True Muonium Research Articles

Production of true para-muonium in linearly polarized photon fusions

True muonium (TM)—the bound state of μ+μ−—has not been discovered yet. It was demonstrated that searching for TM via γγ fusions in heavy ion collisions is feasible due to the enhancement of the atom number. We study the production of the true para-muonium (pTM) in the collisions of linearly polarized photons in the experiments of heavy-ion collisions, calculate the production rate as well as the transverse spectrum of pTM, and explore the discovery potential in nuclear experiments. Our results show that there is a significant correlation between the linearly polarized photon distribution and the transverse momentum distribution of pTM. The optimal kinematic region of the generated pTM is identified, which can provide a theoretical guide to the detection of pTM in experiments. Published by the American Physical Society 2024

True muonium resonant production at e + e − colliders with standard crossing angle

True muonium (TM) (μ + μ −) is the heaviest and smallest bound state not containing hadrons, after TM (τ + τ −) and mu-tauonium (μ ± τ ∓). One of the proposed methods to observe the spin 1 fundamental state of TM, which has the smallest lifetime among TM spin 1 states, was to build an e + e − collider with a large crossing angle (θ ∼ 30°) in order to provide TM with a large boost and detect its decay vertex in e + e −. The following paper will instead show that TM excited states can be observed in relatively large quantities ( O (10)/month) at a e + e − collider with standard crossing angle, after setting their center-of-mass energy to the TM mass (∼2m μ = 211.4 MeV).

Discovering True Muoniums on CMS

The primary focus is on meticulous data analysis of data retrieved from the CMS detector server. A series of cut flows are implemented to eliminate impurity data and refine the dataset. The culmination of these procedures results in a graph emphasizing the balance variable ’B,’ revealing a remarkable symmetry concerning the y-axis. Complementing the data analysis is the creation of a Toy Monte Carlo simulation. This innovative method aims to replicate the experimental signal. Considering uncertainties in experimental data, the kinetic energy in the dimuon rest frame is systematically smeared. Additionally, the momenta of outgoing particles are subjected to variation, adhering to a normal distribution—a process termed the “experimental effect.” The simulated balance spectrum is then meticulously compared with the experimental counterpart. This comparative analysis serves as the litmus test for the presence of True Muonium signals. The outcome of this project bears implications for the understanding of True Muoniums and contributes to the broader discourse in particle physics. The combination of advanced data analysis and simulation techniques enhances our ability to discern the subtleties of particle interactions, offering valuable insights into the fundamental nature of the universe.

MuMuPy: A dimuonium-matter interaction calculator

In this article, we present MuMuPy, a computational library and cloud-based tool for calculating cross sections for the interaction of dimuonium (true muonium) with matter. MuMuPy calculates corresponding form factors and allows one to find the probabilities of dimuonium transitions in the electric field of the nucleus.MuMuPy was developed in the context of the μμ-tron facility, the project of a low-energy electron-positron collider for production and experimental study of dimuonium, proposed in our home institute, Budker Institute of Nuclear Physics.The reliability of MuMuPy was verified by three independent methods, one of which was developed by the authors earlier. Program summaryProgram title: MuMuPyCPC Library link to program files:https://doi.org/10.17632/nr6y34yg29.1Code Ocean capsule:https://codeocean.com/capsule/1734849/tree/v1Licensing provisions: GPLv3Programming language: Python 3.X, FortranNature of problem: Planned experiments at the μμ-tron facility include investigating the interaction of dimuonium with ordinary atoms as it passes through the foil. This requires the creation of a computational infrastructure for a reliable calculation of the interaction of dimuonium with the electric field of the atomic nucleus.Solution method: Three independently developed computational strategies were used, including our own new method based on the identities of hypergeometric functions. A MuMuPy library and a cloud-based tool for calculating the cross sections for the interaction of dimuonium with matter have been developed, which we hope will be used in future studies of true muonium.

