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 photons emission below 1.5 MeV contributes to a change of electron spectrum from monoenergetic one at 105 MeV to a spectrum with a low energy tail for the process of $μ\to e (γ)$ conversion. However the effect of smearing of the initial momentum distribution due to the soft photon emission is small in comparison with a smearing due to energy loss fluctuations in a target. The average energy of soft photons emitted below 1.5 MeV is found to be 40 keV. The soft photon approximation is a good description for $μ\to e (γ)$ conversion process with photons emitted below 1.5 MeV.
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.
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 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 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.
Muon pair production in exclusive radiative decays $χ_{cJ}\to J/ψμμ$, $χ_{bJ}\toΥμμ$ are considered. We present numerical values of the branching fractions and distributions over various kinematical variables.
One-loop QED corrections to the differential width of radiative muon decay are considered. Results can be used to analyze high statistics data of modern and future experiments.
Radiative muon and tau lepton decays are described within the model-independent approach with the help of generalized Michel parameters. The exact dependence on charged lepton masses is taken into account. The results are relevant for modern and future experiments on muon and tau lepton decays.
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.
The first order QED corrections to the polarized muon decay spectrum are considered. The exact dependence on electron and muon masses is kept. Numerical results are presented.
The radiative decay of muon-neutrinos in matter with a scheme of mass-degenerate neutrinos could be the common origin of the appearance of anti-electron-neutrinos at LSND and the disappearance of muons-neutrinos at SuperKamiokande. With the decay probability fixed by the LSND signal, the deficit of atmospheric neutrinos can be satisfactorily reproduced.
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.
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.
High-energy muons can travel large thicknesses of matter. For underground neutrino and cosmic ray detectors the energy loss of muons has to be known accurately for simulations. In this article the next-to-leading order correction to the average energy loss of muons through bremsstrahlung is calculated using a modified Weizsäcker-Williams method. An analytical parametrisation of the numerical results is given.
Recent measurements of the Higgs-muon coupling are directly probing muon mass generation for the first time. We classify minimal models with a one-loop radiative mass mechanism and show that benchmark models are consistent with current experimental results. We find that these models are best probed by measurements of $(g-2)_μ$, even when taking into account the precision of Higgs measurements expected at future colliders. The current $(g-2)_μ$ anomaly, if confirmed, could therefore be a first hint that the muon mass has a radiative origin.
We calculate in closed analytical form the one-photon loop radiative corrections to muon Compton scattering $μ^- γ\to μ^- γ$. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Infrared finiteness of the (virtual) radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $λ$. We find that the anomalous magnetic moment $α/2π$ provides only a very small portion of the full radiative corrections. Furthermore, we extend our calculation of radiative corrections to the muon-nucleus bremsstrahlung process (or …
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…
Process of muon (pion) pair production with small invariant mass in the electron-positron high-energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Dell-Yan picture for differential cross section is valid in the charge-even experimental set-up. Radiative corrections both for electron block and for final state block are taken into account.
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）
The lowest order radiative correction to the differential cross-section of process of muon pair production with emission of hard photon at high energy electron-positron annihilation are calculated. Taking into account the emission of additional soft and hard photon the cross-section can be put in the form of Drell-Yan process in leading logarithmical approximation. Applying the crossing transformation we obtain the cross section of radiative electron-muon high-energy scattering process. Virtual and soft photon emission contributions of non-leading form are tabulated for several typical kinemat…
The leptons are viewed as composite objects, exhibiting anomalous magnetic moments and anomalous flavor-changing transition moments. The decay $μ\to e γ$ is expected to occur with a branching ratio of the same order as the present experimental limit.
We explore muon anomalous magnetic moment (muon $g-2$) in a scotogenic neutrino model with a gauged lepton number symmetry $U(1)_{μ-τ}$. In this model, a dominant muon $g-2$ contribution comes not from an additional gauge sector but from a Yukawa sector. In our numerical $Δχ^2$ analysis, we show that our model is in favor of normal hierarchy with some features. We demonstrate one benchmark point, satisfying muon $g-2$ at the best fit value $25.1\times10^{-10}$.
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 the NNLO radiative corrections of enhanced electroweak strength to the lineshape of the Higgs boson in the processes ($μ^+μ^- \to H \to ZZ$) and ($μ^+μ^- \to H \to t\bar t$), which are of interest for Higgs searches at a possible muon collider. We give the radiative corrections both in the on-shell renormalization scheme and in the pole renormalization scheme. The pole scheme appears to have better convergence properties, in agreement with previous results regarding the position of the Higgs pole in the complex plane.
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 process of the muon (pion) pair production with small invariant mass in the electron--positron high--energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Drell--Yan picture for differential cross section is valid in the charge--even experimental set--up. Radiative corrections both for electron block and for final state block are taken into account.
We have noted that the electron spectrum of muon decay in the leading logarithmic approximation calculated in two lowest orders of the perturbation theory in the paper of Berman (1958), can be reproduced by the parton language. This fact permits one to generalize the result to all orders of the perturbation theory using the structure function method.
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 …
We present results for the corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We improve the precision of previous results.
