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REVIEW 4 major objections 4 minor 40 references

Lepton flavor violating decay of true muonium: $\boldsymbol{(\mu^+ \mu^-) \to \mu^\pm e^\mp}$

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper proposes the decay of true muonium—a bound state of a muon and an antimuon—into a muon-electron pair of different flavor as a new probe of charged lepton flavor violation, and shows the branching ratio could reach 10^-20 under…

desk verdict First CLFV calculation for true muonium, worth a referee's time, but the lifetime averaging and spin projection need fixing before the numbers are trusted. read the letter →

arxiv 2507.01193 v2 pith:NH43H3JV submitted 2025-07-01 hep-ph

Ryotaro Minato , Akira Sato , Ryosuke Suda , Masato Yamanaka This is my paper
classification hep-ph
keywords truemuoniumdimuoniumchargedleptonflavorviolationviolatingdecayeffectivefieldtheorymuoncolliderbranchingratio
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes that the lepton-flavor-violating decay of true muonium—the bound state of a positive and a negative muon—into a muon and an electron, $(\mu^+ \mu^-) \to \mu^\pm e^\mp$, could be a new probe of charged lepton flavor violation. It computes the branching ratio from scalar, vector, and dipole effective operators and finds that, under current experimental bounds on $\mu \to e \gamma$, the branching ratio can reach $\mathcal{O}(10^{-20})$. Because the final state is clean and the process is purely leptonic, a discovery would complement rare-muon searches and could be an early physics opportunity at a muon collider front end, provided enough true muonium can be produced. The estimate requires roughly $5 \times 10^{19}$ true muonium decays for one signal event in the most favorable scenario.

What carries the argument

The decay rate is computed as $\Gamma = \sigma v_{\mathrm{rel}} |\psi(0)|^2$, where $|\psi(0)|^2$ is the squared 1S wave function of true muonium at zero separation, and $\sigma v_{\mathrm{rel}}$ is the nonrelativistic cross section for $\mu^+ \mu^- \to \mu^\pm e^\mp$ obtained from an effective Lagrangian with scalar, vector, and dipole CLFV operators. The branching ratio follows by multiplying by the true muonium lifetime $\tau_{\mathrm{TM}} = 1.51$ ps, a 1:3 weighted average of singlet (two-photon) and triplet ($e^+e^-$) decay lifetimes.

What would settle it

A null search: after accumulating roughly $5 \times 10^{19}$ true muonium decays at a muon collider front end, observing zero $(\mu^+ \mu^-) \to \mu^\pm e^\mp$ events would contradict the maximal vector-L prediction. Equivalently, an improved experimental bound on $\mu \to e \gamma$ that pushes $|g^V_{LL}|^2$ below $2.18 \times 10^{-7}$ at $\Lambda = 1$ TeV would lower the predicted branching ratio below $10^{-20}$ and require more than $10^{20}$ decays, moving the signal out of early-stage reach.

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Extended reading notes

Core claim

The paper's central claim is that true muonium can decay into a same-charge muon-electron pair at an observable rate, with the branching ratio driven by the overlap of the initial-state muon wave functions and the effective CLFV interactions. In the single-operator dominance scenario, the vector-L operator yields the largest allowed branching ratio, $\mathrm{BR} \approx 1.05 \times 10^{-13} (1\,\mathrm{TeV}/\Lambda)^4 |g^V_{LL}|^2$, and with the current bound $|g^V_{LL}|^2 < 2.18 \times 10^{-7}$ at $\Lambda = 1$ TeV this reaches about $2 \times 10^{-20}$, requiring $N_{\mathrm{TM}} \approx 5.2 \times 10^{19}$ true muonium decays per event. The dipole operator, although enhanced by $v/\Lambda$, is more tightly constrained and yields smaller rates. Interference among operators can shift the contours, and the back-to-back final state with $|p| \simeq 3 m_\mu/4$ gives a distinctive signature.

Load-bearing premise

The whole signal estimate rests on the assumption that true muonium can actually be produced in large numbers—on the order of $10^{19}$ atoms—at the muon collider front end, yet the paper gives no production or formation efficiency, and true muonium has not yet been observed.

