⚛️ phenomenology

Toward a Direct Measurement of Partial Restoration of Chiral Symmetry at J-PARC E16 via Density-induced Chiral Mixing

This paper utilizes an effective Lagrangian approach combined with transport simulations to predict that the J-PARC E16 experiment can observe a signal of $\phi$ - $f_1(1420)$ mixing, indicative of partial chiral symmetry restoration, with approximately 2.5 $\sigma$ significance using planned Run2 statistics.

Original authors: Ren Ejima, Philipp Gubler, Chihiro Sasaki, Kenta Shigaki

Published 2026-09-30

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CC BY 4.0

Original authors: Ren Ejima, Philipp Gubler, Chihiro Sasaki, Kenta Shigaki

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

Deep within the heart of every atom, protons and neutrons are held together by a force so powerful it defies our everyday intuition. This force, known as the strong interaction, arises from the behavior of even smaller particles called quarks. In the empty space of a vacuum, quarks are bound so tightly that they form heavy, stable particles, giving matter its weight. However, physicists have long suspected that if you squeeze matter hard enough or heat it up to extreme temperatures, this binding force would weaken. The rules that govern the particles would change, and the heavy particles would begin to behave as if they were lighter, almost as if the universe were resetting itself to a simpler state. This phenomenon is called the restoration of chiral symmetry, a fundamental concept in the theory of how the universe is built. Proving that this happens in a controlled setting has been one of the most elusive goals in nuclear physics, because the conditions required are incredibly difficult to create and measure.

A team of researchers has now proposed a new way to catch a glimpse of this transformation using a massive particle accelerator in Japan. Instead of trying to measure the mass of a single particle directly, which is often clouded by confusing interactions, they looked for a specific "echo" of the symmetry returning. In the world of subatomic particles, every heavy particle has a partner, a twin that is identical in most ways but spins in the opposite direction. In normal conditions, these twins have very different masses. But if chiral symmetry is restored, these twins should become identical, their masses merging into one. The researchers focused on a specific pair: a particle called the phi meson and its heavier partner, the f1(1420). They calculated that if these particles are created inside a dense environment, like the core of an atomic nucleus, the laws of physics should force them to mix together. This mixing would leave a distinct fingerprint in the energy of the particles they decay into, a signal that could finally confirm that the symmetry is indeed returning.

The study, led by scientists from Hiroshima University and other institutions, centers on an upcoming experiment at the J-PARC facility, known as E16. This experiment will fire a beam of protons traveling at 30 billion electron volts into blocks of heavy metal, specifically copper and lead. When these high-speed protons smash into the metal atoms, they create a brief, incredibly dense environment where the rules of the vacuum no longer apply. Inside this dense soup, the researchers predict that the phi meson and the f1(1420) will not remain separate entities. Instead, they will blend, a process driven by the sheer density of the surrounding matter. This blending changes the way the particles move and decay, altering the energy of the electron-positron pairs they eventually produce. By carefully measuring the mass of these electron pairs, the experimenters hope to see a new peak or a broadening of the signal that reveals the presence of the f1(1420) mixing with the phi meson.

To determine if this signal is visible, the team performed detailed computer simulations of the entire collision process. They modeled how the protons travel through the metal, how the phi mesons are created, and how they interact with the dense nuclear matter before decaying. A crucial part of their work involved accounting for the fact that the phi meson lives for a very short time, but long enough that many of them escape the metal target before they can decay. This means they decay in empty space, where the density is zero and no mixing occurs. The researchers had to calculate exactly how many particles decay inside the dense target versus outside of it. They also simulated the background noise, which comes from other particles that look like the signal but are not, and the limitations of the detector itself. They found that the ability to see the mixing signal depends heavily on the strength of the interaction between the two particles and the specific range of speeds at which the particles are moving.

The results of these simulations offer a cautious but promising outlook. The researchers found that if the mixing between the two particles is strong enough, the experiment could detect the signal with a statistical confidence of about 2.5 standard deviations. In the language of science, this is a strong hint, though not yet a definitive proof, which usually requires a higher threshold. The signal is most visible when the experiment focuses on particles moving at moderate speeds, roughly between 0.4 and 0.8 billion electron volts. If the mixing is too weak, the signal is lost in the background noise. If the mixing is too strong, the signal becomes so spread out across different energies that it becomes impossible to distinguish from the surrounding chaos. The team also discovered that the size of the target matters significantly. Using a lead target, which is larger and denser than copper, increases the chances that the particles will decay while still inside the dense environment, making the signal clearer.

