Muonium-Antimuonium Conversion (MACE)

• Muonium-to-antimuonium conversion is a charged lepton flavor violation process that, if observed, would indicate new physics beyond the Standard Model.
• MACE utilizes high-intensity muon beams, enhanced vacuum muonium production, and a triple-coincidence detection system to achieve a sensitivity near 1.3×10⁻¹³ for the conversion probability.
• The experiment’s design incorporates magnetic-field analyses and advanced background suppression techniques to directly test mediator models such as doubly charged scalars and flavor-violating Z' bosons.

The Muonium-to-Antimuonium Conversion Experiment (MACE) is a proposed search for the spontaneous conversion of muonium, $M=\mu^+e^-$, into antimuonium, $\overline{M}=\mu^-e^+$, a charged lepton flavor violation process whose observation would constitute clear evidence for physics beyond the Standard Model. The program combines high-intensity $\mu^+$ beams, improved muonium production in vacuum, and coincidence detection of the antimuonium decay products, with the stated aim of improving the sensitivity to the conversion probability by more than two orders of magnitude relative to the PSI bound from 1999 (Bai et al., 2022).

1. Physics motivation and conceptual significance

Muonium-to-antimuonium conversion occupies a distinctive place within charged lepton flavor violation because the initial and final states are purely leptonic bound states. That feature makes the process theoretically clean and minimizes hadronic uncertainties, so any nonzero signal can be interpreted directly in terms of new interactions in the charged-lepton sector. The whitepaper literature places the process in the broader context of neutrino oscillations, type-II seesaw constructions, Higgs-triplet scenarios, doubly-charged scalars, and other beyond-Standard-Model mechanisms that naturally generate charged lepton flavor violation at potentially observable rates (Bai et al., 2022).

The Standard Model expectation is effectively zero at experimental scales. A dedicated calculation in the minimally extended Standard Model with massive neutrinos gives $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$ for the Dirac case and $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$ for the Majorana case, while the pseudo-Dirac scenario can enhance the rate relative to the pure Dirac case but still remains far below foreseeable sensitivity (Ghosh et al., 7 Apr 2025). This makes the channel qualitatively different from searches in which irreducible Standard Model contributions are merely small rather than negligible.

A common misconception is that neutrino-mass effects alone might generate an observable transition rate once beam intensity becomes sufficiently high. The current theoretical assessments do not support that expectation. Within the minimally extended Standard Model, an observation at the sensitivity targeted by MACE would indicate additional new physics rather than a direct manifestation of ordinary neutrino mass effects (Ghosh et al., 7 Apr 2025).

2. Transition formalism and effective description

The conversion is conventionally described as an oscillation between $|M\rangle$ and $|\overline{M}\rangle$, analogous to neutral-meson mixing, and governed by a $2\times 2$ Hamiltonian whose off-diagonal terms arise from lepton-flavor-violating and, in some formulations, $\Delta L=2$ interactions. In the whitepaper formulation, the dimensionless mixing parameters are

$$x=\frac{\Delta m}{\Gamma},\qquad y=\frac{\Delta\Gamma}{2\Gamma},$$

with $\overline{M}=\mu^-e^+$0, and the time-integrated conversion probability is written as

$\overline{M}=\mu^-e^+$1

This parameterization is useful because it directly connects an experimental limit on the conversion probability to effective operator coefficients or mediator parameters in a broad class of models (Bai et al., 2022).

A more explicit low-energy description uses four-fermion operators,

$\overline{M}=\mu^-e^+$2

with the canonical basis

$\overline{M}=\mu^-e^+$3

Current experimental limits are often quoted as bounds on particular combinations of these $\overline{M}=\mu^-e^+$4 coefficients rather than on a single model parameter (Fukuyama et al., 2021).

Magnetic-field analyses further reduce the relevant parameter space. For the $\overline{M}=\mu^-e^+$5 ground state, only two independent combinations contribute, namely

$\overline{M}=\mu^-e^+$6

and $\overline{M}=\mu^-e^+$7. Their relative physical phase enters interference terms and can, in single-neutral-mediator scenarios, be related to the electron electric dipole moment. This is one reason the field dependence of the transition probability is not merely an experimental detail but an element of model discrimination (Fukuyama et al., 2023).