Monochromatization of e⁺e⁻ Colliders with a Large Crossing Angle

The relative center-of-mass energy spread at $e^+e^-$ colliders is about $10^{-3}$, which is much larger than the widths of narrow resonances produced in the s-channel in $e^+e^-$ collisions. This circumstance greatly lowers the resonance production rates of J/Psi, Upsilon(1S), Upsilon(2S), Upsilon(3S) and makes it extremely difficult to observe resonance production of the Higgs boson. Thus, a significant reduction of the center-of-mass energy spread would open up great opportunities in the search for new physics in rare decays of narrow resonances, the search for new narrow states with small $\Gamma_{e^+e^-}$, the study of true muonium and tauonium, etc. The existing monochromatization scheme is only suitable for head-on collisions, while $e^+e^-$ colliders with crossing angles (the so-called Crab Waist collision scheme) can provide significantly higher luminosity due to reduced collision effects. In this paper, we propose a new monochromatization method for colliders with a large crossing angle. The contribution of the beam energy spread to the spread of the center-of-mass energy is canceled by introducing an appropriate energy-angle correlation at the interaction point; $\sigma_W/W \sim (3-5)10^{-6}$ appears possible. Limitations of the proposed method are also considered.

Fifth force and hyperfine splitting in bound systems

Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8Be and 4He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the X17 could either be a vector, or a pseudoscalar particle. Here, we calculate the effective potentials generated by the X17, for hyperfine interactions in simple atomic systems, for both the pseudoscalar as well as the vector X17 hypotheses. The effective Hamiltonians are obtained in a general form which is applicable to both electronic as well as muonic bound systems. The effect of virtual annihilation and its contribution to the hyperfine splitting also is considered. Because of the short range of the X17-generated potentials, the most promising pathway for the observation of the X17-mediated effects in bound systems concerns hyperfine interactions, which, for $S$ states, are given by modifications of short-range (Dirac-delta) potentials in coordinate space. For the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between the bound lepton and the nucleus exclusively leads to hyperfine effects, but does not affect the Lamb shift. Effects due to the X17 are shown to be drastically enhanced for muonic bound systems. Prospects for the detection of hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium, muonic hydrogen, muonium, true muonium ($\mu^+\mu^-$ bound system), and positronium.

True muonium production in ultraperipheral PbPb collisions

In this paper, we investigate the production of a true muonium state, which is an atom consisting of a ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ bound state, by $\ensuremath{\gamma}\ensuremath{\gamma}$ interactions in ultraperipheral PbPb collisions, considering an accurate treatment of the absorptive corrections and for the nuclear form factor. The rapidity distributions and cross sections are estimated considering the Relativistic Heavy Ion Collider, Large Hadron Collider, and Future Circular Collider energies. Our results indicate that the experimental analysis can be useful to observe the true muonium state.

Discovering true muonium at LHCb

We study the potential of the LHCb experiment to discover, for the first time, the $\mu^+\mu^-$ true muonium bound state. We propose a search for the vector $1^3S_1$ state, $\mathcal{T\!M}$, which kinetically mixes with the photon and dominantly decays to $e^+e^-$. We demonstrate that a search for $\eta \to \gamma \mathcal{T\!M}$, $\mathcal{T\!M}\to e^+e^-$ in a displaced vertex can exceed a significance of 5 standard deviations assuming statistical uncertainties. We present two possible searches: an inclusive search for the $e^+e^-$ vertex, and an exclusive search which requires an additional photon and a reconstruction of the $\eta$ mass.

Discovering true muonium in KL→(μ+μ−)γ

Theoretical and phenomenological predictions of $\mathcal{BR}(K_L\rightarrow (\mu^+\mu^-) \gamma)\sim7\times10^{-13}$ are presented for different model form factors $F_{K_L\gamma\gamma^*}(Q^2)$. These rates are comparable to existing and near-term rare $K_L$ decay searches at J-PARC and CERN, indicating a discovery of true muonium is possible. The model uncertainties are sufficiently small that detection of true muonium could discriminate between the form factor models. Further discussion of potential backgrounds is made.