Editorial extensions

If this is right

  • If the branching ratio reaches $\mathcal{O}(10^{-20})$, a muon collider running before cooling and acceleration could collect enough stopped true muonium decays to see the first CLFV signal from a bound state.
  • A measurement of $(\mu^+ \mu^-) \to \mu^\pm e^\mp$ would constrain combinations of scalar, vector, and dipole operators that $\mu \to e \gamma$ alone cannot separate, because the different operator structures enter with different coefficients in the rate formula.
  • The process offers a purely leptonic, hadron-free prediction, so any observed rate can be compared cleanly with theory.
  • If observed together with other CLFV processes, the decay can help identify the Lorentz structure of the underlying new physics.
  • The back-to-back, fixed-momentum signature ($|p| \simeq 3m_\mu/4$) allows efficient kinematic reconstruction and background rejection in a stopped-decay environment.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's estimate implicitly assumes a specific mixing of 1S states (1:3 singlet-to-triplet). If true muonium is produced in a polarized or spin-selected state, the effective lifetime and decay rate would change, possibly altering the required number of decays; this could be tested by studying the decay in external magnetic fields.
  • The same EFT machinery could be applied to other purely leptonic bound states, such as true tauonium, to search for flavor violation in the tau sector, where current bounds are weaker.
  • A dedicated measurement of true muonium production rates at the muon collider front end—currently absent from the paper—would determine whether $10^{20}$ stopped atoms are feasible; without that, the proposal remains conditional.
  • If the vector-L scenario is realized, the decay $(\mu^+ \mu^-) \to \mu^\pm e^\mp$ would likely be accompanied by a related process $\mu^+ \mu^- \to \mu^\pm e^\mp$ in collisions; comparing bound-state and scattering rates would test the nonrelativistic overlap model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes the charged-lepton-flavor-violating decay of true muonium, (μ+μ−) → μ±e∓, as a new probe of CLFV. Starting from an effective Lagrangian with scalar, vector, and dipole operators (Eq. (2)), the authors derive a compact decay-rate formula (Eqs. (4)–(12)), evaluate single-operator branching ratios (Eqs. (13)–(15)), and compare them with MEG II bounds on μ→eγ (Eq. (16)). They find BR up to O(10^−20) in the vector-L scenario and estimate that about 5×10^19 TM decays would be needed for one event at a muon collider front end (Eq. (17)). The paper also presents two-operator interference contour plots. The main numerical claim is an order-of-magnitude estimate, and the paper explicitly notes that TM has not yet been observed and that abundant production is assumed.

Significance. If correct, this is a genuinely new, purely leptonic CLFV channel with a back-to-back μ±e∓ final state and no hadronic uncertainties; the analytic formulas are transparent and easily adaptable. The paper explicitly benchmarks against the MEG II limit and gives a falsifiable target BR near 10^−20. Its experimental payoff, however, is conditional on unproven TM production, and the spin/lifetime treatment needs correction. Since the order-of-magnitude result is robust to the ~25% lifetime correction and to order-one spin-projection factors, the proposal merits further study after revision.