Perhaps the most intriguing aspect of their findings is what the signal would tell us about the nature of the particles themselves. If the experiment sees this mixing, it would suggest that the f1(1420) is indeed the chiral partner of the phi meson and that their masses are beginning to converge. The simulations indicate that even a partial restoration of the symmetry, where the binding force is weakened by about 30 percent, would be enough to shift the mass of the f1(1420) closer to that of the phi meson. This shift would be large enough to be measured, provided the mixing signal is strong enough to be seen. The researchers emphasize that this is a simulation of what could happen, based on current theories and the planned capabilities of the J-PARC E16 experiment. They have not yet observed this phenomenon, but their work provides a clear roadmap for how to look for it.

The path forward involves waiting for the J-PARC E16 experiment to collect enough data, a process that will take place in two phases, with the second phase offering the necessary statistics to make a meaningful observation. The team suggests that if the signal is found, it will be a major step toward understanding why matter has the mass it does. It would confirm that the heavy weights of particles are not fixed properties of the universe but are instead a result of the environment they live in. By watching these particles mix and their masses change, scientists hope to see the fundamental laws of nature shifting before their eyes, revealing a deeper layer of reality that exists only when matter is squeezed to its limit. Until the data is collected, however, the existence of this mixing remains a compelling prediction, waiting to be tested by the next generation of particle collisions.

Technical Summary: Toward a Direct Measurement of Partial Restoration of Chiral Symmetry at J-PARC E16 via Density-induced Chiral Mixing

Problem Statement
The spontaneous breaking of QCD chiral symmetry is fundamental to the emergence of hadron masses. Theoretical frameworks predict that this symmetry is partially restored in media with finite temperature or density, such as those created in high-energy heavy-ion collisions or fixed-target experiments. A primary signature of this restoration is the degeneracy of chiral partners (hadrons with opposite parity but identical quantum numbers). However, experimental verification has been elusive. Previous attempts to measure in-medium mass shifts of vector mesons (e.g., $\rho$ , $\omega$ , $\phi$ ) via dileptons have yielded contradictory results (e.g., KEK-PS E325 vs. JLab CLAS), largely because observed spectral modifications can be attributed to various medium interactions (width broadening, mass shifts) not uniquely tied to chiral symmetry restoration. Furthermore, in thermal environments, the chiral mixing between vector and axial-vector mesons is suppressed, and the axial-vector partners (which cannot decay directly to dileptons) are Boltzmann-suppressed.

Methodology
This work proposes observing the degeneracy of chiral partners through "density-induced chiral mixing," a phenomenon where vector and axial-vector mesons mix directly in cold, dense matter due to the breaking of charge-conjugation symmetry. The study focuses on the $\phi$ meson and its chiral partner, the $f_1(1420)$ , within the context of the J-PARC E16 experiment, which utilizes 30 GeV proton-nucleus ( $pA$ ) collisions.

The methodology integrates three main components:

Effective Lagrangian Approach: The authors employ an effective Lagrangian that incorporates a density-induced mixing term ( $L_{mix} \propto c \epsilon^{\mu\nu\lambda} \dots$ ) between vector ( $V$ ) and axial-vector ( $A$ ) fields. This term arises from the Chern-Simons term in holographic QCD or the Wess-Zumino-Witten (WZW) action. The mixing strength $c$ is treated as a parameter, ranging from $0.1\rho/\rho_0$ GeV (based on WZW mean-field approximations) to $1.0\rho/\rho_0$ GeV (based on holographic QCD).
Spectral Function Calculation: The in-medium spectral function is computed by solving the dispersion relations for transverse modes, which are modified by the mixing. The model assumes a 30% partial restoration of chiral symmetry at normal nuclear density ( $\rho_0$ ), leading to a reduction in the $f_1(1420)$ mass toward the $\phi$ mass. The $\phi$ meson width is modified by the in-medium kaon cloud, while the $f_1(1420)$ width is modeled to become degenerate with the $\phi$ width at full restoration.
Transport Simulation and Detector Response: The space-time evolution of the $pA$ collision is simulated using the Parton-Hadron String Dynamics (PHSD) transport approach to determine the momentum and density distributions of $\phi$ mesons at the moment of their decay. The final invariant mass spectrum is constructed by convolving the spectral function with the density-momentum distribution, adding experimental backgrounds (simulated via JAM and Geant4), and applying the J-PARC E16 spectrometer's mass resolution (assumed to be 8 MeV).