3. Experimental program, signal topology, and projected reach

The benchmark experimental reference remains the PSI result,

$\overline{M}=\mu^-e^+$8

which has stood for more than two decades. MACE is designed to move beyond that level by more than two orders of magnitude, and the conceptual design frames the target reach as a conversion probability beyond the level of $\overline{M}=\mu^-e^+$9 (Bai et al., 2022, Bai et al., 2024).

The detection concept is built around the decay signature of antimuonium. The whitepaper describes a triple-coincidence strategy based on the simultaneous detection of a 52.8 MeV Michel electron from $\mu^+$0 decay and an atomic-shell positron of approximately 13.5 eV, together with the positron-annihilation photons. The corresponding detector elements are a magnetic spectrometer for charge and momentum identification, a microchannel plate for the low-energy positron, and an electromagnetic calorimeter for the annihilation photons (Bai et al., 2022).

The beam and source strategy is correspondingly aggressive. The whitepaper discusses new or proposed high-power muon beams at the China Spallation Neutron Source through the EMuS project and possible beams at CiADS, with beam intensities of up to $\mu^+$1 envisioned (Bai et al., 2022). The conceptual design gives an explicit sensitivity estimate for a one-year run at $\mu^+$2: with $\mu^+$3 muonium decays in vacuum and a total signal efficiency of $\mu^+$4, the single-event sensitivity is stated as

$\mu^+$5

with the expected background below one event (Bai et al., 2024).

This design philosophy is closely tied to the time structure of the signal. The conversion probability grows with time before the muon decays, while accidental backgrounds fall exponentially. Earlier reviews had already emphasized that late-time selection improves signal-to-background separation, especially in pulsed-beam environments (Jungmann, 2016). MACE adopts that logic in a detector architecture optimized for both timing and topology.

4. Muonium production and detector subsystems

The experiment’s projected sensitivity depends critically on vacuum muonium production. A dedicated simulation study of perforated silica aerogel modeled muonium formation and diffusion with a 3D off-lattice random walk and reported a maximum muonium emission efficiency of $\mu^+$6 and a maximum vacuum yield of $\mu^+$7 with a typical surface muon beam, corresponding to a 2.6 times and a 2.1 times enhancement, respectively (Zhao et al., 2023). The conceptual design also discusses a multi-layer aerogel target in which about $\mu^+$8 of stopped $\mu^+$9 form muonium in vacuum. This suggests that quoted yields are design- and beam-condition dependent (Bai et al., 2024).

The positron transport system is a central MACE-specific innovation. It consists of an electrostatic accelerator and a solenoid beamline, including an S-shaped transport solenoid and a collimation stage tuned to reject higher-transverse-momentum backgrounds. Field simulations in COMSOL and transport simulations based on Geant4 give a geometric acceptance of the signal at $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$0, a position resolution of $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$1, and a transit time of $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$2 with a spread of $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$3. The same study states that the time-of-flight discrimination enables rejection of internal conversion backgrounds by a factor of $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$4 (Lu et al., 11 Aug 2025).

The calorimetric system is likewise specialized for the positron-annihilation signature. A near-$$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$5 CsI(Tl) calorimeter based on a Class I Goldberg polyhedron $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$6 was designed with 622 modules and $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$7 coverage of $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$8 solid angle after beam apertures are removed. Detailed Monte Carlo studies using MACE offline software based on Geant4 report an energy resolution of $$P(M\to\bar{M})_{\text{Dirac}}\approx 2.2\times 10^{-95}$$9 at 511 keV and a total signal efficiency of $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$0 for annihilation $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$1-ray events (Chen et al., 2024).

These subsystem studies are not auxiliary engineering notes; they define the experiment’s attainable reach. In MACE, the low-energy positron is not a secondary embellishment to the fast electron channel but the decisive discriminator that makes a background-suppressed search feasible.

5. Backgrounds, irreducible limitations, and magnetic-field effects

The dominant reducible backgrounds are standard muon decays, accidental coincidences, cosmic rays, and the rare Standard Model process $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$2. The whitepaper states that the rare Standard Model decay has a small branching fraction and a further negligible impact once energy and momentum cuts and detector resolution are taken into account (Bai et al., 2022). The calorimeter study similarly reports cosmic-ray backgrounds negligible after geometrical and veto cuts, with fewer than two events per year (Chen et al., 2024).

Internal conversion backgrounds receive additional suppression from the positron transport system. Because the signal positron is an atomic positron of order 13.6 eV, whereas internal-conversion positrons are much more energetic, the transport optics and time-of-flight window provide a strong kinematic filter. The dedicated transport study summarizes the total internal-conversion background selection efficiency as $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$3, corresponding to seven orders of magnitude of suppression (Lu et al., 11 Aug 2025).