major comments (4)
  1. [Sec. II, Eq. (3)] The lifetime τTM = 1.51 ps is the arithmetic mean of the singlet and triplet lifetimes, but for an incoherent 1:3 spin mixture the total decay rate is the population-weighted average of the rates. Using the quoted values τ(2γ) = 0.602 ps and τ(e+e−) = 1.81 ps, the correct effective lifetime is τ_eff = (1/4 × 1/0.602 ps + 3/4 × 1/1.81 ps)^−1 = 1.21 ps. All branching ratios in Eqs. (13)–(15) and Fig. 3 are therefore overestimated by a factor 1.51/1.21 ≈ 1.25. This is a straightforward correction, but it should be applied before the numerical benchmarks are quoted.
  2. [Sec. II, Eq. (4)] The decay width is computed as Γ = σv_rel |ψμ|^2 with σv_rel averaged over initial spins of free muons and with a single 1S wavefunction squared. For a bound state, each spin channel of the 1S state has its own decay width, obtained after projecting the operator in Eq. (2) onto the singlet and triplet wavefunctions. Scalar, vector, and dipole operators have different spin selection rules (for example, a scalar current can project onto the S=0 configuration, while an axial-vector current can project onto S=1), so the relative rates for para- and ortho-true-muonium are not universally equal. The present formula implicitly assumes that the spin-averaged matrix element equals the bound-state matrix element in each spin channel. Please re-derive the singlet and triplet rates for each operator and either present separate branching ratios for the two spin states or demonstrate that the spin average in Eq. (6) is valid for the specific operator. This affects the relative ranking of the scalar, vector, and dipole scenarios, and hence the central claim.
  3. [Sec. III, after Eq. (17)] The experimental prospects are quantified only by N_TM = BR^−1 ≈ 5.2×10^19 decays. No TM production rate, formation efficiency, stopping or collection efficiency, or running time is provided, and the paper itself notes that TM has not yet been directly observed (Sec. I, Refs. [29]–[33]). The muon rates at the muon collider front end (3×10^15 μ−/s and 2×10^15 μ+/s) by themselves do not imply that TM can be produced at a useful rate; production requires bringing the two beams into a bound state with low relative velocity. The sentence claiming possible discovery in the early muon-collider stage should be either removed or replaced by a quantitative feasibility condition, such as the required TM production rate given a detector efficiency and run time.
  4. [Sec. III, Eq. (16)] The mapping from the MEG II bound BR(μ→eγ) < 3.1×10^−13 to the coupling bounds in Eq. (16) is not shown; the only citation is Ref. [39]. Because these bounds set the scale of all the numerical results (Eqs. (13)–(15), Figs. 2–4), please include the explicit one-loop (or tree-level) formulae used, including the loop factors and chirality structures, so that a reader can reproduce the values 3.35×10^−10, 2.72×10^−8, 2.18×10^−7, and 1.64×10^−20. This is particularly important for the scalar and vector operators, where the μ→eγ amplitude arises at one loop and may contain logarithms or mass-ratio enhancements.
minor comments (4)
  1. [Sec. II, first paragraph] The phrase 'unpolarized muons for the 1S initial state' conflates a statistical mixture with a bound-state spin eigenstate; please clarify that the 1:3 singlet/triplet ratio is an incoherent production assumption.
  2. [Eq. (2)] The dipole normalization v A_L σμν Fμν leaves A_L/R dimensionless, but the field-strength normalization and the definition of v are not stated; please define the conventions used for Fμν and v.
  3. [Fig. 3] The horizontal axis label 'CLFV coupling' lacks units, and the dashed excluded segments are difficult to distinguish in grayscale; please add units and use distinct line styles or markers.
  4. [Eq. (17)] The estimate N_TM = BR^−1 assumes one signal event with 100% detection efficiency; please state this assumption explicitly and, if possible, include a background estimate for the back-to-back μ±e∓ signature.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; the branching-ratio derivation is self-contained against the external MEG II limit and standard bound-state input.

full rationale

The central calculation is not circular. The effective Lagrangian (Eq. 2) defines free operator coefficients; the decay-rate formula Gamma = sigma v_rel |psi|^2 (Eq. 4) combines a standard nonrelativistic bound-state factor with a cross section computed from that Lagrangian, and the TM lifetimes are taken from external references [37,38]. The coupling bounds in Eq. (16) are derived from the independent MEG II upper limit BR(mu^+ -> e^+ gamma) < 3.1e-13 using Lavoura's one-loop formulas [39]; no quantity fitted to the target observable is recycled as a prediction. The final branching ratios (Eqs. 13-15) are functions of those bounded coefficients and are therefore constrained by, but not equal to, the input bounds by construction. The author-affiliated citations (Refs. [26,35]) concern muonic-atom CLFV and TM production apparatus; they are not load-bearing for the branching-ratio derivation. The paper's own caveat that abundant TM production is assumed and that detailed investigations remain is an external feasibility limitation, not a circular step. The spin/lifetime averaging point raised in review is a possible physics-consistency issue, not circularity. No exhibited step reduces the claimed prediction to its own input.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central calculation depends on the EFT operator basis, the nonrelativistic bound-state formalism, and the external MEG II bounds. No new particles are introduced. The main free input is the benchmark scale Λ = 1 TeV and the choice of couplings at their experimental upper bounds. The TM production assumption is the least supported input.

