We have determined in detail the electron spectrum in the decay of bound muons. These results are especially relevant for the upcoming muon-electron conversion experiments.
In models where lepton number is considered to be a spontaneously-broken global symmetry a massless Goldstone boson, the majoron (J), appears. We describe a procedure to explore the muon-electron-majoron coupling using the results from mu-e conversion search experiments. To accomplish that, we determine how the energy spectrum of the muon decay into an electron and a majoron is modified by binding effects in a muonic atom. We find that the future mu-to-e conversion experiments may be able to produce bounds on the mu->eJ rate which are comparable with the present ones from direct searches.
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 $μ^-\to e^-$ 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 $μ^-\to e^-$ conversion rates for all stable isotopes and estimate nuclear-str…
In this article, we investigate the $μ^-\to e^-X$ process in a muonic atom, where $X$ is a light neutral boson. By calculating the spectrum of the emitted electron for several cases, we discuss the model-discriminating power of the process. We report the strong model dependence of the spectrum near a high-energy endpoint. Our findings show that future experiments using muonic atoms are helpful to identify the properties of exotic bosons.
We suggest that $e\to μ$ conversion in low-energy electron-nucleus scattering is a new and potentially observable indirect signal of supersymmetry and should be searched for in experiment. We estimate the rate for this process in a straightforward calculation taking into account the existing constraint from non-observation of the $μ\to eγ$ decay and find the cross-section to be $σ< 10^{-8} $fb.
A detailed study of the muonic analogue of neutrinoless double beta decay, (muon^-,muon^+) conversion, has been carried out for the A=44 nuclear system. We studied several lepton number violating (LNV) mechanisms potentially triggering this process: exchange by light and heavy Majorana neutrinos as well as exchange by supersymmetric particles participating in R-parity violating interactions. The nuclear structure has been taken into account within the renormalized Quasiparticle Random Phase Approximation method. To our knowledge, this is the first realistic treatment of nuclear structure aspec…
Transition rates for coherent muon-electron conversion in muonic atoms, mu+N --> e+N, are computed for various types of muon number violating interactions. Attention is paid to relativistic atomic effects, Coulomb distortion, finite nuclear size, and nucleon distributions. Discrepancies with previously published results are pointed out and explained. Results are presented for several elements of current and future experimental interest.
Lepton flavor violation (LFV) has been discovered in the neutrino sector by neutrino oscillation experiments. The minimally extended Standard Model (SM) to include neutrino masses allows LFV in the charged sector (CLFV) at the loop-level, but at rates that are too small to be experimentally observed. Lepton number violation (LNV) is explicitly forbidden even in the minimally extended SM, where the observation of a LNV process would be unambiguous evidence of physics beyond the SM. The search for the LNV and CLFV process $μ^- + N(A,Z) \to e^+ + N'(A,Z-2)$ (referred to as $μ^- \to e^+$ conversio…
Muon-electron conversion in nuclei is considered in the framework of the Dualized Standard Model. The ratio $B_{μ-e}$ of the conversion rate to the total muon capture rate is derived, and computed for several nuclei in a parameter-free calculation using parameters previously determined in different physical contexts. The values obtained all lie within the present experimental bounds, but some are so close as to seem readily accessible to experiments already being planned. Similar considerations are applied also to muon-electron conversion in muonium but give rates many orders of magnitude belo…
We present the first detailed computation of the conversion of a bound muon into an electron mediated by a doubly charged $SU(2)$ singlet scalar. Although such particles are not too exotic, up to now their contribution to $μ$-$e$ conversion is unknown. We close this gap by presenting a detailed calculation, which will allow the reader not only to fully comprehend the discussion but also to generalise our results to similar cases if needed. We furthermore compare the predictions, for both the general case and for an example model featuring a neutrino mass at 2-loop level, to current experimenta…
We study the lepton number violating muon-positron conversion in nuclei mediated by the exchange of virtual light Majorana neutrinos. We found that a previously overlooked imaginary part of this amplitude plays an important role. The numerical calculation has been made for the experimentally interesting muon-positron conversion in Ti48 using realistic renormalized proton-neutron QRPA wave functions. We also discuss the very similar case of the neutrinoless double beta decay of Ca48 The ratio of muon-positron conversion over the total muon absorption has been computed taking into account the cu…
In a few years, the COMET experiment at J-PARC and the Mu2e experiment at Fermilab will probe the $μ-e$ conversion rate in the vicinity of $\mathcal{O}(10^{-17})$ for an Al target with high experimental sensitivity. Within the framework of the minimal supersymmetric extension of the Standard Model with local $B-L$ gauge symmetry (B-LSSM), we analyze the lepton flavor violating (LFV) process of $μ-e$ conversion in nuclei. Considering the constraint of the experimental upper limit of the LFV rare decay $μ\rightarrow eγ$, the $μ-e$ conversion rates in nuclei within the B-LSSM can achieve $\mathca…
In a supersymmetric extension of the standard model with local gauged baryon and lepton numbers (BLMSSM), there are new sources for lepton flavor violation, because the right-handed neutrinos, new gauginos and Higgs are introduced. We investigate muon conversion to electron in nuclei within the BLMSSM in detail. The numerical results indicate that the $μ\rightarrow e $ conversion rates in nuclei within the BLMSSM can reach the experimental upper bound, which may be detected in the future experiments.
