⚛️ phenomenology

New approach to the estimation of the lowest boundary of an axion mass

This paper theoretically estimates the lowest boundary of the axion mass to be greater than 5.885 microelectron-Volts by analyzing the energy spectrum of electrons in magnetic fields and applying these results to hyperfine transitions in hydrogen atoms and solar axion emission.

Original authors: Sevinj O. Huseynova, Vali A. Huseynov, Nigar E. Musazade, Sevinj Y. Rzayeva

Published 2026-07-17✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Sevinj O. Huseynova, Vali A. Huseynov, Nigar E. Musazade, Sevinj Y. Rzayeva

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 by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is filled with a mysterious, invisible fog that we can't see, touch, or smell, yet it holds the galaxies together. Scientists call this "dark matter," and for decades, they've been hunting for its identity. One of the most popular suspects is a ghostly particle called the axion. Think of an axion as a tiny, shy messenger that barely interacts with anything else in the universe, making it incredibly hard to catch. To solve a deep puzzle in physics about why the universe behaves the way it does, these axions must have a very specific, tiny weight (or mass). If they are too light, they might not exist at all; if they are too heavy, they break the rules of how stars and atoms work. Figuring out exactly how heavy an axion can be is like trying to find the perfect weight for a key that unlocks the secrets the cosmos. If we get the weight wrong, the key won't fit the lock.

In this paper, a team of researchers from Azerbaijan develops a method to determine the lowest possible weight an axion could have. They don't use a giant telescope or a massive particle collider; instead, they use a clever thought experiment involving the most famous atom in the universe: the hydrogen atom. They look at how an electron (the tiny particle orbiting the atom) behaves when it's in a magnetic field. They know that if an axion is too light, an electron in a hydrogen atom would constantly "spit out" an axion, losing energy and causing the atom to fall apart. But we know hydrogen atoms are stable and don't just fall apart. So, the authors argue, the axion must be heavy enough that the electron can't spit it out. By calculating the exact energy difference between the electron's spin states in a hydrogen atom, they determine a "floor" for the axion's mass. They conclude that an axion must weigh at least 5.885 × 10⁻⁶ eV. If it were any lighter, our hydrogen atoms would be unstable, and the universe would look very different.

The researchers also look at the Sun, specifically the dark, cool patches on its surface called sunspots, where magnetic fields are strong. They suggest that if axions are being emitted by electrons in these sunspots, the magnetic field strength there gives us a clue that the axion mass is likely around 10⁻⁵ eV. This is a bit heavier than their calculated minimum, which fits nicely with their theory. Essentially, they are saying: "If axions exist and are this light, hydrogen atoms would be falling apart, which they aren't. Therefore, axions must be at least this heavy." It's a way of using the stability of the atoms around us to set a safety limit on how light these cosmic ghosts can be.

Technical Summary: New Approach to the Estimation of the Lowest Boundary of an Axion Mass

Problem Statement
The determination of the axion mass remains a critical unresolved issue in Particle Physics, Astrophysics, and Cosmology. While various models (such as KSVZ and DFSZ) and experimental constraints (from CAST, CAPP, and astrophysical observations) have narrowed the plausible mass range, the specific theoretical lower boundary for the axion mass has not been definitively established. This paper addresses the question of how to theoretically determine the lowest possible boundary for the axion mass ( $m_a$ ) and what that value is.

Methodology
The authors propose a theoretical framework based on the conservation of energy and the stability of the hydrogen atom. The methodology proceeds through three interconnected physical analyses:

Electron in a Magnetic Field: The authors analyze the energy spectrum of an electron in a constant, homogeneous magnetic field ( $H$ ), explicitly accounting for the electron's anomalous magnetic moment ( $a_e$ ). They derive the energy difference ( $\Delta E_L$ ) between two adjacent Landau sublevels corresponding to different spin projections ( $\zeta = \pm 1$ ).
Magnetic Moment Reversal: They calculate the maximum potential energy difference ( $\Delta U$ ) associated with the reversal of an electron's magnetic moment in an external magnetic field, confirming it coincides with the maximum Landau level transition energy.
Hyperfine Structure in Hydrogen: The core of the argument applies these concepts to the hydrogen atom. The electron in hydrogen exists in the Coulomb field of the proton and the magnetic field generated by the proton's magnetic moment ( $\mu_p$ ). The authors examine the hyperfine structure splitting of the $s$ -levels, specifically the triplet-singlet transition ( $S=1$ to $S=0$ ).

Key Physical Argument
The central premise is that if the axion mass were less than or equal to the maximum energy difference available in a specific physical transition, the electron in that system would continuously emit axions to reach a lower energy state. Such continuous emission would render the hydrogen atom unstable, contradicting experimental observation.

Therefore, the condition for the stability of the hydrogen atom imposes a lower bound on the axion mass:
$m_a > (\Delta E_{hf})_{max}$
where $(\Delta E_{hf})_{max}$ is the maximum energy difference corresponding to the triplet-singlet transition in the hydrogen atom's ground state ( $n=1$ ), calculated with allowance for the electron's anomalous magnetic moment.

Key Contributions and Results

Derivation of the Lower Bound: By equating the maximum energy difference in the Landau sublevel transitions (and magnetic moment reversal) to the hyperfine splitting energy, the authors derive an expression for the lowest boundary of the axion mass ( $m_a^{lb}$ ) in terms of fundamental constants:
$m_a^{lb} = \frac{8}{3} \alpha^4 k_p (1 + a_e) \frac{m_e^2}{m_p}$
where $\alpha$ is the fine-structure constant, $k_p$ is the proton g-factor, $a_e$ is the electron anomalous magnetic moment, and $m_e$ and $m_p$ are the electron and proton masses, respectively.
Numerical Estimation: The calculation yields a specific numerical value for the lowest boundary:
$m_a > 5.885 \times 10^{-6} \text{ eV}$
Magnetic Field Constraint: The paper establishes a relationship between the axion mass and the minimum magnetic field strength ( $H_{min}$ $H_{min}$ ) required for axion synchrotron emission ( $e^- \to e^- + a$ $e^{-} \to e^{-} + a$ ) to occur. The authors find that $H_{min}$ $H_{min}$ is directly determined by the axion mass.
- For the calculated lower bound ( $m_a^{lb}$ ), the minimum magnetic field strength is approximately $5.079 \times 10^2$ Gauss.
- The paper notes that if axions are emitted by electrons in solar sunspots (where magnetic fields reach $\sim 10^3 - 10^4$ Gauss), the axion mass would likely fall in the range of $\sim 10^{-5}$ eV.

Significance and Claims
The paper claims to provide a theoretical method for establishing the lowest boundary of the axion mass based on the stability of the hydrogen atom. The authors conclude that the axion mass must be greater than $5.885 \times 10^{-6}$ eV; otherwise, the hydrogen atom would be unstable due to continuous axion emission driven by the interaction between the electron and proton magnetic moments.

Furthermore, the work suggests that the minimum magnetic field strength required for axion emission is a function of the axion mass. By correlating this with observed magnetic fields in solar sunspots, the authors estimate a likely lower boundary for the axion mass in the range of $\sim 10^{-5}$ eV. This result is presented as consistent with existing experimental constraints, such as those from the CAST experiment. The authors emphasize that this approach offers a theoretical determination of the lower mass limit, addressing a persistent puzzle in modern physics.

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