free parameters (3)
  • New physics scale Λ = 1 TeV
    Chosen by hand as a benchmark for numerical estimates; results scale as Λ^-4 and the paper notes larger Λ reduces the maximum branching ratio at fixed MEG II bound.
  • CLFV couplings g and A = Upper bounds from MEG II (Eq. 16)
    Set to the current experimental upper bounds to maximize the branching ratio; these are inputs from experiment, not fitted parameters.
  • Singlet/triplet fraction = 1:3
    Assumed for unpolarized muons forming 1S TM, used to obtain the average lifetime and spin-averaged rate.
assumptions (5)
  • domain assumption The effective Lagrangian (Eq. 2) is the most general set of scalar, vector, and dipole CLFV operators relevant to this process.
    The calculation assumes these operator types dominate and that single-operator dominance holds for the numerical bounds.
  • domain assumption The bound-state decay rate factorizes as Γ = σv_rel |ψ(0)|^2.
    Standard short-range annihilation formula; valid when the interaction range is much smaller than the Bohr radius, which holds here since the final-state momentum is ~m_μ.
  • standard math The 1S wavefunction at the origin is |ψ(0)|^2 = (α μ_TM)^3/π.
    Hydrogen-like QED bound state formula, used in Eq. (5).
  • domain assumption The MEG II upper limits on μ→eγ translate to the coupling bounds in Eq. (16) via one-loop diagrams for scalar/vector operators and tree level for dipole.
    These loop calculations are cited from Ref. [39] and not reproduced; the derived bounds are central to the numerical values.
  • ad hoc to paper True muonium can be produced with the assumed unpolarized 1S spin mixture in sufficient numbers.
    No production mechanism or efficiency is calculated; the paper relies on an effective TM source at the muon collider front end.

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Cite this review

Pith. "Pith review of Lepton flavor violating decay of true muonium: $\boldsymbol{(\mu^+ \mu^-) \to \mu^\pm e^\mp}$." pith.science (2026). https://pith.science/paper/NH43H3JV

@misc{pith2026250701193,
  author       = {Pith},
  title        = {Pith review of: Lepton flavor violating decay of true muonium: $\boldsymbol(\mu^+ \mu^-) \to \mu^\pm e^\mp$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NH43H3JV}},
  note         = {Machine review of arXiv:2507.01193}
}
abstract

We propose a new channel for probing charged lepton flavor violation (CLFV): the decay of true muonium into a lepton pair of different flavor, $(\mu^+ \mu^-) \to \mu^\pm e^\mp$. This purely leptonic two-body decay provides a clean experimental signature in the form of energetic, oppositely charged leptons. It is sensitive not only to photonic dipole interactions but also to four-fermion contact interactions, and is free from hadronic uncertainties in theoretical predictions. We evaluate the branching ratios induced by scalar-, vector-, and dipole-type CLFV operators. Our results show that the branching ratio can reach up to $\mathcal{O}(10^{-20})$ within current experimental bounds. This decay mode may be discovered as an early-stage physics opportunity of the muon collider program by utilizing the large number of muons produced at its front end.

Figures

Figures reproduced from arXiv: 2507.01193 by the authors.

Figure 1
Figure 1. FIG. 1. CLFV decay of TM for contact interaction (a) and for photonic dipole interaction (b,c). [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Current upper bounds on the effective couplings for each type of CLFV operator derived [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. , with Λ = 1 TeV. The dashed regions indicate parameter ranges already excluded by µ → eγ constraints. Among the four scenarios, the dipole-type operator yields the most suppressed branching ratio due to a more stringent bound compared to other operators. This is because the dipole operator contributes to µ → eγ at tree level, whereas scalar and vector operators induce the decay only via loop processes. Although we … view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Contours of constant branching ratio BR(( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Works this paper leans on

40 extracted references · 19 canonical work pages

  1. [29]

    The Production and Discovery of True Muonium in Fixed-Target Experiments

    A. Banburski and P. Schuster, The Production and Discovery of True Muonium in Fixed- Target Experiments, Phys. Rev. D 86, 093007 (2012), arXiv:1206.3961 [hep-ph]

    work page Pith review arXiv 2012

  2. [33]

    Discovering True Muonium at LHCb

    X. Cid Vidal, P. Ilten, J. Plews, B. Shuve, and Y. Soreq, Discovering true muonium at LHCb , Phys. Rev. D 100, 053003 (2019), arXiv:1904.08458 [hep-ph]

    work page Pith review arXiv 2019

  3. [39]

    Lavoura, General formulae for f1 → f2γ, Eur

    L. Lavoura, General formulae for f1 → f2γ, Eur. Phys. J. C 29, 191–195 (2003), arXiv:hep- ph/0302221

    work page arXiv 2003

  4. [1]

    Kuno and Y

    Y. Kuno and Y. Okada, Muon decay and physics beyond the standard model , Rev. Mod. Phys. 73, 151–202 (2001), arXiv:hep-ph/9909265

    arXiv 2001

  5. [2]

    Raidal et al

    M. Raidal et al. , Flavour physics of leptons and dipole moments , Eur. Phys. J. C 57, 13–182 (2008), arXiv:0801.1826 [hep-ph]

    arXiv 2008

  6. [3]

