The Axion’s Shadow: How Multiple Dark Matter Candidates Complicate the Search

Author: Denis Avetisyan

A new review examines how interactions between multiple axion-like particles could impact both their detectability and their role in solving the strong CP problem.

The study identifies scenarios where pairs of quantum chromodynamics (QCD) particles and dark axions circumvent existing detection projections, a phenomenon illustrated within the parameter space defined by the findings presented in Figure 5 and leveraging the labeling conventions established in Figure 6.

This paper explores the cosmological and phenomenological consequences of multi-axion scenarios, including anomalous couplings and the formation of domain walls.

The persistent mystery of dark matter and the strong CP problem motivates searches for the QCD axion, yet increasingly complex theoretical frameworks challenge its simple detection. This paper, ‘How well can the QCD axion hide?’, investigates the consequences of extending the Standard Model with multiple axion fields, revealing how their interplay modifies predicted couplings and cosmological signatures. We demonstrate that constraints on the QCD axion’s photon coupling, traditionally derived from domain wall arguments-requiring $E/N \geq 8/3$ -can be relaxed in multi-axion scenarios, potentially diminishing detectability even as other axion-like particles remain within reach of next-generation experiments. Given these nuanced parameter space effects, what regions offer the most promising avenues for finally unveiling-or concealing-the QCD axion?

The Universe Whispers: A Missing Component

The existence of dark matter is inferred from a wealth of astrophysical observations – from galactic rotation curves to the cosmic microwave background – yet its fundamental composition continues to challenge physicists. While comprising approximately 85% of the matter in the universe, dark matter does not interact with light, rendering it invisible to traditional detection methods. This persistent mystery has spurred intense investigation into various candidate particles, with the axion emerging as a particularly compelling possibility. Initially proposed as a solution to the strong CP problem in quantum chromodynamics, the axion possesses properties that naturally align with the requirements for cold dark matter. Ongoing experiments, employing sensitive detectors and utilizing strong magnetic fields, are actively searching for the faint signals that would confirm the axion’s existence and finally illuminate this elusive component of the cosmos.

The persistent conundrum of the strong CP problem – the unexpected absence of a charge-parity violating term in the strong nuclear force – unexpectedly offers a potential solution to the dark matter mystery. This problem led to the theoretical proposal of the QCD axion, a compelling dark matter candidate arising from a new symmetry breaking scale in the Standard Model. The axion’s properties, like its extremely weak interaction with ordinary matter, naturally align with the observed characteristics of dark matter. However, the QCD axion isn’t the sole contender; numerous alternative axion-like particles (ALPs) have emerged from various theoretical frameworks, including string theory and extra-dimensional models. These ALPs differ in their mass, coupling strengths, and production mechanisms, offering a broader landscape for potential dark matter detection efforts and necessitating diverse experimental approaches beyond those specifically designed for the QCD axion.

The prevailing theories surrounding axions as potential dark matter necessitate a specific cosmological timeline. These models largely depend on the assumption of a ‘Post-Inflationary Scenario,’ meaning axions weren’t produced during the universe’s initial, rapid expansion – inflation – but rather after it. This has profound implications for how these particles would have originated and populated the early universe. If produced post-inflation, axions are thought to have formed through a process called misalignment, where their initial quantum fluctuations gradually evolved into a coherent field. The density of axions produced this way is incredibly sensitive to the axion’s mass and the specific details of the post-inflationary universe, making precise calculations vital for comparing theoretical predictions with ongoing experimental searches. Without this specific cosmological context, predictions about the abundance and detectability of axion dark matter become unreliable, highlighting the interconnectedness of particle physics and cosmology in solving the dark matter puzzle.

