Researchers propose utilizing muonium, a fleeting particle composed of a muon and electron, as a novel quantum sensor to search for axion dark matter. Combining theoretical calculations with simulation results, the team demonstrates that a muonium-based experimental approach could tighten constraints on the axion-muon coupling beyond current limits from muon g-2 measurements, specifically for axion masses between 18 and 130 μeV. This work establishes a new spectroscopic channel in muonium that enables searches for axion and axion-like particle dark matter, offering a complementary path to existing dark matter detection efforts.

Muonium Spectroscopy Probes Axion Dark Matter

High-intensity muon beams offer a pathway to detecting axion dark matter through a Muonium-based Axion Search utilizing resonant quantum transitions between hyperfine states, a technique the authors term MASH. This potential improvement stems from a novel spectroscopic channel established within muonium, opening a new avenue for probing axion and axion-like particle dark matter candidates. The proposed experiment uses the unique properties of muonium, an atom comprised of a muon and an electron, to function as a quantum sensor sensitive to the subtle influence of dark matter.

Astrophysical observations indicate that approximately 27% of the universe’s total energy density is composed of dark matter, yet its fundamental nature remains elusive; current detection methods rely on either direct detection of Weakly Interacting Massive Particles (WIMPs) or indirect searches for axions. Muonium spectroscopy offers a complementary laboratory probe, independent of supernova modeling and virtual-loop interpretations that affect other techniques, allowing researchers to explore a poorly accessible coupling sector.

The rate of resonant quantum transitions within muonium is predicted to be proportional to the square of the axion-muon coupling strength when an energy gap matches the axion’s mass. Specifically, the experiment aims to detect resonant transitions induced by the oscillating axion dark matter field within a controlled atomic system.

The induced signal events are calculated as (g_(aμ)^(2L))_(DM)^(2ρ)NT, where R represents the transition rate per muonium, $t_{i}$ is the interaction time, NT denotes the muonium intensity, and T is the total measurement time. The sensitivity of this method hinges on the axion-muon coupling, $g_{a μ}$ , the length of the magnetic field region, L, and the local dark matter density, $ρ_{D M}$ , which is estimated to be around 0.3 to 1.0 GeV/cm³.

This reliance on multiple parameters allows for a nuanced understanding of the interaction between axions and the muonium atom. The effective interaction between axions and leptons within muonium is described by the equation = μ,e) $g_{a l} (m_{a σ})_{l} \cdot v_{a}$ $a_{0}$ sin(ω_at), where $v_{a}$ represents the axion velocity, approximately (10)^(-2)c in this setup, and $a_{0}$ = $\sqrt{2 ρ_{D M}} / m_{a}$ denotes the axion field amplitude.

The center angular frequency of the dark matter field, $ω_{a}$ , is approximately equal to the axion mass, $m_{a}$ , accounting for the velocity of the dark matter particle. When the Zeeman splitting energy gap, Δ E≈ 9.23 + 57.67B + 9.23 sqrt(1 + (6.31B)^2) microelectronvolts, matches the axion mass, resonant transitions occur between the $m_{F}$ = 0 and $m_{F}$ = 1 states.

The team, comprised of researchers from the Advanced Energy Science and Technology Guangdong Laboratory, the Institute of Modern Physics, CAS, and several universities in China and the United Kingdom, has combined theoretical modeling with simulation results to validate this approach. This method offers a distinct advantage over existing dark matter searches, as muon g-2 measurements are sensitive to virtual axion or ALP loop effects, but the resulting bounds are model dependent.

Astrophysical limits, derived from observations of supernova SN1987A, constrain axion emission from supernova cores, but rely on complex modeling of dense nuclear matter, neutrino transport, and muon abundance. By utilizing a controlled laboratory environment, muonium spectroscopy bypasses these uncertainties, providing an independent verification of axion properties. The ability to probe axions with masses between 18 and 130 microelectronvolts represents a step in the ongoing effort to unravel the mysteries of dark matter and its interactions with ordinary matter.

Axion-Muon Coupling Limits from Muon g-2 & Astrophysics

Muonium, a hydrogen-like atom composed of a muon and an electron, presents an ideal platform for precision tests beyond the Standard Model due to its purely leptonic nature. The team’s work focuses on measuring ALP-induced transitions involving muons, a coupling currently less explored than axion-electron or axion-photon interactions due to the muon’s short lifespan and associated experimental challenges.

The spin flip of the muonium system provides a distinct experimental signature, allowing for the selective ionization and detection of ALP-excited muonium atoms, resulting in an excess counting rate at the ALP resonance condition. A signal of approximately ten events, the researchers estimate, would allow sensitivity to the ALP-muon coupling.

Optimization of the experimental setup involved a two-parameter scan over the injection energy and magnetic field length, L, assuming a local dark matter density of 0.3 GeV/cm^3. The analysis revealed a trade-off: lower energy enhances conversion but increases decay losses due to reduced velocity, while a longer magnetic field length extends interaction time but also amplifies beam divergence. The resulting sensitivity, calculated according to a specific equation, approaches the current limit deduced from the discrepancy between experimental measurement and theoretical prediction of the muon g-2 for one month of data acquisition.