    J. L. Hewett et al. , Fundamental Physics at the Intensity Frontier (2012), arXiv:1205.2671 [hep-ex]

    arXiv 2012

  7. [4]

    Calibbi and G

    L. Calibbi and G. Signorelli, Charged Lepton Flavour Violation: An Experimental and Theo- retical Introduction, Riv. Nuovo Cim. 41, 71–174 (2018), arXiv:1709.00294 [hep-ph]

    arXiv 2018

  8. [5]

    R. H. Bernstein and P. S. Cooper, Charged Lepton Flavor Violation: An Experimenter’s Guide, Phys. Rept. 532, 27–64 (2013), arXiv:1307.5787 [hep-ex]

    arXiv 2013

Show all 40 references
  1. [6]

    Davidson, B

    S. Davidson, B. Echenard, R. H. Bernstein, J. Heeck, and D. G. Hitlin, Charged Lepton Flavor Violation (2022), arXiv:2209.00142 [hep-ex]. 9

    2022 arXiv

  2. [7]

    Ardu and G

    M. Ardu and G. Pezzullo, Introduction to Charged Lepton Flavor Violation , Universe 8, 299 (2022), arXiv:2204.08220 [hep-ph]

    2022 arXiv

  3. [8]

    Kuno (COMET), A search for muon-to-electron conversion at J-PARC: The COMET experiment, PTEP 2013, 022C01 (2013)

    Y. Kuno (COMET), A search for muon-to-electron conversion at J-PARC: The COMET experiment, PTEP 2013, 022C01 (2013)

    2013

  4. [9]

    Abramishvili et al

    R. Abramishvili et al. (COMET), COMET Phase-I Technical Design Report , PTEP 2020, 033C01 (2020), arXiv:1812.09018 [physics.ins-det]

    2020 arXiv

  5. [10]

    Bartoszek et al

    L. Bartoszek et al. (Mu2e), Mu2e Technical Design Report (2014), arXiv:1501.05241 [physics.ins-det]

    2014 arXiv

  6. [11]

    A. M. Baldini et al. (MEG II), The design of the MEG II experiment , Eur. Phys. J. C78, 380 (2018), arXiv:1801.04688 [physics.ins-det]

    2018 arXiv

  7. [12]

    Afanaciev et al

    K. Afanaciev et al. (MEG II), A search for µ+ → e+γ with the first dataset of the MEG II experiment, Eur. Phys. J. C 84, 216 (2024), [Erratum: Eur.Phys.J.C 84, 1042 (2024)], arXiv:2310.12614 [hep-ex]

    2024 arXiv

  8. [13]

    Arndt et al

    K. Arndt et al. (Mu3e), Technical design of the phase I Mu3e experiment , Nucl. Instrum. Meth. A 1014, 165679 (2021), arXiv:2009.11690 [physics.ins-det]

    2021 arXiv

  9. [14]

    Blondel et al

    A. Blondel et al. , Research Proposal for an Experiment to Search for the Decay µ → eee (2013), arXiv:1301.6113 [physics.ins-det]

    2013 arXiv

  10. [15]

    Adachi et al

    I. Adachi et al. (Belle-II), Search for lepton-flavor-violating τ − → µ−µ+µ− decays at Belle II , JHEP 09, 062, arXiv:2405.07386 [hep-ex]

    arXiv

  11. [16]

    Byrum et al

    K. Byrum et al. (Mu2e-II), Mu2e-II: Muon to electron conversion with PIP-II (2022), arXiv:2203.07569 [hep-ex]

    2022

  12. [17]

    G. D. Maso et al. , Future facilities at PSI, the High-Intensity Muon Beams (HIMB) project , EPJ Web Conf. 282, 01012 (2023)

    2023

  13. [18]

    Aoki et al

    M. Aoki et al. (C. Group), A New Charged Lepton Flavor Violation Program at Fermilab , Snowmass 2021 (2022), arXiv:2203.08278 [hep-ex]

    2022 arXiv

  14. [19]

    Voena (Study Group for Future µ → eγ Searches), Future µ → eγ experiments, PoS Muon4F uture2023, 025 (2024)

    C. Voena (Study Group for Future µ → eγ Searches), Future µ → eγ experiments, PoS Muon4F uture2023, 025 (2024)

    2024

  15. [20]

    Cavoto, A

    G. Cavoto, A. Papa, F. Renga, E. Ripiccini, and C. Voena, The quest for µ → eγ and its experimental limiting factors at future high intensity muon beams , Eur. Phys. J. C 78, 37 (2018), arXiv:1707.01805 [hep-ex]

