⚛️ phenomenology

ALP interactions with mesons and baryons at $\mathcal{O}(1/f_a)$ : a general field redefinition invariant approach

This paper establishes a field-redefinition-invariant framework for describing ALP interactions with mesons and baryons at $\mathcal{O}(1/f_a)$ , deriving general couplings, identifying a novel invariant ALP-baryon interaction, and demonstrating that baryon-antibaryon decay widths can dominate over mesonic channels in the 2–3 GeV mass range for gluophilic benchmarks.

Original authors: Jorge Alda, Stefano Rigolin

Published 2026-10-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jorge Alda, Stefano Rigolin

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

In the vast, invisible landscape of particle physics, there exists a class of hypothetical particles known as axion-like particles. These are not the heavy, familiar building blocks of matter like protons or neutrons, but rather ghostly, lightweight entities that might explain some of the universe's deepest mysteries, such as why matter and antimatter behave differently or what constitutes the invisible dark matter that holds galaxies together. For decades, physicists have focused on how these particles interact with light and other fundamental forces. However, a crucial piece of the puzzle has remained difficult to solve: how these particles behave when they encounter the dense, complex world of atomic nuclei, specifically in the energy range where they could be produced in high-energy collisions or decay into ordinary matter. This region is a theoretical no-man's-land, sitting between the low-energy world where simple rules apply and the high-energy world where complex calculations take over. Understanding this transition is vital because the speed at which these particles decay determines whether they would be seen instantly in a detector or travel far enough to leave a trail, a distinction that shapes how scientists search for them.

A team of researchers has now mapped this difficult territory with a new, more robust approach. They developed a method to describe how these hypothetical particles interact with protons, neutrons, and other heavy particles called baryons, without relying on arbitrary mathematical tricks that could distort the results. Previous attempts to describe these interactions often required physicists to choose a specific way of writing down the equations, a choice that could accidentally hide or invent effects that do not actually exist. The new study removes this ambiguity by identifying the specific combinations of numbers that remain constant regardless of how the equations are written. This ensures that the predictions are based on physical reality rather than mathematical convenience. By applying this rigorous framework, the team was able to derive the most complete description to date of how these particles talk to the building blocks of matter, including interactions that change the type of particle involved, a feature that had been largely ignored in previous models.

One of the most significant discoveries in this work is the identification of a previously overlooked way these particles can interact with protons and neutrons. In the complex mathematics governing the strong force that holds nuclei together, there is a subtle, hidden structure that acts like a second, independent channel for these interactions. While earlier theories dismissed this channel as irrelevant for standard processes, the researchers found that when the particle in question is a dynamic, moving axion-like particle, this channel becomes active and significant. It provides a new way for the particle to couple to matter, one that depends on a specific property of the particle's mass and the topological nature of the strong force. This finding changes the predicted strength of these interactions, which is critical for calculating how long these particles might live and how they would appear in experiments.

The researchers also explored how these particles might cause rare decays in heavy, unstable particles known as hyperons. These decays, where a hyperon transforms into a proton and an invisible particle, offer a unique window into the nature of the axion-like particle. The study shows that these baryon decays are sensitive to a specific type of interaction that cannot be seen in the more common decays of lighter particles like kaons. By comparing their theoretical predictions with recent data from particle colliders, the team was able to place new, tighter limits on the possible strength of these interactions. They demonstrated that even if these particles start out with simple, uniform properties at the highest energy scales, the complex journey through the laws of physics as they move to lower energies can generate new, uneven interactions that are detectable today.

Perhaps the most striking result concerns the fate of these particles when they are heavy enough to break apart into pairs of protons and antiprotons. For a long time, physicists assumed that in this mass range, the particles would primarily decay into lighter mesons or into a spray of quarks and gluons that quickly turn into a cloud of hadrons. The new analysis reveals that the direct decay into pairs of heavy baryons is far more important than previously thought. In a specific scenario where the particle interacts strongly with the gluons that bind quarks together, the combined rate of these baryon pair decays can exceed the rate of individual, well-known meson decays for particle masses between 2 and 3 GeV. This means that in the search for these particles, scientists must pay much closer attention to the heavy, two-particle final states. The study also highlights that the exact size of this effect depends on a specific, uncertain parameter, meaning the contribution could be anywhere from a small fraction to a dominant portion of the total decay rate.

This work provides a solid, reliable foundation for future searches. By stripping away the mathematical ambiguities that plagued earlier models, the researchers have given experimentalists a clear set of rules to follow. They have shown that the interactions between these hypothetical particles and the heavy matter of our universe are richer and more complex than previously imagined, involving hidden channels and flavor-changing processes that were once thought to be negligible. The findings suggest that the search for these particles must look beyond the familiar light particles and into the heavier, more complex decays, where the true signature of these elusive entities might finally be revealed. The path forward is now clearer, guided by a description that respects the fundamental symmetries of nature and accounts for the intricate dance of forces that governs the subatomic world.

Technical Summary: ALP Interactions with Mesons and Baryons at O(1/fa): A General Field Redefinition Invariant Approach

Problem Statement
Axion-like particles (ALPs) in the MeV–GeV mass range present a significant challenge for phenomenological descriptions. While Chiral Perturbation Theory ( $\chi$ PT) is valid for $m_a \lesssim 1$ GeV and perturbative QCD (pQCD) for $m_a \gtrsim 2\text{--}3$ GeV, the intermediate region is difficult to describe due to the breakdown of the chiral expansion and the onset of hadronic resonances. A critical theoretical issue in this regime is the unphysical dependence of calculated amplitudes on the arbitrary chiral rotation used to remove the ALP–gluon interaction. Previous attempts to bridge this gap (e.g., Refs. [14, 16, 17]) suffered from such basis dependence. Furthermore, existing field-redefinition-invariant formulations (Refs. [18, 19]) have been restricted to flavor-conserving ALP–quark interactions. However, generic ultraviolet (UV) models often induce flavor-changing interactions at low energies through renormalization-group evolution and matching, necessitating a general framework that includes non-diagonal flavor structures.

