Spinning in the Dark: How Axions Could Influence Particle Systems

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Author: Denis Avetisyan

New research explores the collective behavior of spinning particles when exposed to hypothetical axion fields, revealing subtle forces with potential implications for dark matter detection.

This study develops a quantum hydrodynamic framework to model the dynamic effects of axion-fermion coupling on many-particle systems with spin.

Existing theoretical frameworks often struggle to fully capture the interplay between spin dynamics, inertial effects, and weak, long-range interactions. This is addressed in ‘Dynamic effects of external axion fields in a system of many particles with spin’, which develops a many-particle quantum hydrodynamic model to describe the collective behavior of spinning particles subject to both rotation and external axion fields. The resulting formalism reveals novel spin-dependent forces and torques, demonstrating how spin and current densities could serve as sensitive probes for axion-like dark matter. Could this approach pave the way for new experimental strategies in the search for these elusive particles and deepen our understanding of dark matter interactions?

The Vanishing Symmetry: Introducing the Axion

Quantum chromodynamics, the theory describing the strong nuclear force, unexpectedly predicts violations of charge-parity (CP) symmetry – a fundamental principle stating that physics should remain the same if a particle is mirrored and its charge is reversed. However, experiments show no evidence of these violations, creating a puzzle known as the Strong CP Problem. To resolve this discrepancy, physicists proposed the existence of a new, hypothetical particle called the axion. This particle wouldn’t directly interact with ordinary matter in ways currently observed, yet its presence would subtly alter the behavior of strong interactions, effectively ‘canceling out’ the predicted CP violations. The axion’s existence isn’t directly confirmed, but its theoretical necessity arises from a deep inconsistency within established physics, making it a compelling subject of ongoing research and a potential link to understanding the universe’s missing mass.

The axion’s appeal extends beyond simply resolving the intricacies of the Strong CP Problem; it simultaneously addresses the long-standing mystery of dark matter. Cosmological models indicate that a substantial portion of the universe’s mass is non-baryonic – not composed of protons and neutrons – and exhibits gravitational effects without interacting with light. The axion, a hypothetical particle born from the theoretical solution to the Strong CP Problem, possesses precisely these characteristics. Calculations suggest that axions, produced abundantly in the early universe, would have the right properties – weak interactions and a suitable mass range – to account for a significant fraction, or even all, of the observed dark matter. This dual role – a solution to a fundamental physics puzzle and a potential explanation for a dominant component of the cosmos – has propelled the axion to the forefront of particle physics research, motivating numerous experimental efforts dedicated to its detection.

Successfully detecting axions, a leading dark matter candidate, hinges on precisely characterizing two key properties: its mass and its coupling strength. The coupling strength is often expressed through the ‘axion decay constant’, which dictates how readily an axion interacts with standard model particles – a weaker interaction makes detection significantly harder. Current experiments employ diverse strategies, from resonant cavities tuned to specific axion masses to searches for the faint electromagnetic signals produced by axions in strong magnetic fields, but each is sensitive to a limited range of possible masses and coupling strengths. Refinements in theoretical models, coupled with advancements in detector technology, are therefore critical to narrowing the search parameters and ultimately confirming-or refuting-the axion’s role in resolving the mysteries of dark matter and the Strong CP Problem. The challenge lies in the vastness of the potential parameter space; even small uncertainties in estimated mass or coupling constant necessitate expanded and more sensitive experimental designs.

Echoes in the Void: Experimental Strategies

The CAST and IAXO experiments leverage the Primakoff effect to detect axions, employing strong magnetic fields – typically 9 Tesla in CAST and up to 8 Tesla in IAXO – to enhance the conversion probability of axions into detectable photons. This conversion occurs via coherent mixing, where axions interact with the magnetic field and virtual photons within a resonant cavity. The interaction strength is proportional to the axion-photon coupling constant and the magnetic field strength. By directing a high-intensity laser beam through the magnetic field within the cavity, these experiments search for the faint X-ray photons produced by axion conversion, effectively probing the parameter space of axion models.

Light Shining Through Walls (LSW) experiments investigate the hypothetical ability of axions to overcome electromagnetic barriers. These experiments typically involve a strong magnetic field region, where axions, if present, could convert into photons. This photon beam is then directed towards an opaque wall, intended to block conventional light. Detection of photons on the far side of the wall would indicate that axions were able to traverse the barrier, implying a weak coupling between axions and photons. The experimental setup requires high-intensity photon sources, sensitive detectors, and precise control over background noise to distinguish potential axion signals from spurious events. Variations in the experimental design include the use of different wall materials and magnetic field configurations to optimize the search for axions with specific properties.

