⚛️ nuclear theory

Neutron Skin from Conserved Charge Measurements at Collider Experiments

This paper proposes and validates a novel method for extracting the neutron skin thickness of lead nuclei in $p$ + $^{208}$ Pb collisions by analyzing a double ratio of net electric charge to net baryon number across different event multiplicities, utilizing a comprehensive (3+1)D relativistic hydrodynamic framework to provide predictions for experiments at LHCb and the LHC.

Original authors: Grégoire Pihan, Akihiko Monnai, Björn Schenke, Chun Shen

Published 2026-07-24

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CC BY 4.0

Original authors: Grégoire Pihan, Akihiko Monnai, Björn Schenke, Chun Shen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, cosmic construction site where the smallest building blocks—protons and neutrons—huddle together to form the heavy nuclei that make up the matter in our world. Inside these tiny atomic cores, protons (which carry a positive electric charge) and neutrons (which are electrically neutral) usually mix together like a well-stirred bowl of soup. But sometimes, the neutrons get a little shy and push themselves out to the very edge, forming a fuzzy, extra-thick layer around the core. Scientists call this the "neutron skin." Measuring how thick this skin is might sound like a niche hobby for nuclear physicists, but it's actually a crucial clue for understanding the entire universe. The thickness of this skin tells us how "stiff" or "squishy" the matter inside neutron stars is, which helps us figure out how big these cosmic giants can get before they collapse. It's like trying to guess how hard a pillow is by poking it from the outside; if we know how the skin behaves, we can understand the secrets of the densest objects in the cosmos.

Now, imagine trying to measure this fuzzy skin on a lead atom. It's incredibly difficult because neutrons don't have an electric charge, so they don't bounce off electrons in a way that's easy to see. Usually, scientists have to use fancy tricks involving particle beams or even the weak force of nature to get a peek. But in this new study, a team of researchers proposes a clever, high-speed way to measure this skin using the world's most powerful particle smashers: the Large Hadron Collider (LHC). Instead of gently probing a stationary atom, they suggest smashing a single proton into a massive lead nucleus at nearly the speed of light and watching what flies out.

The researchers, Grégoire Pihan and his colleagues, came up with a "double ratio" trick to solve the puzzle. Think of it like a game of tag played in a crowded room. If you have a room full of people (the lead nucleus) where the shy kids (neutrons) are hiding in the corners, and you send one runner (the proton) in, the outcome depends on where the runner hits. If the runner hits the very edge of the room (a "peripheral" collision), they are more likely to bump into the shy kids hiding in the corners. If the runner smashes right through the middle (a "central" collision), they hit everyone mixed together.

The team realized that by comparing two different types of collisions, they could isolate the effect of the neutron skin. They looked at the ratio of electric charge (carried by protons and other charged particles) to the total number of baryons (protons and neutrons combined) in the debris. In collisions where the proton hits the edge, a thick neutron skin means the runner bumps into more neutrons and fewer protons, changing the balance of the debris. In the middle-hitting collisions, the skin doesn't matter as much because the runner hits the whole mix. By taking the ratio of these two scenarios—a "double ratio"—the messy details of the explosion cancel out, leaving a clean signal that changes directly with the thickness of the neutron skin.

Using super-computer simulations that act like a virtual time machine for these collisions, the team modeled what would happen when a proton hits a lead nucleus at two different energies: one matching the LHC's main collider mode (5.02 TeV) and another matching a fixed-target experiment (72 GeV). They found that their proposed double ratio is indeed a sensitive ruler. As they artificially thickened the neutron skin in their simulations, the double ratio dropped in a predictable, almost straight-line pattern. This suggests that if experimentalists can measure this ratio in real life, they can read off the thickness of the neutron skin directly.

The study highlights that this method works best when looking at particles flying off at very sharp angles (high rapidity), far from the center of the collision. In these regions, the signal is cleanest and least confused by other messy effects of the collision. The researchers showed that for the LHC's collider mode, the signal is robust enough that a measurement could potentially match the precision of the best current methods, like the PREX-II experiment, which uses a completely different technique involving electron scattering.

While the paper doesn't claim to have measured the skin yet—since this requires actual data from the LHC—it strongly suggests that this new method is a viable and powerful tool. The simulations show that the observable reacts systematically to changes in the skin's thickness, offering a "novel and rather direct means" to measure it. The team acknowledges that there are some systematic uncertainties to iron out, such as how exactly protons and neutrons stop and slow down during the crash, but they argue that the core idea holds up. If the LHC experiments can pull this off, it would open a brand-new window into the structure of heavy nuclei, allowing scientists to check their understanding of nuclear matter with a fresh pair of eyes. It's a bit like realizing you can measure the thickness of a tree's bark not by scraping it, but by watching how a thrown stone bounces off the tree's edge versus its trunk.