Methodology
The authors develop a general, field-redefinition-invariant framework for ALP interactions with hadrons at leading order in $1/f_a$ , $O(1/f_a)$ , outside the odd-intrinsic-parity Wess–Zumino–Witten (WZW) sector.

Invariant Wilson Coefficients: Starting from the most general CP-conserving ALP–QCD Lagrangian, the authors analyze the transformation properties under general axial and vector quark field redefinitions. They identify specific combinations of Wilson coefficients that remain invariant under these transformations. These include the anomalous gluonic combination $c_{GA} = c_G + \langle c_A^q \rangle$ and the flavor-off-diagonal combinations $c_{AP}^q = c_A^q - c_P^q$ and $c_{VS}^q = c_V^q - c_S^q$ .
Chiral Matching and LSZ Reduction: These invariant coefficients are matched onto the $U(3)$ chiral theory using the Callan–Coleman–Wess–Zumino (CCWZ) formalism. The authors employ the Lehmann–Symanzik–Zimmermann (LSZ) reduction formula to account for ALP–meson mixing. Crucially, they exploit the freedom of ALP-dependent quark field redefinitions to choose a specific parametrization where the ALP–meson mixing components vanish at $O(1/f_a)$ .
No-Mixing Parametrization: In this specific parametrization, physical amplitudes with one external ALP are derived entirely from direct interaction vertices. The effects of the ALP–gluon coupling are encoded in the $U(1)_A$ topological sector. This ensures that the resulting couplings are manifestly independent of the initial quark field basis.
Baryon Octet Extension: The framework is applied to the baryon octet. The authors retain a second independent singlet axial structure in the $U(3)$ baryon Lagrangian (originally introduced for external vacuum angles but previously discarded for dynamical ALPs). This structure generates a new, independent invariant ALP–baryon interaction proportional to the anomalous gluonic coupling.
Phenomenological Continuation: To address the GeV-scale region where chiral perturbation theory breaks down, the authors construct a phenomenological continuation of the ALP–baryon couplings. This model matches the low-energy chiral results to the asymptotic scaling of baryonic form factors derived from hard-scattering counting, introducing a matching scale $\mu_*$ .

Key Contributions and Results

General Flavor Structure: Unlike previous works, this framework explicitly includes general flavor-conserving and flavor-changing quark couplings. It demonstrates that flavor-changing interactions can be generated from flavor-diagonal UV boundary conditions via running and matching, and that omitting them a priori is theoretically inconsistent for generic UV models.
New Baryon Interaction: The authors identify, for the first time, an independent invariant ALP–baryon interaction arising from a second topological singlet structure in the $U(3)$ baryon Lagrangian. This interaction is proportional to the anomalous ALP–gluon coupling and depends on a low-energy constant $\tilde{S}_B$ , which is not fixed by standard quark axial charges.
Flavor-Changing Hyperon Decays: The derived flavor-changing couplings are used to constrain ALP interactions using rare hyperon decays ( $\Sigma^+ \to p + \text{inv}$ , $\Xi^0 \to \Lambda + \text{inv}$ from BESIII; $\Sigma^+ \to p\mu^+\mu^-$ from LHCb). The analysis shows that baryonic decays provide direct sensitivity to the axial $s \to d$ coefficients, which are inaccessible in pseudoscalar meson decays.
UV Model Matching: Using the QED–DFSZ model as an explicit example, the authors show that running from high scales generates significant flavor-changing couplings, reinforcing the necessity of including them in low-energy descriptions.
Baryon–Antibaryon Decays: In the few-GeV mass range ( $2 \text{ GeV} \le m_a \le 3 \text{ GeV}$ ), the authors estimate exclusive ALP decay widths into baryon–antibaryon pairs. They find that the sum of these exclusive baryonic widths can exceed individual exclusive mesonic widths (e.g., $a \to \omega\omega$ , $a \to \eta^{(\prime)}\pi\pi$ ) in a "gluophilic" benchmark. However, the total exclusive baryonic width remains a sub-dominant fraction (0.1–5%) of the inclusive pQCD estimate, suggesting that significant contributions from multi-hadron final states are missing.

Significance and Claims
The paper claims to provide a systematic, field-redefinition-invariant interface between ultraviolet ALP couplings and hadronic amplitudes without requiring a preliminary chiral rotation to remove the gluonic operator. By extending this formalism to include flavor-changing interactions and the full baryon octet, the authors address a gap in the theoretical description of ALPs in the GeV regime.

The authors modestly note that their description is valid at $O(1/f_a)$ and leading chiral order, assuming perturbative ALP–meson mixing ( $f_\pi/f_a \ll 1$ ) and away from mass degeneracies. They acknowledge that the extension to the GeV scale relies on a phenomenological model for form factors and matching scales, introducing theoretical uncertainties. Nevertheless, the work establishes that baryonic channels are a non-negligible component of ALP phenomenology in the few-GeV region and that flavor-changing hyperon decays offer complementary probes to meson decays for constraining ALP parameter space.

More like this