A more subtle issue is the irreducible QED floor from hard Bhabha scattering. In an ordinary muonium decay, a fast positron and the bound electron can exchange energy through internal Bhabha scattering, thereby producing the same slow-$$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$4 plus fast-$$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$5 topology as an antimuonium decay. A 2025 analysis computes this rate and concludes that it is negligible for MACE, but becomes larger than the signal for conversion probabilities less than $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$6. The same work shows that measuring the helicity of the fast electron would reduce the floor to $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$7 (Ghosh et al., 29 Oct 2025).

Magnetic fields are not only relevant for charged-particle transport but also enter the conversion probability itself by lifting the degeneracies of the muonium hyperfine states. The field-dependent analysis identifies characteristic probability ratios for different mediator classes: $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$8 for doubly charged scalars, $$P(M\to\bar{M})_{\text{Majorana}}\approx 8.0\times 10^{-56}$$9 for doubly charged vectors, and a continuous range from $|M\rangle$0 to $|M\rangle$1 for neutral mediators (Fukuyama et al., 2023). This makes the operating field of MACE part of the physics interpretation, not merely part of the apparatus.

6. Model interpretation, complementarity, and broader impact

The principal value of MACE is that an experimental bound on $|M\rangle$2 maps efficiently onto broad families of beyond-Standard-Model scenarios. In the most general Standard Model gauge-invariant bilepton framework with $|M\rangle$3 couplings, the projected MACE sensitivity is described as the most powerful probe of the $|M\rangle$4 charged-lepton-flavor-violating coupling for mediator masses up to several TeV, exceeding current or near-future collider reach in the $|M\rangle$5–$|M\rangle$6 sector (Li et al., 2021).

Specific model studies sharpen that statement. For a doubly charged Higgs in type-II seesaw-like settings, one analysis finds that after imposing $|M\rangle$7 and $|M\rangle$8 constraints, the minimal type-II seesaw predicts a conversion probability below $|M\rangle$9, beyond MACE sensitivity, whereas a hybrid seesaw scenario permits MACE to probe doubly-charged Higgs masses up to 3 TeV for fixed $|\overline{M}\rangle$0 eV and to reach $|\overline{M}\rangle$1 eV for fixed $|\overline{M}\rangle$2 (Han et al., 2021). In models with doubly charged scalars relevant to neutrinoless double beta decay, the pattern of observation between $|\overline{M}\rangle$3 and muonium-antimuonium conversion distinguishes Liu-Gu, Zee-Babu, and hybrid or soft-breaking realizations (Fukuyama et al., 2022).

Recent phenomenological work extends this complementarity. A 146 GeV real scalar explanation of a CMS $|\overline{M}\rangle$4 excess yields a preferred mode with peaked value $|\overline{M}\rangle$5, and the projected sensitivities of Mu2e, COMET, Mu3e, MACE, MEG II, Belle II, STCF, and the HL-LHC are stated to probe the corresponding region of coupling space within the next decade (Gao et al., 3 Jul 2026). In a maximal flavor-violating $|\overline{M}\rangle$6 model, the projected MACE sensitivity of approximately $|\overline{M}\rangle$7 is described as the strongest probe of muonium-antimuonium oscillation in the relevant mass range and about one order of magnitude better than the $|\overline{M}\rangle$8 bound for $|\overline{M}\rangle$9 (Liu et al., 2024).

MACE is therefore best understood not as an isolated rare-event search but as one element of a coordinated charged-lepton-flavor-violation program. The whitepaper explicitly places its future results alongside COMET, Mu2e, Mu3e, and MEG-II, while the field-dependence study emphasizes that MACE at CSNS and the planned J-PARC experiment probe complementary magnetic-field regimes (Bai et al., 2022, Fukuyama et al., 2023). A plausible implication is that, if a signal were observed, combining the absolute rate, the magnetic-field dependence, and external limits from other cLFV channels would substantially narrow the space of viable mediators.

In that sense, MACE serves two roles simultaneously. Experimentally, it is a next-generation attempt to improve the direct bound on $2\times 2$0 conversion by more than two orders of magnitude. Theoretically, it is a clean leptonic test of flavor structure, mediator quantum numbers, and the relation between lepton-flavor violation, lepton-number violation, and neutrino-mass generation.