Predicting and Discovering True Muonium (μ+μ−)

The recent observation of discrepancies in the muonic sector motivates searches for the yet undiscovered atom true muonium (μ+μ−). To leverage potential experimental signals, precise theoretical calculations are required. I will present the on-going work to compute higher-order corrections to the hyperfine splitting and the Lamb shift. Further, possible detection in rare meson decay experiments like REDTOP and using true muonium production to constrain mesonic form factors will be discussed.

Astrophysical signatures of leptonium

More than 10^43 positrons annihilate every second in the centre of our Galaxy yet, despite four decades of observations, their origin is still unknown. Many candidates have been proposed, such as supernovae and low mass X-ray binaries. However, these models are difficult to reconcile with the distribution of positrons, which are highly concentrated in the Galactic bulge, and therefore require specific propagation of the positrons through the interstellar medium. Alternative sources include dark matter decay, or the supermassive black hole, both of which would have a naturally high bulge-to-disc ratio. The chief difficulty in reconciling models with the observations is the intrinsically poor angular resolution of gamma-ray observations, which cannot resolve point sources. Essentially all of the positrons annihilate via the formation of positronium. This gives rise to the possibility of observing recombination lines of positronium emitted before the atom annihilates. These emission lines would be in the UV and the NIR, giving an increase in angular resolution of a factor of 10^4 compared to gamma ray observations, and allowing the discrimination between point sources and truly diffuse emission. Analogously to the formation of positronium, it is possible to form atoms of true muonium and true tauonium. Since muons and tauons are intrinsically unstable, the formation of such leptonium atoms will be localised to their places of origin. Thus observations of true muonium or true tauonium can provide another way to distinguish between truly diffuse sources such as dark matter decay, and an unresolved distribution of point sources.

Hadronic vacuum polarization in true muonium

In order to reduce the theoretical uncertainty in the prediction, the leading-order hadronic vacuum polarization contribution to the hyperfine splitting of true muonium is reevaluated in two ways. A more complex pionic form factor and better estimates of the perturbative QCD contributions are used to study the model dependence of the previous calculation. The second, more accurate method directly integrates the Drell ratio $R(s)$ to obtain ${C}_{1,\mathrm{HVP}}=\ensuremath{-}0.04874(9)$. This corresponds to an energy shift in the hyperfine splitting (HFS) of $\mathrm{\ensuremath{\Delta}}{E}_{\mathrm{HFS},\mathrm{HVP}}^{\ensuremath{\mu}}=\ensuremath{-}8202(16)$ MHz and represents a factor-of-50 reduction in the theoretical uncertainty from hadronic sources. We also compute the contribution in positronium, which is too small at present to detect.

Applying Bayesian inference to Galileon solutions of the muon problem

We derive corrections to atomic energy levels from disformal couplings in Galileon theories. Through Bayesian inference, we constrain the cutoff radii and Galileon scale via these corrections. To connect different atomic systems, we assume the various cutoff radii related by a one-parameter family of solutions. This introduces a new parameter $\alpha$ which is also constrained. In this model, we predict shifts to muonic helium of $\delta E_{He^3}=1.97^{+9.28}_{-1.87}$ meV and $\delta E_{He^4}=1.69^{+9.25}_{-1.61}$ meV as well as for true muonium, $\delta E_{TM}=0.06^{+0.46}_{-0.05}$ meV.

Hyperfine splitting in a true muonium toO(mμα6): Two-photon-annihilation contribution from other flavors

The two-photon-annihilation contribution to the true muonium hyperfine splitting arising from $e$ and $\tau$ loops is obtained analytically at order $m_\mu\alpha^6$. The contribution to the hyperfine splitting is $-2.031092873 m_\mu\alpha^6/n^3\pi^2=-793.926988/n^3$ MHz. The contribution to the triplet true muonium decay rate has also been obtained and was found to be $9.825708266 m_\mu\alpha^6/n^3\pi^2=3840.737698/n^3$ MHz. Additional results have been computed for other purely leptonic bound states.