    2018 arXiv

  16. [21]

    Kuno, PRISM/PRIME, Nucl

    Y. Kuno, PRISM/PRIME, Nucl. Phys. B Proc. Suppl. 149, 376–378 (2005)

    2005

  17. [22]

    Aggarwal et al

    L. Aggarwal et al. (Belle-II), Snowmass White Paper: Belle II physics reach and plans for the next decade and beyond (2022), arXiv:2207.06307 [hep-ex]

    2022 arXiv

  18. [23]

    Banerjee et al

    S. Banerjee et al. , Snowmass 2021 White Paper: Charged lepton flavor violation in the tau sector (2022), arXiv:2203.14919 [hep-ph]

    2022 arXiv

  19. [24]

    Kuno and Y

    Y. Kuno and Y. Okada, Proposed µ → eγ Search with Polarized Muons , Phys. Rev. Lett. 77, 434–437 (1996), arXiv:hep-ph/9604296 [hep-ph]

    1996 arXiv

  20. [25]

    Farzan, Tracing CP-violation in Lepton Flavor Violating muon decays , JHEP 07, 054, arXiv:hep-ph/0701106

    Y. Farzan, Tracing CP-violation in Lepton Flavor Violating muon decays , JHEP 07, 054, arXiv:hep-ph/0701106

    arXiv

  21. [26]

    Koike, Y

    M. Koike, Y. Kuno, J. Sato, and M. Yamanaka, New Process for Charged Lepton Flavor Violation Searches: µ−e− → e−e− in a Muonic Atom , Phys. Rev. Lett. 105, 121601 (2010), arXiv:1003.1578 [hep-ph]. 10

    2010 arXiv

  22. [27]

    Horikawa and K

    K. Horikawa and K. Sasaki, Muonium-antimuonium conversion in models with dilepton gauge bosons, Phys. Rev. D 53, 560–563 (1996), arXiv:hep-ph/9504218

    1996 arXiv

  23. [28]

    W. S. Hou and G. G. Wong, Magnetic field dependence of muonium-antimuonium conversion , Phys. Lett. B 357, 145–150 (1995), arXiv:hep-ph/9505300

    1995 arXiv

  24. [30]

    P. V. Chliapnikov, Numbers of µ±π∓, µ+µ− and K+K− atoms and Coulomb pairs in the DIRAC experiment, DIRAC Note 2014-05 (2014)

    2014

  25. [31]

    C. A. Bertulani, D. Bhandari, and F. S. Navarra, Unveiling the properties of the dimuonium at the energies available at the Large Hadron Collider at CERN , Eur. Phys. J. A 60, 43 (2024), arXiv:2307.12387 [hep-ph]

    2024 arXiv

  26. [32]

    Gargiulo, E

    R. Gargiulo, E. Di Meco, and S. Palmisano, Feasibility study of true muonium observation with the Belle II existing dataset , Phys. Rev. D 111, 112002 (2025), arXiv:2501.17753 [hep-ph]

    2025 arXiv

  27. [34]

    P. J. Fox, S. R. Jindariani, and V. D. Shiltsev, DIMUS: super-compact Dimuonium Spec- troscopy collider at Fermilab , JINST 18 (08), T08007, arXiv:2203.07144 [hep-ex]

    arXiv

  28. [35]

    Itahashi, H

    T. Itahashi, H. Sakamoto, A. Sato, and K. Takahisa, Low Energy Muon Apparatus for True Muonium Production, JPS Conf. Proc. 8, 025004 (2015)

    2015

  29. [36]

    Itahashi, T

    T. Itahashi, T. H. Lang, and C. Van Tao, Simulation Study of Frictional Cooling for True Muonium Production, JPS Conf. Proc. 18, 011024 (2017)

    2017

  30. [37]

    S. M. Bilenky, V. H. Nguyen, L. L. Nemenov, and F. G. Tkebuchava, Production and decay of (muon-plus muon-minus)-atoms , Yad. Fiz. 10, 812–814 (1969)

    1969

  31. [38]

    Hughes and B

    V. Hughes and B. Maglic, True Muonium, Bull. Am. Phys. Soc. 16, 65 (1971)

    1971

  32. [40]

    Accettura et al

    C. Accettura et al. (International Muon Collider), The Muon Collider , (2025), arXiv:2504.21417 [physics.acc-ph]. 11

    2025

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