The interaction between ALPs and leptons, both muons and electrons, is described by a Lagrangian: ℒ
int
=
−
∑
l
=
μ,
e
$g_{l}$
$f_{a}$
∂_μ
a
ψ
¯
l
$γ^{μ}$
$γ^{5}$
ψ_l, where g_l represents model-dependent couplings of order one, f_a is the axion decay constant, and ψ_l denotes the fermion fields, with a representing the ALP field. This framework allows for a precise understanding of how ALPs interact with fundamental particles within the muonium system.

The data collected during the experiment will be made available from the authors upon reasonable request, furthering the potential for collaborative analysis and validation of the findings. This innovative technique promises to complement existing dark matter searches and potentially reveal the elusive nature of axions, contributing to a more complete understanding of the universe’s hidden mass.

Muonium as a Precision Sensor Beyond the Standard Model

This experimental technique establishes a novel spectroscopic channel within muonium, offering a complementary search method for these elusive particles across an axion mass range of 18-130 μeV. The binary nature of muonium spin states provides a distinct advantage, enabling rapid spin switching and suppressing systematic backgrounds through clear state discrimination, a feature that enhances the sensitivity of experiments probing new physics. Development of muon facilities, including the HIMB project and the China Initiative Accelerator Driven System, are projected to deliver muon intensities exceeding (10)^(10) muons per second, significantly expanding opportunities for precision muonium experiments.

This work presents a comprehensive study of muonium as a precision probe for ALPs, proposing an experimental design optimized to measure ALP-induced transitions involving muons; current laboratory constraints on the axion-muon coupling largely stem from comparisons between Standard Model predictions and experimental measurements of the muon g-2 anomaly, but these bounds are model-dependent and susceptible to cancellation effects from additional couplings or new states. Detailed simulations, performed using the musrSim package based on Geant4, validated the experimental design and optimized key parameters, including a 10 nm thick carbon foil target. The model incorporated muonium formation through muon interactions in the carbon foil, accounting for energy loss and secondary electron emission, and was benchmarked against previous work conducted at the Paul Scherrer Institute.

Performance quantification under representative conditions revealed that multiple scattering in the carbon foil dominated the emittance of the outgoing muonium beam, constraining the achievable spot size at the detector. The availability of high-intensity muon beams is essential for realizing the full potential of muonium spectroscopy as a precision sensor.

Resonant Hyperfine Transitions Detect Axion-Like Particles

A resonant energy gap within muonium atoms, exotic bound states of an electron and a muon, could reveal axion-like particles (ALPs), according to new simulations detailed in recent work. Researchers propose that by precisely measuring transitions between hyperfine states in muonium, they may surpass existing limits on the coupling strength between muons and these hypothetical dark matter candidates, potentially probing a mass range of 18 to 130 micro-electron volts.

This approach offers a direct search method, differing from constraints derived from muon g-2 measurements which are subject to model-dependent interpretations. The experiment relies on inducing transitions between specific muonium energy levels when the energy gap between them aligns with the mass of an ALP. Achieving sufficient sensitivity hinges on maintaining a stable magnetic field, with simulations indicating fluctuations below 0. 3 Gauss are necessary to match a transit-time broadening of 0. 5 MHz.

Maintaining this field without crossing zero is also critical to prevent unintended transitions between hyperfine states. The experimental design incorporates a solenoid magnet to create the necessary field, with muonium atoms entering a scan region after initial formation and filtering. The simulations, built using the musrSim package based on Geant4, validated the feasibility of this approach and demonstrated effective suppression of background signals. Optimal beam and field parameters were identified through detailed modeling, ensuring the experiment’s sensitivity to the target ALP mass range.

The predicted Zeeman splitting energy gap, approximately 9. 23 + 57. 67B + 9. 23 sqrt(1 + (6. 31B)^2) microelectronvolts, where B is the magnetic field strength, is key to this resonant detection. The potential to exceed current dark matter detection limits stems from the ability to accumulate larger statistics than possible with indirect methods like the muon g-2 bound.

While the muon g-2 provides the strongest existing constraints from terrestrial experiments, its interpretation relies on theoretical assumptions. “Using the Geant4 simulation framework, we validated the feasibility of the design, demonstrated effective background suppression, and identified optimal beam and field parameters,” the authors write, highlighting the thoroughness of their simulations.

The success of this technique is contingent on access to high-intensity muon beams, a resource becoming increasingly available with the development of next-generation facilities. The simulations confirm that the proposed design effectively minimizes background noise and optimizes signal detection. The team’s work demonstrates a clear pathway toward tightening constraints on the elusive nature of ALPs, potentially revealing their contribution to the universe’s hidden mass.

👉 More information
🗞 Muonium Spectroscopy as a Quantum Sensor for Axion Dark Matter
✍️ Feng Fang, Kim Siang Khaw, Ce Zhang, Qiaoli Yang, Liangwen Chen, Jie Yang, Lei Yang and Zhiyu Sun
🧠 DOI: http://link.aps.org/doi/10.1103/483j-ct1h

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