Key Contributions

Mechanism Identification: The paper identifies that in cold, dense matter, chiral mixing is driven by baryon density rather than thermal pion loops, allowing for significant mixing even at zero temperature where thermal suppression of axial-vector states is absent.
Momentum Dependence: The study highlights the critical role of the particle's 3-momentum ( $\vec{p}$ ). The mixing effect scales with $c|\vec{p}|$ , meaning higher momentum enhances mixing but reduces the probability of the meson decaying inside the dense target nucleus. This creates a trade-off requiring an optimal momentum window.
Target Comparison: The authors systematically compare Copper (Cu) and Lead (Pb) targets. They demonstrate that while larger targets (Pb) increase the probability of in-medium decay, the broadening of the spectral signal due to strong mixing and dispersion relation modifications can obscure the degeneracy signal.

Results

Signal Visibility: For small mixing strengths ( $c \approx 0.1-0.2 \rho/\rho_0$ GeV), the $f_1(1420)$ signal is barely visible or indistinguishable from background. For very large mixing strengths ( $c \approx 1.0 \rho/\rho_0$ GeV), the signal becomes a broad structure distributed around the vacuum mass, making it difficult to resolve the approach toward degeneracy.
Optimal Conditions: The most significant signal is found for an intermediate mixing strength of $c \approx (0.4 \pm 0.1)\rho/\rho_0$ GeV. In this regime, the broadening effects of the dispersion relation and the mass shift toward degeneracy partially cancel, resulting in a relatively narrow peak.
Statistical Significance: With the planned Run2 statistics for J-PARC E16 and a Pb target, the $f_1(1420)$ signal can be observed with a statistical significance of approximately 2.5 $\sigma$ under ideal conditions (optimal momentum range of $0.4-0.8$ GeV and $c \approx 0.4 \rho/\rho_0$ GeV).
Chiral Restoration Sensitivity: Assuming 30% chiral symmetry restoration, the shift in the $f_1(1420)$ mass is sufficient to be distinguishable from the vacuum state given the spectrometer's resolution. Even with only 10% restoration, the contribution moves closer to the $\phi$ peak.
Tail Interpretation: The study notes that chiral mixing generates a low-mass tail in the $\phi$ invariant mass distribution due to modified transverse dispersion relations. This tail could be mistaken for a direct $\phi$ mass shift, necessitating careful analysis of angular distributions or momentum dependence to distinguish the two effects.

Significance and Claims
The paper claims that observing the $f_1(1420)$ signal in the dilepton spectrum at J-PARC E16 would constitute a direct measurement of the partial restoration of chiral symmetry, distinct from generic medium interactions. The authors assert that if the mixing strength falls within the intermediate range ( $c \approx 0.4 \rho/\rho_0$ GeV) and sufficient statistics are collected (Run2), the experiment can:

Detect the presence of the axial-vector partner $f_1(1420)$ in a dilepton channel.
Observe the movement of the $f_1(1420)$ mass toward the $\phi$ mass, providing evidence for the degeneracy of chiral partners.
Distinguish density-induced chiral mixing from simple mass shifts or width broadening.

The authors remain modest regarding the certainty of the mixing strength parameter $c$ , noting that its exact value is unknown and that the signal is highly sensitive to this parameter. They emphasize that a precise baseline (e.g., from $pp$ collisions) is necessary to isolate genuine density effects. Ultimately, the work provides a theoretical motivation and a specific kinematic strategy for the J-PARC E16 experiment to probe the relationship between hadron masses and spontaneously broken chiral symmetry.

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