The coherent muon-electron conversion rates in various nuclei are calculated for general lepton flavor violating interactions. We solve the Dirac equations numerically for the initial state muon and the final state electron in the Coulomb force, and perform the overlap integrals between the wave functions and the nucleon densities. The results indicate that the conversion branching ratio increases for a light nucleus up to the atomic number Z ~ 30, is largest for Z = 30 -- 60, and becomes smaller for a heavy nucleus with Z > (~ 60). We also discuss the uncertainty from the input proton and neu…
We study the effect of the Higgs-exchange diagram for the lepton flavor violating muon-electron conversion process in nuclei in the supersymmetric seesaw model. The contribution is significant for a large value of tan beta and a small value of a neutral heavy Higgs boson mass, in which case the ratio of the branching ratios of B(mu N -> e N) / B(mu -> e gamma) is enhanced. We also show that the target atom dependence of the conversion branching ratio provides information on the size of the Higgs exchange diagram.
We study the $μ$-$e$ conversion in muonic atoms via an exchange of family gauge boson (FGB) $A_{2}^{\ 1}$ in a $U(3)$ FGB model. Within the class of FGB model, we consider three types of family-number assignments for quarks. We evaluate the $μ$-$e$ conversion rate for various target nuclei, and find that next generation $μ$-$e$ conversion search experiments can cover entire energy scale of the model for all of types of the quark family-number assignments. We show that the conversion rate in the model is so sensitive to up- and down-quark mixing matrices, $U^{u}$ and $U^{d}$, where the CKM matr…
The muon-to-electron conversion in nuclei like aluminum, titanium and gold is studied in the context of a class of mirror fermion model with non-sterile right-handed neutrinos having mass at the electroweak scale. At the limit of zero momentum transfer and large mirror lepton masses, we derive a simple formula to relate the conversion rate with the on-shell radiative decay rate of muon into electron. Current experimental limits (SINDRUM II) and projected sensitivities (Mu2e, COMET and PRISM) for the muon-to-electron conversion rates in various nuclei and latest limit from MEG for the radiative…
Within framework of the $μ$ from $ν$ Supersymmetric Standard Model ($μν$SSM), three exotic right-handed neutrino superfields induce new sources for lepton-flavor violation. In this work, we investigate muon conversion to electron in nuclei within the $μν$SSM in detail. With a 125 GeV Higgs, the numerical results indicate that the $μ-e$ conversion rates in nuclei within the $μν$SSM can reach the experimental upper bound, which could be detected with the future experimental sensitivities.