Assuming the model accounts for all observed dark matter, minimal QCD axion photon coupling is constrained by current and future experiments (represented by solid, dotted, light, and hatched regions) across different scenarios defined by parameters <span class="katex-eq" data-katex-display="false">j_2</span>, <span class="katex-eq" data-katex-display="false">k_1</span>, and <span class="katex-eq" data-katex-display="false">k_2</span>, and dependent on the scaling of the dark axion mass as <span class="katex-eq" data-katex-display="false">(T/T_D)^{-\alpha}</span> with <span class="katex-eq" data-katex-display="false">\alpha \approx 0</span> or <span class="katex-eq" data-katex-display="false">\alpha \approx n</span>. — Assuming the model accounts for all observed dark matter, minimal QCD axion photon coupling is constrained by current and future experiments (represented by solid, dotted, light, and hatched regions) across different scenarios defined by parameters $j_2$ , $k_1$ , and $k_2$ , and dependent on the scaling of the dark axion mass as $(T/T_D)^{-\alpha}$ with $\alpha \approx 0$ or $\alpha \approx n$ .

The Seed of Darkness: Misalignment and the Axion Field

The misalignment mechanism postulates that dark matter arises from the zero-mode of an axion field initially displaced from its minimum energy configuration. This initial misalignment creates an energy density that evolves with the expansion of the universe; as the universe cools, the axion field oscillates around its minimum, effectively freezing out as cold dark matter. The resulting dark matter density is directly proportional to the initial misalignment angle $\theta_i$ and inversely proportional to the axion mass $m_a$ . Consequently, the observed dark matter abundance provides a strong constraint on the allowed parameter space of axion models, linking the axion mass and initial misalignment angle to the measured dark matter density of approximately $2.2 \times 10^{-{27}} \text{ kg/m}^3$ .

The generation of dark matter via the misalignment mechanism is fundamentally determined by the initial misalignment angle, $\theta_i$ , and the axion mass, $m_a$ . The misalignment angle represents the initial displacement of the axion field from its minimum energy state, while the axion mass dictates the oscillation frequency and, consequently, the energy density. Both parameters are intrinsically linked to the Quantum Chromodynamics (QCD) scale, $\Lambda_{QCD}$ , which governs the strength of strong interactions. Specifically, the axion mass is inversely proportional to the axion decay constant, $f_a$ , and $f_a$ is related to $\Lambda_{QCD}$ . Therefore, variations in the QCD scale directly influence the axion mass and, consequently, the predicted relic abundance of dark matter produced through this misalignment process. Precise knowledge of $\Lambda_{QCD}$ is thus crucial for accurately modeling and constraining viable axion dark matter candidates.

The relic abundance of axions produced via the misalignment mechanism serves as a crucial observational constraint for validating axion models. This abundance, dependent on the axion mass and initial misalignment angle, must match the observed dark matter density. Current calculations indicate that for QCD axions undergoing level crossings – transitions between different potential minima – the required mass to achieve this relic abundance falls within the range of up to $10^{-2} \text{ eV}$ . Consequently, experimental searches for axions are heavily guided by this mass range, focusing on detection techniques sensitive to axions with these specific properties to confirm or refute the misalignment mechanism as a viable dark matter production pathway.

The parameter space reveals viable axion masses and dark matter abundance ratios, constrained by supernova observations (green line) and dependent on whether axion masses are temperature-independent (left) or follow a power law similar to QCD axions (right).

Echoes of Symmetry: Cosmic Strings and Domain Walls

Multi-axion dark matter models, positing the existence of more than one axion particle, predict the spontaneous formation of Cosmic Strings during symmetry breaking in the early universe. These Cosmic Strings are one-dimensional topological defects, representing locations where the axion field’s value is undefined; their tension and energy density are determined by the axion decay constant and the symmetry breaking scale. Importantly, these strings contribute to the overall dark matter density and, through gravitational effects, influence the distribution of dark matter on cosmological scales. Simulations indicate that the network of Cosmic Strings will scale as the inverse of the cosmic time, potentially leaving observable signatures in the cosmic microwave background and large-scale structure.

