<p>We propose the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>e</mi><mo>−</mo></msup><mi>γ</mi></math> process in a muonic atom as a novel means to investigate charged lepton flavor violation (CLFV). We demonstrate its sensitivity in probing effective CLFV operators associated with both single and double photon fields. In comparison to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><mi>γ</mi></math> using free positive muon decays at rest, the emitted electron and photon in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>e</mi><mo>−</mo></msup><mi>γ</mi></math> exhibit nonmonochromatic spectra, presenting nontrivial case. We derive the decay rate formula and demonstrate that the potential rate of the process is significant enough to motivate exploration in future muon CLFV experiments.</p>

Japan

Yuichi Uesaka

Masato Yamanaka

Yoshitaka Kuno

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>μ</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>e</mi><mo>−</mo></msup><mi>γ</mi></math> in a muonic atom as a probe for effective lepton-flavor-violating operators involving photon fields

The muonium-to-antimuonium transition experiment is about to be updated. Notably, the experiment at Japan Proton Accelerator Research Complex (J-PARC) can explore the magnetic field dependence of the transition probability. In this paper, we investigate the information that we can extract from the transition probabilities across different magnetic field strengths, while also taking into account a planned transition experiment at China Spallation Neutron Source (CSNS). There are two model-independent parameters in the transition amplitude, and we ascertain the feasibility of determining these parameters, including their relative physical phase, from experimental measurements. This physical phase can be related to the electron electric dipole moment, which is severely constrained by experiments. The underlying mediator responsible for the transition can be either doubly charged particles or neutral particles. In the former case, typical magnetic fields yield specific probability ratios, while the latter presents a range of the probability ratio. We investigate several models with neutral mediators and elucidate that the probability ratio is linked to the sign of new physics contribution to the electron <math><mi>g</mi><mo>−</mo><mn>2</mn></math>. The pivotal role of the J-PARC transition experiment in shedding light on these insights is emphasized.

Takeshi Fukuyama

Yukihiro Mimura

Insights from the magnetic field dependence of the muonium-to-antimuonium transition

We investigate a possibility that the <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></math> conversion is discovered prior to the <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> conversion, and its implications to the new physics search. We focus on the specific model including the mixing of the <math><mi>S</mi><mi>U</mi><msub><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub></math> doublet- and singlet-type scalar leptoquarks, which induces not only the lepton flavor violation but also the lepton number violation. Such a structure is motivated by R-parity violating (RPV) supersymmetric models, where a sbottom mediates the conversion processes. We formulate the <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></math> rate in analogy with the muon capture in a muonic atom, and numerically evaluate it using several target nuclei. The lepton flavor universality test of pion decay directly limits the <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></math> rate, and the maximally allowed <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></math> branching ratio is <math><mo>∼</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>18</mn></mrow></msup></math> under the various bounds on RPV parameters. We show that either <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> or <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup></math> signals can be discovered in near future experiments. This indicates that parallel searches for these conversions will give us significant information on the pattern of coupling constants.

Joe Sato

Kohei Sugawara

Determination of coupling patterns by parallel searches for → And → In Muonic Atoms

The lepton number and flavor violations are important possible ingredients of the lepton physics. The neutrinoless double beta decay and the transition of the muonium into antimuonuim are related to those violations. The former can give us an essential part of fundamental physics, and there are plenty of experimental attempts to observe the process. The latter has also been one of the attractive phenomena, and the experimental bound will be updated in planned experiments at new high-intensity muon beamlines. In models with a doubly charged scalar, not only can those two processes be induced, but also the active neutrino masses can be induced radiatively. The flavor violating decays of the charged leptons constrain the flavor parameters of the models. We study how the muonium-to-antimuonium transition rate can be as large as the current experimental bound, and we insist that the updated bound of the transition rate will be useful to distinguish the models to generate the neutrinoless double beta decay via the doubly charged scalar. We also study a possible extension of the model to the left-right model which can induce the neutrinoless double beta decay.

Neutrinoless double beta decay and the muonium-to-antimuonium transition in models with a doubly charged scalar

The lepton-flavor-violating conversion of a muon into an electron in the field of a nucleus is one of the most sensitive probes of physics beyond the Standard Model and the experiments Mu2e, COMET, and DeeMe will explore uncharted terrain in the near future. An observation of this <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> conversion process opens up the possibility to distinguish the underlying operator or new-physics model by exploiting the target-nucleus dependence of the conversion rate. To facilitate the choice of optimal targets we provide <math><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></math> conversion rates for all stable isotopes and estimate nuclear-structure uncertainties. Our results enable studies of mixed or enriched target materials that are particularly promising for distinguishing scenarios in which the muon converts either on protons or neutrons.