The decay $μ^-\to e^- \barν_eν_μ$ 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 $μ^-\to e^-$ conversion and thus requires a precise understanding. We calculate the electron-energy spectra of muon decays in orbit near the electron energy endpoint 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 $μ^-\to e^-$ conversion experimen…
In general, attempts to extend the standard model will include extra gauge structure. We parameterize string and technicolor models for a Z' boson with primitive lepton flavor violating interactions. Calculations for its muon conversion rate (mu N -> e N) on Titanium are made and used to show the potential of forthcoming experiments MECO at Brookhaven National Laboratory and PRIME at the Japan Hadron Facility (to be renamed). For reasonable choices of parameters, such U(1) bosons with masses the order 10 TeV and mu-e Z' charge as low as ~10^-5 are demonstrated to be accessible for MECO and PRI…
We present an estimate of the electron to muon conversion cross section in fixed-target elastic electron scattering. The matrix element $<μ| j_\mathrm{em}^μ(0) | e>$ is calculated analytically in two scenarios introducing suitable approximations. We consider on the one hand side the case of three light Dirac neutrinos with CKM-type leptonic mixing and on the other hand a typical see-saw scenario. We evaluate the coulombic contribution to the scattering cross section in the limit of vanishing energy transfer to the nucleus and, thus, obtain a realistic estimate for the total conversion cross se…
The non-photonic neutrino exchange mechanism of the lepton flavor violating muon-electron conversion in nuclei is revisited. First we determine the nucleon coupling constants for the neutrino exchange mechanism in a relativistic quark model taking into account quark confinement and chiral symmetry requirements. This includes a new, previously overlooked tree-level contribution from neutrino exchange between two quarks in the same nucleon. Then for the case of an additional sterile neutrino we reconsider the coherent mode of this process. The presence of a mixed sterile-active neutrino state he…
Electron-muon conversion in nuclei and rare decays induced by LFV dark photon
Bogoliubov Laboratory of Theoretical Physics, JINR(鲍戈留博夫理论物理实验室,俄罗斯联合核子研究所);Matrosov Institute for System Dynamics and Control Theory SB RAS(马特罗索夫系统动力学与控制理论研究所,俄罗斯科学院西伯利亚分院);Millennium Institute for Subatomic Physics at the High-Energy Frontier (SAPHIR) of ANID(智利国家研究与创新发展局高能前沿亚原子物理学千年研究所(SAPHIR));Center for Theoretical and Experimental Particle Physics, Facultad de Ciencias Exactas, Universidad Andres Bello(安德烈斯贝洛大学精确科学学院理论与实验粒子物理中心);Institut für Theoretische Physik, Universität Tübingen, Kepler Center for Astro and Particle Physics(蒂宾根大学理论物理研究所,开普勒天体与粒子物理中心)
We demonstrate the potential of forthcoming mu -> e gamma and mu-e conversion experiments to implicate or disfavor solutions to the gauge hierarchy problem before the advent of the CERN Large Hadron Collider. Solutions of dynamical electroweak symmetry breaking, little Higgs, supersymmetry, and extra dimensions are considered. Correlations of mu -> e gamma and mu-e conversion branching ratios are analyzed for discriminating patterns. Measurements of these exotic muon decays may have compelling implications for supersymmetric solutions.
We study lepton number violating (LNV) process of muon-positron conversion in nuclei mediated by the exchange of light and heavy Majorana neutrinos. Nuclear structure calculations have been carried out for the case of experimentally interesting nucleus 48Ti in the framework of renormalized proton-neutron Quasiparticle Random Phase Approximation. We demonstrate that the imaginary part of the amplitude of light Majorana neutrino exchange mechanism gives an appreciable contribution to the muon-positron conversion rate. This specific feature is absent in the allied case of neutrinoless double beta…
We compute the muon to electron conversion in the type-I seesaw model, as a function of the right-handed neutrino mixings and masses. The results are compared with previous computations in the literature. We determine the definite predictions resulting for the ratios between the muon to electron conversion rate for a given nucleus and the rate of two other processes which also involve a mu-e flavour transition: mu -> e gamma and mu -> eee. For a quasi-degenerate mass spectrum of right-handed neutrino masses -which is the most natural scenario leading to observable rates- those ratios depend on…
We analyze the lepton flavor violating process $μ-e$ conversion in the framework of the minimal R-symmetric supersymmetric standard model. The theoretical predictions are determined by considering the experimental constraint on parameter $δ^{12}$ from the lepton flavor violating decay $μ\rightarrow e γ$. The numerical results show that $γ$ penguins and Z penguins dominate the predictions on CR($μ-e$,Nucleus), and the contributions from Higgs penguins and box diagrams are insignificant. The theoretical predictions on conversion rate CR($μ-e$,Nucleus) in a Al or Ti target can be enhanced close t…