The CASPEr experiment investigates the potential interaction between axions and nuclear spins, specifically focusing on axion-induced modifications to the precession frequency of polarized 129Xe nuclei. This approach leverages the predicted coupling between axions and the nuclear magnetic moment, which would manifest as a measurable shift in the Larmor frequency. The experiment utilizes a strong magnetic field to align the nuclear spins and employs SQUID magnetometry to detect minute changes in the precession frequency, seeking deviations from the expected value that could indicate axion interactions. Data analysis focuses on identifying signals above the background noise level, accounting for systematic errors and environmental influences that could mimic an axion-induced effect.

Axion detection experiments are fundamentally predicated on precise calculations derived from the Lagrangian density describing the interaction between axions and photons. This Lagrangian, typically expressed as L = g_{a\gamma} a \mathbf{E} \cdot \mathbf{B}, where g_{a\gamma} represents the axion-photon coupling constant, a is the axion field, and \mathbf{E} and \mathbf{B} are the electric and magnetic fields respectively, dictates the probability of axion-photon conversion or interaction. Experimental designs, including those employing strong magnetic fields or searching for photon transmission through opaque materials, are optimized based on the predicted interaction strength derived from this Lagrangian. Accurate determination of g_{a\gamma}, and therefore the expected signal strength, is crucial for setting experimental sensitivity and interpreting results; variations in the Lagrangian due to different axion models directly impact the predicted interaction rates and necessitate adjustments in experimental parameters.

The Quantum Mirror: Modeling Axion Behavior

The quantum evolution of axions, specifically their spin dynamics, is fundamentally described by the Pauli-Schrödinger equation. This equation, a modification of the time-dependent Schrödinger equation incorporating the Pauli matrices, accounts for the axion’s intrinsic angular momentum and its interaction with external fields. The axion’s wave function, \Psi(\mathbf{r}, t) , is coupled to a spin vector field, allowing for the calculation of spin precession, relaxation, and response to gradients in the axion field. The Pauli term introduces effects not present in scalar field treatments, enabling the modeling of spin-dependent phenomena and providing a necessary framework for investigating axion behavior in electromagnetic and gravitational environments. Accurate solutions to the Pauli-Schrödinger equation are essential for predicting axion signatures in experiments designed to detect these weakly interacting particles.

The Foldy-Wouthuysen transformation is a canonical transformation utilized in relativistic quantum mechanics to decouple particle states with positive and negative energies. When applied to axion modeling in non-inertial frames, this technique effectively removes spurious oscillatory terms arising from the rotating frame, allowing for a more accurate description of axion dynamics. The transformation achieves this by systematically eliminating terms that couple states of differing energies in the Hamiltonian, resulting in a simplified equation of motion focused on the physically relevant positive-energy solutions. This is crucial for simulations involving rapidly rotating or accelerating systems where the non-inertial effects would otherwise dominate and obscure the intrinsic axion behavior. The resulting Hamiltonian then accurately reflects the physics within the rotating frame without artificial contributions from the frame’s acceleration.

Many-particle quantum hydrodynamics allows for the investigation of collective axion behavior beyond single-particle descriptions. Applying this framework to systems of multiple axions reveals previously unpredicted force terms and torques not present in simpler models. Specifically, calculations demonstrate a spin-dependent force proportional to the gradient of the axion field, and a torque acting on spin density proportional to the time derivative of the axion field. These emergent phenomena are analogous to the spin Hall effect, indicating a coupling between axion spin and its dynamical environment. The resulting equations of motion incorporate new terms dependent on both spatial gradients and temporal variations of the axion field, influencing collective behavior and potentially leading to observable effects in systems with a high density of axions.

Calculations reveal a spin-dependent force acting on axions proportional to the gradient of the axion field, and a torque on spin density proportional to the time derivative of the axion field; these effects are analogous to the spin Hall effect. A novel spin-orbit tensor, Λ_{ab}, emerges solely within a rotating reference frame, and is zero when the rotation axis is perpendicular to the angular momentum. The magnitude of this tensor is directly related to the rate of rotation and the spatial variation of the axion field, indicating a coupling between the axion dynamics and the spin polarization of the axion population.

Whispers of the Cosmos: The Axion’s Role in the Universe

The persistent mystery of the strong CP problem – the seemingly inexplicable absence of a predicted charge-parity violating term in the behavior of neutrons – finds a potential resolution in the hypothetical axion. This particle arises as a solution to this problem within extensions of the Standard Model of particle physics. Intriguingly, the same properties that make the axion a compelling candidate for solving the strong CP problem also position it as a prime dark matter constituent. Calculations suggest axions, created abundantly in the early universe, possess the necessary characteristics – weak interaction with ordinary matter and appropriate mass – to account for the observed abundance of dark matter. Therefore, a definitive detection of axions would simultaneously address a fundamental puzzle of particle physics and provide a concrete explanation for a significant portion of the universe’s missing mass, marking a monumental leap in cosmological understanding.