Technical Summary: Neutron Skin from Conserved Charge Measurements at Collider Experiments

Problem Statement
Precise determination of the neutron skin thickness ( $\Delta R_{np} \equiv R_n - R_p$ ) of heavy nuclei, such as $^{208}\text{Pb}$ , is critical for constraining the density dependence of the nuclear symmetry energy, a key component of the equation of state (EOS) for neutron stars. While the proton radius ( $R_p$ ) is well-constrained via elastic electron scattering, extracting the neutron radius ( $R_n$ ) remains challenging. Existing methods, including parity-violating electron scattering (PREX/CREX), hadronic scattering, and dipole polarizability, have yielded results with significant discrepancies; notably, PREX-II reports a large skin thickness ( $0.283 \pm 0.071$ fm) that exceeds other model predictions by approximately $1.5\sigma$ . Recent indirect constraints from relativistic nuclear collisions via Bayesian analysis lack direct sensitivity to electric charge distributions. This paper proposes a novel, more direct method to constrain the neutron skin using conserved charge measurements in proton-nucleus ( $p+A$ ) collisions at collider experiments.

Methodology
The authors propose a "double ratio" observable constructed from the rapidity distributions of net electric charge ( $Q$ ) and net baryon number ( $B$ ) (or a proxy, net proton number $p$ ). The observable is defined as:
$R_{c_1, c_2}^{X,Y} = \frac{N_X(c_1)/N_Y(c_1)}{N_X(c_2)/N_Y(c_2)}$
where $X$ and $Y$ represent conserved charges (specifically $Q$ and $B$ , or $Q$ and $p$ ), and $c_1$ and $c_2$ denote peripheral (80–100%) and central (0–20%) collision classes, respectively.

The physical mechanism relies on the correlation between event activity (multiplicity) and impact parameter. In peripheral collisions, the projectile proton interacts with the edge of the target nucleus. If a neutron skin exists, the surface is neutron-rich, leading to a higher probability of proton-neutron interactions compared to central collisions. This alters the ratio of participating protons to neutrons, thereby affecting the final-state distribution of net electric charge relative to net baryon number. Central collisions serve as a baseline less sensitive to surface effects.

The study employs a comprehensive $(3+1)$ D relativistic hydrodynamic framework using the iEBE-MUSIC event-by-event simulation code. Key components include:

Initial State: A 3D-Glauber model with an isospin-dependent Woods-Saxon parametrization to sample nucleon positions. The neutron skin thickness is controlled by varying the diffuseness parameter ( $\Delta a_{np}$ ) while keeping the proton distribution fixed.
Hydrodynamic Evolution: The system evolves according to conservation laws for energy-momentum and conserved charge currents ( $B$ and $Q$ ). The simulation includes bulk and shear viscosity (DNMR second-order equations) and utilizes the neos-4D equation of state, which incorporates charge-dependent lattice-QCD constraints.
Hadronization and Transport: Particlization occurs at a switching energy density ( $\epsilon_{sw} = 0.2$ GeV/fm $^3$ ) via the Cooper-Frye prescription, followed by hadronic rescattering and decays modeled by UrQMD.
Stopping Mechanisms: The model accounts for potential differences in the stopping of baryon charge versus electric charge (e.g., via baryon junctions), though the authors note the method's robustness even if these mechanisms vary.

Key Results
The authors present predictions for $p+^{208}\text{Pb}$ collisions at two center-of-mass energies:

$\sqrt{s_{NN}} = 5.02$ TeV: Corresponding to the LHC collider mode.
$\sqrt{s_{NN}} = 72$ GeV: Corresponding to the LHCb SMOG2 fixed-target setup.

Dependence on Neutron Skin: The double ratio exhibits an approximately linear dependence on the neutron skin thickness ( $\Delta R_{np}$ ). As $\Delta R_{np}$ increases, the double ratio decreases monotonically from unity.
Rapidity Dependence: The observable is most robust in the fragmentation region ( $5.5 < y_{lab} < 7.5$ ), where the final-state ratio closely mirrors the initial-state distribution. In the forward region ( $4.5 < y_{lab} < 5.5$ ), the ratio is more sensitive to final-state effects such as thermal smearing and species-dependent emission (e.g., pions vs. baryons), which can introduce systematic shifts.
Proxy Validity: The study demonstrates that using net protons ( $p$ ) as a proxy for net baryons ( $B$ ) yields nearly identical results to the $Q/B$ ratio, making the $Q/p$ double ratio a viable experimental observable since neutrons are difficult to detect directly.
Systematic Uncertainties: The authors quantify uncertainties arising from baryon stopping mechanisms, charge diffusion during hydrodynamic expansion, and the specific modeling of the Woods-Saxon profile. These effects are estimated to be within a few percent, preserving the sensitivity of the observable.

Significance and Claims
The paper claims to offer a "novel and rather direct means" of measuring the neutron skin of colliding nuclei using conserved charge ratios. The primary significance lies in:

Direct Sensitivity: Unlike previous indirect methods relying on global flow or multiplicity, this method directly probes the spatial distribution of protons and neutrons via their conserved charges.
Experimental Feasibility: The $Q/p$ double ratio in the forward rapidity window ( $4.5 < y < 5.5$ ) is identified as the most promising candidate for near-term measurement at the LHC.
Complementarity: The method provides an independent constraint on the symmetry energy and neutron skin, potentially helping to resolve discrepancies between PREX-II and other theoretical/experimental determinations.
Scalability: The methodology is applicable to other heavy nuclei (e.g., $^{48}\text{Ca}$ ) in high-energy $p+A$ collisions.

The authors emphasize that while systematic uncertainties related to particlization and stopping may complicate fixed-target comparisons, the collider-mode predictions are robust and ready for experimental testing.

Technical Summary: Neutron Skin from Conserved Charge Measurements at Collider Experiments

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