We study nuclear muon-electron (mu-e) conversion in the general framework of effective Lagrangian approach without referring to any specific realization of the physics beyond the standard model (SM) responsible for lepton flavor violation (LFV). All the possible types of short range interactions (non-photonic mechanisms), i.e. (pseudo-)scalar, (axial-)vector and tensor, are included in our formalism. We show that the mu-e conversion in the strange nucleon sea via the scalar interactions is comparable with that in the valence quarks. This provides an insight into the strange quark couplings bey…
We present a new class of constraints to the lepton-family number and R-parity violating couplings from muonium conversion, $μ^{-} + {_{22}^{48}} Ti \to e^{-} + {_{22}^{48}} Ti$, a class of tau decays, $τ\to l +$ (light meson) with $l= μor e$, and $J/ψ$ and $π^0$ decays into a lepton pair. We find that $μ^{-} + {_{22}^{48}} Ti \to e^- + {_{22}^{48}} Ti$ provides one of the strongest constraints along with $Δm_{K}, Δm_{B}$, $μ\to e γ$ and the neutrinoless double $β$ decay. Search for these lepton-family number violating (LFNV) decays forbidden in the standard model is clearly warranted in vario…
The flavor violating $μ^--e^-$ conversion in nuclei is studied within the minimal supersymmetric standard model. We focus on the R-parity violating contributions at tree level including the trilinear and the bilinear terms in the superpotential as well as in the soft supersymmetry breaking sector. The nucleon and nuclear structure have consistently been taken into account in the expression of the $μ^--e^-$ conversion branching ratio constructed in this framework. We have found that the contribution of the strange quark sea of the nucleon is comparable with that of the valence quarks. From the …
There is no guarantee that the violation of lepton number, assuming it exists, will primarily manifest itself in neutrinoless double beta decay ($0νββ$). Lepton-number violation and lepton-flavor violation may be related, and much-needed information regarding the physics that violates lepton number can be learned by exploring observables that violate lepton flavors other than electron flavor. One of the most promising observables is $μ^- \rightarrow e^+$ conversion, which can be explored by experiments that are specifically designed to search for $μ^- \rightarrow e^-$ conversion. We survey lep…
A lepton-flavor violating (LFV) Z' boson may mimic some of the phenomena usually attributed to supersymmetric theories. Using a conservative model of LFV Z' bosons, the recent BNL E821 muon g-2 deviation allows for a LFV Z' interpretation with a boson mass up to 4.8 TeV while staying within limits set by muon conversion, mu -> e gamma, and mu -> eee. This model is immediately testable as one to twenty e^+e^- -> mu tau events are predicted for an analysis of the LEP II data. Future muon conversion experiments, MECO and PRIME, are demonstrated to have potential to probe very high boson masses wi…
We determine the $\mathcal{O}(α)$ correction to the energy spectrum of electrons produced in the decay of muons bound in atoms. We focus on the high-energy end of the spectrum that constitutes a background for the muon-electron conversion and will be precisely measured by the upcoming experiments Mu2e and COMET. The correction suppresses the background by about 15\%.
A class of potential backgrounds for Higgs boson searches in the W W to di-lepton channel at both the Tevatron and Large Hadron Collider is presented. Backgrounds from W photon production with external conversion of the on-shell photon in detector material to an asymmetric electron-positron pair, with loss of the trailing electron or positron has been treated adequately in Higgs searches. Here we consider analogous backgrounds from the production of a W with an off-shell photon and with the internal conversion of the off-shell photon in vacuum to an asymmetric lepton-anti-lepton pair. While th…
In detection of electrons from $μ\to e $ conversion process the monochromatic electron spectrum is transformed due to a photon emission and fluctuations of energy loss in a target. The selection criterion of $μ\to e (γ)$ conversion events is an electron momentum above the threshold momentum of 103.5 MeV/c, which corresponds to the maximum energy loss of 1.5 MeV. Radiative corrections including a virtual photon correction and soft photon emission below 1.5 MeV lead to a reduction by about 10% in the probability of $μ\to e $ conversion process calculated without radiative corrections. The soft p…
The variation of the coherent branching ratio $R_{μe}$ (ratio of the $μ^-\to e^-$ reaction rate divided by the total muon-capture rate) through the periodic table is studied by using exact muon wave functions. It was found that, by using very heavy nuclei (e.g. \nuc{197}Au, the SINDRUM II target) as $μ^-\to e^-$ conversion stopping-targets, the above ratio is favored by a factor of about four to five than by using light ones (e.g. \nuc{48}Ti, chosen as PRIME target).