Cosmic Strings, initially formed in multi-axion models, are not static entities; they can undergo further evolution resulting in String Bundles. These bundles arise from the interaction and winding of multiple Cosmic Strings around each other, effectively increasing the dimensionality and complexity of the resulting topological defects. The formation of String Bundles contributes to a more nuanced dark matter distribution than that predicted by isolated Cosmic Strings, potentially providing additional gravitational lensing signatures and affecting the overall power spectrum of density fluctuations. The increased structural complexity introduced by these bundles requires more sophisticated simulations to accurately model their impact on cosmological observables and differentiate these models from simpler scenarios.

Domain walls are topological defects that can arise in multi-axion models due to symmetry breaking. Their formation presents a cosmological challenge as they contribute significantly to the energy density of the universe, potentially exceeding observational limits. To ensure cosmological viability within this analysis, the number of domain walls is constrained to 1. This specific configuration minimizes their overall contribution to the universe’s energy density while still allowing for their potential observational signatures, such as gravitational lensing or contributions to the cosmic microwave background. The maintenance of this low domain wall number is a key assumption in evaluating the feasibility of these multi-axion dark matter models.

Cosmic string networks evolve differently depending on which potential-dark matter or quantum chromodynamics (QCD)-dominates first, with QCD dominance leading to the formation of cosmic bundle structures under the assumption <span class="katex-eq" data-katex-display="false">j_2 = 2j</span>. — Cosmic string networks evolve differently depending on which potential-dark matter or quantum chromodynamics (QCD)-dominates first, with QCD dominance leading to the formation of cosmic bundle structures under the assumption $j_2 = 2j$ .

The Hunt for Ghosts: Helioscopes and Haloscopes Illuminate the Darkness

The elusive nature of axions necessitates inventive detection strategies, prominently featuring Helioscope Experiments. These experiments operate on the premise that axions are produced within the Sun’s core via quantum processes, and subsequently stream outwards. By precisely aiming detectors at the Sun, researchers seek to capture the faint signature of these solar axions as they interact with strong magnetic fields. This interaction, predicted by theoretical models, induces a conversion of axions into detectable photons. The challenge lies in distinguishing this exceedingly weak signal from background noise, demanding highly sensitive detectors and meticulous shielding. Success in this endeavor would not only confirm the existence of axions, but also offer insights into the Sun’s internal workings and the fundamental laws governing particle physics.

Haloscope experiments represent a distinct approach to axion detection, relying on the predicted conversion of these elusive particles into detectable photons within a strong magnetic field. These experiments utilize highly sensitive resonant cavities, precisely tuned to encourage photon production if axions are present. As an axion traverses the magnetic field, it interacts with the cavity, potentially converting into a photon with a frequency determined by the cavity’s resonant mode. By systematically scanning the resonant frequency and monitoring for faint photon signals, haloscopes aim to establish evidence for the existence of axions, even those comprising a subdominant fraction of dark matter. The strength of the signal is intrinsically linked to the axion’s coupling to photons and the volume of the resonant cavity, driving ongoing efforts to construct larger and more sensitive haloscope detectors.

The ability of both helioscope and haloscope experiments to detect axions hinges critically on the strength of the particle’s coupling to photons – a fundamental property dictating how readily an axion transforms into a detectable photon. Current experimental sensitivity is limited by a lower bound of $10^{-{15}} \text{ GeV}^{-1}$ for this photon coupling strength; this represents the minimum interaction level that these instruments can currently resolve. Importantly, this detection threshold applies even in scenarios where the dominant form of axion isn’t the widely discussed QCD axion, meaning these experiments can still probe a broader range of theoretical axion-like particles, expanding the potential for discovery beyond specific models.

The parameter space explored in Figure 5 reveals variations in the coupling between QCD axions and photons.