High resolution nonperturbative light-front simulations of the true muonium atom

Through the development of a parallel code called TMSWIFT, an extensive light-front quantization study of the nonperturbative spectrum of the bound state $(\mu^+\mu^-)$, true muonium, has been performed. Using Pad\'{e} approximants, it has been possible to extract continuum and infinite-cutoff limits for the singlet and triplet states for a range of values of the coupling constant $\alpha$. This data set allows for an investigation of the $\alpha$ dependence of the light-front spectra, the results of which are compared to standard calculations. Decay constants have also been obtained. Improved calculations have been undertaken for the energy shifts due to the presence of a second, lighter flavor ($e$). Finally, initial results for three-flavor ($e$, $\mu$, $\tau$) calculations are presented.

Nonperturbative True Muonium on the Light Front with TMSWIFT

The true muonium $(\mu\bar{\mu})$ bound state presents an interesting test of light-cone quantization techniques. In addition to exhibiting the standard problems of handling non-perturbative calculations, true muonium requires correct treatment of $e\bar{e}$ Fock-state contributions. Having previously produced a crude model of true muonium using the method of iterated resolvents, our current work has focused on the inclusion of the box diagrams to improve the cutoff-dependent issues of the model. Further, a parallel computer code, TMSWIFT, allowing for smaller numerical uncertainties, has been developed. This work focuses on the current state of these efforts to develop a model of true muonium that is testable at near-term experiments.

Can galileons solve the muon problem?

The leptonic bound states positronium and muonium are used to constrain galileon contributions to the Lamb shift of muonic hydrogen. Through the application of a variety of bounds on lepton compositeness, it is shown that either the assumption of equating the charge radius of a particle with its galileon scale radius is incompatible with experiments or the scale of galileons must be $M>1.33$ GeV, too large to solve the muon problem. The possibility of stronger constraints in the future from true muonium are discussed.

Possibility of observable signatures of leptonium from astrophysical sources

The formation of Ps in our Galaxy is well measured, and has led to important and unanswered questions on the origin of the positrons. In principle it should be possible to form analogous systems from mu and tau leptons, viz. true muonium and true tauonium. However the probability of formation for these systems is greatly reduced due to the intrinsically short lifetimes of the mu and tau leptons. Likewise, the decay of the atoms is hastened by the high probability of the constituent particles decaying. Nevertheless, if sufficient numbers of mu and tau pairs are produced in high energy astrophysical environments there may be significant production of true muonium and true tauonium, despite the small probabilities. This paper addresses this possibility. We have calculated the pair production spectra of mu and tau leptons from photon-photon annihilation and electron-positron annihilation in astrophysical environments. We have computed the cross-sections for radiative recombination and direct annihilation of the pairs, and the decay constants for the various allowable decays, and the wavelengths and energies of the recombination and annihilation signatures. In this way we have calculated the probabilities for the formation of true muonium and true tauonium, and the branching ratios for the various observable signatures. We have estimated the expected fluxes from accretion discs around microquasars and active galactic nuclei, and from interactions of jets with clouds and stars. We find that accretion discs around stellar mass black holes in our own Galaxy should have observable signatures at X-ray and gamma-ray energies that are in principle observable with current observatories.

Electroweak corrections to the true muonium hyperfine splitting

In contrast to other atomic systems, in true muonium ($\mu^+\mu^-$) the leading-order $Z$ boson corrections to the hyperfine splitting are shown to be experimentally accessible in the near future. This contribution ($-109$ MHz) constitutes a necessary contribution to a full $\mathcal{O}(m\alpha^7)$ calculation of the true muonium hyperfine splitting. This would enable a number of solutions to the muon problem to be constrained. Additionally, we compute the general expression for a pseudovector coupling to particle-antiparticle bound states at leading order, including the annihilation channel.

True muonium on the light front

Applying Discretized Light Cone Quantization, we perform the first calculation of the spectrum of true muonium, the atom, as modified by the inclusion of an Fock component. The shift in the mass eigenvalue is found to be largest for triplet states. If me is taken to be a substantial fraction of , the integrated probability of the electronic component of the state is found to be as large as . Initial studies of the Lamb shift for the atom are performed. Directions for making the simulations fully realistic are discussed.