The exotic neutrinoless $μ^- - e^-$ nuclear conversion is studied within the conventional extensions of the standard model as well as in the minimal supersymmetric (SUSY) models with and without R-parity conservation. The dependence of the $μ^- - e^-$ conversion rates on the nucleon and nuclear structure is consistently taken into account. Using our calculated transition matrix elements and the available experimental data on the branching ratio $R_{μe^-}$ for $^{48}$Ti and $^{208}$Pb as well as the expected experimental sensitivity for $^{27}$Al employed as a target in the planned at Brookhave…
Experimental searches for lepton-flavor-violating coherent muon-to-electron conversion in the field of a nucleus, have been proposed to reach the unprecedented sensitivity of 10^(-16) - 10^(-18) per stopped muon. At that level, they probe new interactions at effective-mass scales well beyond 1000 TeV. However, they must contend with background from ordinary bound muon decay. To better understand the background-spectrum shape and rate, we have carried out a detailed analysis of Coulombic-bound-state muon decay, including nuclear recoil. Implications for future experiments are briefly discussed.
Contact interactions of a muon, an electron and two photons can contribute to the decay $μ\to e γγ$, but also to the conversion of a muon into an electron in the electric field of a nucleus. We calculate the $μ\to e$ conversion rate, and show that for the coefficients of operators involving the combination $FF \propto |\vec{E}|^2$ (as opposed to $F\tilde{F} \propto \vec{E} \cdot \vec{B}$), the current bound on $μ\to e$ conversion is more sensitive than the bound on $μ\to e γγ$.
We present results of a study of the muon decay in orbit (DIO) contribution to the signal region of muon - electron conversion. Electrons from DIO are the dominant source of background for muon - electron conversion experiments because the endpoint of DIO electrons is the same as the energy of electrons from elastic muon - electron conversion. The probability of DIO contribution to the signal region was considered for a tracker with Gaussian resolution function and with a realistic resolution function obtained in the application of pattern recognition and momentum reconstruction Kalman filter …
We use the BNL E821 measurement of g - 2, the anomalous magnetic moment of the muon, to normalize, within a supersymmetric GUT framework, constrained MSSM (CMSSM) predictions for processes that violate charged-lepton flavour conservation, including mu to e gamma, mu to e conversion and K^0_L to mu e. We illustrate our analysis with two examples of lepton mass matrix textures motivated by data on neutrino oscillations. We find that mu to e gamma may well occur at a rate within one or two (two or three) orders of magnitude of the present experimental upper limit if g - 2 is within the one- (two-…
In very dense environments, neutrinos can undergo fast flavor conversions on scales as short as a few centimeters provided that the angular distribution of the neutrino lepton number crosses zero. This work presents the first attempt to establish whether the non-negligible abundance of muons and their interactions with neutrinos in the core of supernovae can affect the occurrence of such crossings. For this purpose we employ state-of-the-art one-dimensional core-collapse supernova simulations, considering models that include muon-neutrino interactions as well as models without these reactions.…
The production of very high energy muons inside an extensive air shower is observable at $ν$ telescopes and sensitive to the composition of the primary cosmic ray. Here we discuss five different sources of these muons: pion and kaon decays; charmed hadron decays; rare decays of unflavored mesons; photon conversion into a muon pair; and photon conversion into a $J/ψ$ vector meson decaying into muons. We solve the cascade equations for a $10^{10.5}$ GeV proton primary and find that unflavored mesons and gamma conversions are the two main sources of $E\ge 10^{8.5}$ GeV muons, while charm decays d…
Little Higgs models provide a natural explanation of the little hierarchy between the electroweak scale and a few TeV scale, where new physics is expected. Under the same inspiring naturalness arguments, this work completes a previous study on lepton flavor-changing processes in the Littlest Higgs model with T-parity exploring the channel that will eventually turn out to be the most sensitive, μ-e conversion in nuclei. All one-loop contributions are carefully taken into account, results for the most relevant nuclei are provided and a discussion of the influence of the quark mixing is included.…
The Effective Theory of Muon-to-Electron Conversion
University of California, Berkeley(加州大学伯克利分校);Institute for Nuclear Theory, University of Washington(华盛顿大学核理论研究所);Lawrence Berkeley National Laboratory(劳伦斯伯克利国家实验室);Los Alamos National Laboratory(洛斯阿拉莫斯国家实验室)
We compute the dominant, logarithmically enhanced radiative corrections to the electron spectrum in the bound muon decay in the whole experimentally interesting range. The corrected spectrum fits well the TWIST results. The remaining theoretical error, dominated by the nuclear charge distribution, can be reduced in the muon-electron conversion searches by measuring the spectrum slightly below the New Physics signal window.