Beyond the Standard Echo: A Wider Landscape for Dark Matter

The search for dark matter increasingly investigates scenarios beyond the traditionally favored single-axion model. Current research explores ‘multi-axion’ frameworks, positing that dark matter may be composed of multiple axion-like particles, each with differing masses and coupling strengths. Crucially, the parameter space for these searches is significantly broadened when considering the ‘Dark Confinement Scale’ – a theoretical energy level associated with the strong interaction within the dark sector. This scale dictates the masses and interactions of dark matter particles, influencing their detectability. A lower Dark Confinement Scale implies lighter axions and weaker interactions, requiring more sensitive detectors, while a higher scale suggests heavier particles more readily observable through existing experiments. By incorporating the Dark Confinement Scale into multi-axion models, scientists can map out a more comprehensive landscape for dark matter detection, increasing the probability of finally identifying the elusive substance that comprises a significant portion of the universe.

The accurate determination of level crossing phenomena represents a pivotal step towards unraveling the intricacies of axion dark matter. These crossings, occurring as parameters within axion models are varied, manifest as sharp changes in the solutions to the Schrödinger equation governing the axion field. Consequently, precise measurements of these level crossings allow researchers to rigorously test the validity of theoretical predictions and constrain the parameter space of possible axion models. Discrepancies between predicted and observed crossing points can immediately highlight flaws in the theoretical framework, prompting refinements and guiding future searches. Furthermore, the sensitivity of these crossings to subtle changes in model parameters enables the potential discovery of previously unknown axion properties and interactions, offering a pathway to a more complete understanding of dark matter’s composition and behavior.

The pursuit of dark matter’s true nature necessitates a synergistic approach, uniting increasingly sophisticated theoretical frameworks with the capabilities of next-generation experimental facilities. Current investigations into axion models-leading candidates for dark matter-suggest that the interaction between dark matter axions and photons may be weaker than previously anticipated, potentially due to the influence of Grand Unified Theories (GUTs). This suppression of the axion-photon coupling presents a significant challenge for detection, requiring experiments to push sensitivity boundaries and explore novel search strategies. Future progress hinges on refining theoretical predictions-particularly those incorporating GUT symmetries-and deploying experiments capable of probing the extended parameter space dictated by multi-axion models and the Dark Confinement Scale, ultimately aiming to reveal the fundamental properties of these elusive particles and finally illuminate the composition of the dark universe.

The results, analogous to those in Figure 8, demonstrate the same trends but are specifically for the dark axion photon coupling.

The exploration of multi-axion dynamics reveals a universe far more interconnected than initially assumed. This paper’s focus on anomalous couplings and domain walls demonstrates how seemingly isolated fields can exert profound influence on one another, shaping the landscape of dark matter detectability. It echoes a sentiment captured by Jean-Paul Sartre: “Hell is other people.” While applied to interpersonal relationships, the principle resonates here; the existence of multiple axion fields, interacting and influencing each other’s behavior, complicates the search for a singular, isolated solution to the strong CP problem. The system doesn’t simply exist; it’s defined by its dependencies, a network where the fate of one field is inextricably linked to the others.

What Lies Beyond the Horizon?

The proliferation of axion candidates, as this work demonstrates, isn’t a solution-it’s a deferral. The strong CP problem, and the dark matter mystery it attempts to address, were never singular puzzles demanding elegant solutions. They are symptoms of a deeper, structural incompleteness. Each added axion field, each proposed interaction, merely expands the parameter space where failure can hide. Architecture is, after all, how one postpones chaos, not defeats it.

Future explorations will inevitably focus on the interplay between these fields. The cosmological consequences of multi-axion dynamics – the formation and decay of domain walls, the subtle shifts in dark matter density – are not merely technical challenges. They are emergent properties of a system striving, inevitably, toward entropy. There are no best practices – only survivors, those configurations that linger longest before succumbing to the inevitable.

The hunt for the axion, then, transcends particle physics. It becomes a study in the resilience of order-a temporary reprieve from the universe’s fundamental indifference. Order, it should be remembered, is just cache between two outages. The true question isn’t whether an axion exists, but how long can any semblance of stability endure.

Original article: https://arxiv.org/pdf/2604.08657.pdf

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