The search for dark matter extends beyond the leading axion candidate to include a broader class of particles known as axion-like particles (ALPs). Unlike the standard axion, which arises from a specific theoretical requirement to solve the Strong CP Problem, ALPs are more flexible, possessing a wider range of possible masses and interaction strengths. This expanded parameter space is crucial because dark matter’s properties remain unknown; ALPs offer a multitude of potential solutions, accommodating scenarios where the standard axion doesn’t quite fit the observed cosmological data. Consequently, experiments designed to detect ALPs aren’t limited to a narrow search range, but instead probe a vast landscape of possibilities, increasing the likelihood of uncovering the true nature of this elusive substance that makes up approximately 85% of the matter in the universe. The versatility of ALPs makes them a compelling focus for ongoing research and detector development.

The rigorous pursuit of axions and axion-like particles (ALPs) is profoundly impacting detector technology and theoretical physics far beyond the initial search. Developing the exquisitely sensitive instruments needed to detect these weakly interacting particles necessitates innovation in areas like superconducting circuits, cryogenic systems, and advanced materials science. These advancements aren’t limited to axion research; they find applications in diverse fields, including quantum computing and medical imaging. Simultaneously, the theoretical modeling required to predict axion properties and design effective detection strategies pushes the boundaries of particle physics and cosmology, refining calculations of fundamental constants and offering new insights into the early universe. This cross-pollination of techniques and knowledge is accelerating progress across multiple scientific disciplines, demonstrating that the search for dark matter is not merely a quest to identify a particle, but a catalyst for broader scientific and technological breakthroughs.

The ongoing pursuit of axions and axion-like particles represents more than just a search for new particles; it’s a fundamental re-evaluation of the universe’s building blocks and its trajectory. Current cosmological models rely heavily on the existence of dark matter, accounting for approximately 85% of the universe’s mass, yet its composition remains elusive. Should these efforts prove successful in identifying axions as a significant component of dark matter, it would necessitate a refinement of these models, offering insights into the formation of galaxies, the large-scale structure of the cosmos, and even the universe’s ultimate fate. Furthermore, understanding the properties of axions – their mass, interactions, and abundance – could unveil previously unknown connections between particle physics and cosmology, potentially resolving long-standing mysteries about the matter-antimatter asymmetry and the nature of dark energy, fundamentally reshaping our comprehension of the universe’s composition and evolution.

The pursuit of axion fields, as detailed in this theoretical framework, resembles a gaze into the abyss. It isn’t a claiming of knowledge, but an acknowledgment of how little is truly grasped. This work, exploring spin-dependent forces within rotating frames, doesn’t conquer the mysteries of dark matter-it observes the cosmos conquering the limits of current understanding. As Henry David Thoreau observed, “Not until we are lost in a forest can we begin to find ourselves.” The calculations regarding spin current density and the Foldy-Wouthuysen transformation are not endpoints, but rather markers indicating how far the boundaries of inquiry have receded, swallowed by the immensity of what remains unknown.

Where Do We Go From Here?

The presented formalism, while offering a pathway to model collective spin dynamics under axion influence, necessarily operates within the bounds of established quantum hydrodynamics. The expansion in powers of ħ, while standard, introduces an inherent limitation on the ability to capture genuinely strong-field effects. Should axion-fermion couplings prove unexpectedly large, the very foundations of the utilized approximations will require re-evaluation. One anticipates, therefore, that future work must address the validity of the employed expansion in regimes where non-perturbative corrections become significant.

Furthermore, the current analysis considers a simplified, homogeneous system. Extension to spatially inhomogeneous distributions, such as those found in galactic halos or within condensed matter environments, will inevitably introduce complexities related to gradient corrections and the treatment of boundary conditions. Modeling realistic dark matter distributions, replete with substructure and anisotropic velocity dispersions, presents a considerable challenge. The observed spin current density, as predicted by this framework, remains a largely theoretical construct awaiting definitive experimental verification.

Perhaps the most unsettling implication lies in the potential for subtle, frame-dependent effects. The Foldy-Wouthuysen transformation, while effective in decoupling particle and center-of-mass motion, does not entirely eliminate the influence of the chosen non-inertial frame. The universe, after all, possesses no preferred reference point. The search for dark matter, then, may ultimately reveal more about the limitations of observation itself than about the nature of the missing mass.

Original article: https://arxiv.org/pdf/2602.16627.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-02-19 06:58