The formalism for the neutrinoless muon positron conversion is investigated in detail and the relevant nuclear matrix elements for light intermediate neutrinos in the case of the experimentally interesting A=27 system are calculated. The nucleus is going to be used as a stopping target in the MECO experiment at Brookhaven, one of the most sensitive probes expected to reach a sensitivity in the branching ratio within the next few years, which will be an improvement of three orders of magnitude. The relevant transition operators are constructed utilizing a variety of mechanisms present in curren…
Neutrinos in a core-collapse supernova can undergo fast flavor conversions with a possible impact on the explosion mechanism and nucleosynthesis. We perform the first non-linear simulations of fast conversions in the presence of three neutrino flavors. The recent supernova simulations with muon production call for such an analysis, as they relax the standard $ν_{μ,τ}=\barν_{μ,τ}$ (two-flavor) assumption. Our results show the significance of muon and tau lepton number angular distributions, together with the traditional electron lepton number ones. Indeed, our three-flavor results are potential…
A study of mu-tau conversion via the deep inelastic scattering process μN -> τX, with N a nucleon, is performed taking into account the effects from both spin-0 and spin-1 unparticles with lepton flavor violating (LFV) couplings. This process has attracted attention in the past as it may be at the reach of a future neutrino or muon factory. For the model parameters, we use the most recent constraints on the unparticle LFV couplings from the experimental limits on the muon anomalous magnetic moment and the LFV decay τ-> 3μ, whereas for the unparticle scale Λ_U and scale dimension d_U we use the…
Constraints from the muon anomalous magnetic dipole moment and lepton flavor violating processes are translated into lower bounds on v_Delta*m_H++ in the Higgs Triplet Model by considering correlations through the neutrino mass matrix. The discrepancy of the sign of the contribution to the muon anomalous magnetic dipole moment between the measurement and the prediction in the model is clarified. It is shown that mu to e gamma, tau decays (especially, tau to mu e e), and the muonium conversion can give a more stringent bound on v_Delta*m_H++ than the bound from mu to eee which is expected naive…
We present a detailed computation of the expected rate for Geomagnetic Conversion of Solar Axions to X-rays (GECOSAX) along the orbit of an x-ray satellite. We use realistic satellite orbits and propagation in time. A realistic model for the Earth's magnetic field, which properly accounts for its spatial non-uniformity, is used. We also account for the effect of the Earth's atmosphere on the propagation of x-rays in our calculation of axion-photon conversion probability. To estimate possible sensitivities to the axion-photon coupling g_{aγ}, we use an actual measurement of the expected backgro…
The Mu2e and COMET collaborations will search for nucleus-catalyzed muon conversion to positrons ($μ^-\rightarrow e^+$) as a signal of lepton number violation. A key background for this search is radiative muon capture where either: 1) a real photon converts to an $e^+ e^-$ pair "externally" in surrounding material, or 2) a virtual photon mediates the production of an $e^+e^-$ pair "internally". If the $e^+$ has an energy approaching the signal region then it can serve as an irreducible background. In this work we describe how the near end-point internal positron spectrum can be related to the…