United States

Julian Heeck

Robert Szafron

Isotope dependence of muon-to-electron conversion

The constructions of the new high-intensity muon beamlines are progressing in facilities around the world, and new physics searches related to the muons are expected. The facilities can observe the transverse positron polarization of the polarized <math><mrow><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> decay to test the standard model. The transition of muonium into antimuonium (Mu-to-<math><mover><mi>Mu</mi><mo>¯</mo></mover></math> transition), which is one of the interesting possibilities in the models beyond the standard model, can be also tested. An observation of the transition in the near future would have a great impact since it would indicate that there is an approximate discrete symmetry in the lepton sector. If the Mu-to-<math><mover><mi>Mu</mi><mo>¯</mo></mover></math> transition operator is generated, a new muon decay operator can exist, and it may interfere with the standard model muon decay operator to induce the corrections to the transverse positron polarization in the <math><msup><mi>μ</mi><mo>+</mo></msup></math> decay. We examine the possibility that the Mu-to-<math><mover><mi>Mu</mi><mo>¯</mo></mover></math> transition and the correction to the transverse positron polarization are related, and we show that the two are related in the model of a neutral flavor gauge boson. We also investigate the models to generate the Mu-to-<math><mover><mi>Mu</mi><mo>¯</mo></mover></math> transition, such as an inert <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math> doublet, an <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><msub><mo>)</mo><mi>L</mi></msub></math> triplet for the type-II seesaw model, a dilepton gauge boson, and a left-right model. The nonzero value of the transverse polarization for one of the two directions, <math><mrow><msub><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub></mrow></math>, violates the time-reversal invariance, and the experimental constraint of the electron electric dipole moment can provide a severe constraint on <math><mrow><msub><mrow><mi>P</mi></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub></mrow></math>, depending on the model.

Transverse positron polarization in the polarized <math><msup><mi>μ</mi><mo>+</mo></msup></math> decay related with the muonium-to-antimuonium transition

We study charged lepton flavor violation (CLFV) associated with heavy quark pair production in lepton-nucleon deep-inelastic scattering ℓ  i  N → ℓ  j  q   <math> <mover> <mi>q</mi> <mo>¯</mo> </mover> </math>  $$ \overline{q} $$  X. Here ℓ  i  and ℓ  j  denote the initial and final leptons; N and X are respectively the initial nucleon and arbitrary final hadronic system. We employ a model Lagrangian in which a scalar and pseudoscalar mediator generates the CLFV. We derive heavy quark structure functions for scalar and pseudoscalar currents and compute momentum distributions of the final lepton for the process. Our focus is on the heavy quark mass effects in the final lepton momentum distribution. We clarify the necessity of inclusion of the heavy quark mass to obtain reliable theory predictions for the CLFV signal searches in the deep-inelastic scattering.

Yuichiro Kiyo

Michihisa Takeuchi

Charged lepton flavor violation associated with heavy quark production in deep inelastic lepton-nucleon scattering via scalar exchange

The decay <math><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>e</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub><msub><mi>ν</mi><mi>μ</mi></msub></math> of a muon that is bound to a nucleus poses an unavoidable background for experiments such as Mu2e, COMET, and DeeMe searching for lepton-flavor-violating <math><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>e</mi><mo>−</mo></msup></math> conversion and thus requires a precise understanding. We calculate the electron-energy spectra of muon decays in orbit near the electron energy end point for all stable isotopes and estimate uncertainties due to the nuclear charge distribution. Our results enable background studies of mixed or enriched target materials that are necessary for the next generation of <math><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>e</mi><mo>−</mo></msup></math> conversion experiments.

Isotope dependence of muon decay in orbit

Muonium is a bound state composed of an antimuon and an electron, and it constitutes a hydrogenlike atom. Because of the absence of the hadronic matter in the bound state, the muonium is a useful probe to explore new physics being free from the hadronic uncertainties. The process of the muonium-to-antimuonium transition is considered to be effective to identify fundamental interactions which relate to the lepton flavor and lepton number violation. New experiments are being planned at J-PARC in Japan and CSNS in China, and it is expected to attract more attention in the near future. In this paper, we will study what kind of model can be verified in the next generation of the muonium-to-antimuonium transition search experiments while escaping the limitations from other experiments. Though the transition probability is strongly suppressed by the lepton flavor conservation in the standard model, it can be much larger by the exchanges of neutral and doubly charged bosons, and by box loop diagrams in new physics beyond the standard model. We study the neutrino models with heavy Majorana neutrinos at TeV scale, a type-II seesaw model, left-right models, and models for radiative neutrino masses such as the Zee-Babu model in particular, in addition to other possible models to induce the sizable transition probability, which can be tested in the forthcoming experiments.

Models of the muonium to antimuonium transition

We analyze the distributions of energy, the opening angle, and the invariant mass in muonic neutrino trident production processes, <math><msub><mi>ν</mi><mi>μ</mi></msub><mo>→</mo><msub><mi>ν</mi><mi>μ</mi></msub><mi>μ</mi><mover><mi>μ</mi><mo>¯</mo></mover></math>, in a minimal gauged <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mrow><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></mrow></msub></math> model, in which the discrepancy of the anomalous magnetic moment of muon can be solved. It is known that the total cross section of neutrino trident production has parameter degeneracy in the new gauge boson mass and gauge coupling constant, and therefore other observables are needed to determine these parameters. From numerical analyses, we find that the muon energy and invariant mass distributions show the differences among the new physics parameter sets with which the total cross section has the same value, while the antimuon energy and opening angle distributions are not sensitive to the parameters.

Takashi Shimomura

Kinematical distributions of coherent neutrino trident production in gauged <math><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> model