifications should vary with $b_A$. For instance, shadowing is often attributed to multiple scattering, which is more probable in central collisions (small $b_A$) where nuclear density is high. Conversely, peripheral collisions (large $b_A$) might probe nucleons near the nuclear surface (potentially with a neutron skin) that behave more like free nucleons.
• The Gap: While the $b_A$-dependence has been proposed for decades, no experiment has successfully isolated and directly constrained this dependence. Previous measurements have been inclusive, averaging over all impact parameters.

2. Methodology

The ATLAS Collaboration utilized Ultra-Peripheral Collisions (UPCs) of Lead (Pb) nuclei at $\sqrt{s_{NN}} = 5.02$ TeV. In UPCs, the impact parameter between the two nuclei ($b_{AA}$) is larger than twice the nuclear radius, ensuring that only electromagnetic interactions (photon-induced processes) occur, avoiding strong hadronic interactions.

Key Experimental Strategy:
The experiment distinguishes between different impact parameters within the target nucleus ($b_A$) by analyzing the forward neutron emission from the struck nucleus.

• $0_n0_n$ Topology (Large $b_A$): Events where no forward neutrons are detected in either Zero-Degree Calorimeter (ZDC). This topology selects events where the struck nucleus remains intact (or is only very weakly excited). Theoretical arguments suggest these events correspond to peripheral collisions (large $b_A$), where the photon strikes a nucleon near the edge of the nucleus.
• $0_nX_n$ Topology (Mixed $b_A$): Events where the photon-emitting nucleus emits no neutrons ($0_n$), but the struck nucleus emits at least one forward neutron ($X_n$). This indicates the struck nucleus was significantly excited and broke up, a process more likely in central or semi-central collisions (smaller $b_A$) where the photon strikes deeper into the nuclear density.

Measurement Process:

1. Data Sample: 1.72 nb$^{-1}$ of Pb+Pb data collected in 2018.
2. Process: Measurement of $\gamma + A \to \text{jets}$ (photonuclear jet production).
3. Kinematics:
   • Jets are reconstructed using the anti-$k_t$ algorithm ($R=0.4$).
   • The kinematics are defined by the photon momentum fraction ($z^-$) and the nuclear parton momentum fraction ($x^+$).
   • The analysis focuses on the non-diffractive region (selected via rapidity gap requirements) to isolate hard scattering.
4. Observable: The ratio of the differential cross-sections:
   $$R = \frac{\sigma(\gamma + A \to \text{jets})_{0_n0_n}}{\sigma(\gamma + A \to \text{jets})_{0_nX_n}}$$
   This ratio is measured as a function of $x^+$.
5. Background Suppression: Template fits using the $\Delta\eta_2$ variable (rapidity gap to the second closest track) were used to separate the signal ($\gamma+A$) from diffractive ($\gamma+\mathbb{P}$) and photon-photon ($\gamma+\gamma$) backgrounds.

3. Key Contributions

• First Direct Observation: This is the first experimental evidence demonstrating that nPDF modifications are not uniform but vary with the impact parameter $b_A$.
• Topology-Based Selection: The paper successfully utilizes the presence or absence of forward neutrons as a proxy for the impact parameter, effectively "slicing" the nucleus into peripheral and central interaction regions without requiring direct measurement of the collision geometry.
• Validation of Peripheral Nucleons: It provides experimental confirmation that nucleons at the periphery of a heavy nucleus (probed in $0_n0_n$ events) exhibit parton distributions consistent with free nucleons, whereas those in the interior (probed in $0_nX_n$ events) show standard nuclear modifications.

4. Results

• Shape of the Ratio: The measured ratio of cross-sections ($0_n0_n / 0_nX_n$) shows a clear, increasing trend as a function of $x^+$.
  • At low $x^+$, the ratio is suppressed, indicating that the $0_n0_n$ sample (peripheral) has less shadowing than the $0_nX_n$ sample (central).
  • At high $x^+$, the ratio approaches unity or exceeds it, consistent with the EMC effect being weaker or absent in peripheral collisions.
• Statistical Significance: The deviation from the null hypothesis (that nPDFs are identical for both topologies) is observed with a significance of 6.0$\sigma$.
• Comparison with Theory:
  • The data are compared to theoretical predictions using nCTEQ15 and nNNPDF3.0 nPDFs.
  • Theoretical models that assume no nuclear modification for the peripheral ($0_n0_n$) case (i.e., treating them as free nucleons) while applying standard nPDFs to the inclusive case describe the data shape well.
  • Models assuming uniform nPDF modifications across all impact parameters fail to describe the $x^+$ dependence of the ratio.

5. Significance

• Paradigm Shift in nPDFs: The results challenge the standard assumption in global nPDF fits that nuclear modifications are independent of the impact parameter. Future fits must incorporate $b_A$-dependence to accurately describe heavy-ion data.
• Interpretation of Heavy Ion Data: This finding has profound implications for interpreting data from the LHC and RHIC heavy-ion programs. It suggests that "central" and "peripheral" collisions probe fundamentally different partonic structures within the nucleus.
• Future Probes: The methodology establishes a robust technique for studying the spatial distribution of partons. This approach is directly applicable to future facilities, including the High-Luminosity LHC (HL-LHC) and the proposed Electron-Ion Collider (EIC), where impact-parameter dependent nPDFs can be mapped with high precision.
• Nuclear Structure: The observation supports theoretical models linking the EMC effect to Short-Range Correlations (SRCs) and nuclear density variations, suggesting that the "edge" of the nucleus behaves differently from its core.

In conclusion, the ATLAS Collaboration has provided the first definitive experimental evidence that the parton distributions of nucleons near the edge of a lead nucleus differ significantly from those near the center, fundamentally altering our understanding of nuclear structure in high-energy physics.