Electroweak radiative corrections to muon capture on nuclei are computed and found to be sizable. They enhance the capture rates for hydrogen and helium by 2.8% and 3.0% respectively. As a result, the value of the induced pseudoscalar coupling, g_P^exp, extracted from a recent hydrogen 1S singlet capture experiment is increased by about 21% to g_P^exp = 7.3 +/- 1.2 and brought into good agreement with the prediction of chiral perturbation theory, g_P^theory=8.2 +/- 0.2. Implications for helium capture rate predictions are also discussed.
The evidence for dark matter signals a new class of particles at the TeV scale, which may manifest themselves indirectly through loop effects. In a simple model we show that these loop effects may be responsible for the enhanced muon anomalous magnetic moment, for the neutrino mass, as well as for leptogenesis in a novel way. This scenario can be verified at LHC experiments.
An expression for the Dalitz plot of the semileptonic decay of a charged kaon, including radiative corrections to order O[απ)(q/M_1)], where q is the four-momentum transfer and M_1 is the mass of the decaying kaon, is obtained. Contributions of both the three- and four-body regions are accounted for. Besides, the emitted muon is considered to be polarized so the analysis is also focused on evaluating the radiative corrections to the longitudinal, transverse, and normal polarization components of the muon. The final formulas, with the triple integration of the bremsstrahlung photon variables re…
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…
Electrons emitted in the radiative decay mu^- -> e^- anti-nu_e nu_mu gamma have a significant probability of being right-handed, even in the limit m_e -> 0. Such ``wrong-helicity'' electrons, arising from helicity-flip bremsstrahlung, contribute an amount alpha/(4 pi) Gamma_0 to the muon decay width (Gamma_0 = G_F^2 m^5_mu/ (192 pi^3)). We use the helicity-flip splitting function D_hf (z) of Falk and Sehgal (Phys. Lett. B 325, 509 (1994)) to obtain the spectrum of the right-handed electrons and the photons that accompany them. For a minimum photon energy E_gamma = 10 MeV (20 MeV), approximatel…
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…
Muon pair production through the radiative return is of importance for a measurement of the hadronic production cross section in two ways: it provides an independent calibration and it may give rise to an important background for a measurement of the pion form factor. With this motivation the Monte Carlo event generator PHOKHARA is extended to include next-to-leading order radiative corrections to the reaction $e^+e^-\to μ^+μ^-γ$. Furthermore, virtual ISR corrections to FSR from pions are introduced, which extends the applicability of the generator into a new kinematical regime. Finally, the e…
The recent experimental status, including the confirmation of the muon $g-2$ anomaly at Fermilab, indicates a Beyond Standard Model (BSM) satisfying the following properties: 1) it enhances the $g-2$ 2) suppresses flavor violations, such as $μ\to e γ$, 3) suppresses CP violations, such as the electron electric dipole moment (EDM). In this letter, I show that if the masses of heavy leptons are generated radiatively, the eigenbasis of the mass matrix and higher dimensional photon operators can be automatically aligned. As a result, the muon $g-2$ is enhanced but the EDM of the electron and $μ\to…
We discuss the decay tau^- -> nu_tau pi^- pi^0 gamma in terms of a model with the correct low-energy structure and with the relevant resonance degress of freedom. The nontrivial radiative dynamics becomes visible for large photon momenta only. We use the model to calculate electromagnetic corrections for the two-pion contribution to hadronic vacuum polarization extracted from photon-inclusive two-pion decays. The corrections are insensitive to the details of the model and depend on the pion form factor only. Putting all relevant isospin violating corrections together, we obtain a shift Delta a…
We propose a leptoquark model simultaneously to explain anomalies of muon anomalous magnetic dipole moment and $b\to s μ\barμ$ in light of experimental reports very recently. Here, we satisfy several stringent constraints such as $μ\to eγ$ and meson mixings. In addition, we find these leptoquarks also play an role in generating tiny neutrino masses at one-loop level without introducing any additional symmetries. We have numerical analysis and show how degrees our parameter space is restricted.
This is the second of a series of papers on the radiative corrections of order $α^2 (Zα)$, $α(Zα)^2$, and various logarithmic terms of order $α^4$, to the hyperfine structure of the muonium ground state. This paper deals with the $α(Zα)^2$ correction. Based on the NRQED bound state theory, we isolated the term of order $α(Zα)^2$ exactly. Our result $+16.904 2 (11) α(Zα)^2 E_F / π$ for the non-logarithmic part is consistent with the $α(Zα)^2$ part of Sapirstein's calculation and the recent result of Pachucki, and reduces the numerical uncertainty in the $α(Zα)^2$ term by two orders of magnitude…
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…
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the muon factor. The contribution produced by electron polarization insertions are enhanced by the large logarithm of the electron-muon mass ratio. We obtained all single-logarithmic and nonlogarithmic radiative-recoil corrections of order $α^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.
A self-consistent version of the left-right (LR) symmetric model is used to examine tree- as well as one-loop level radiative corrections to the muon decay. It is shown that constraints on the heavy sector of the model parameters are different when going beyond tree-level physics. In fact, in our case, the only useful constraints on the model can be obtained from the one-loop level calculation. Furthermore, corrections coming from the subset of SM particles within the LR model have a different structure from their SM equivalent, e.g. the top quark leading term contribution to $Δρ$ within the L…
Analytic calculation are presented of the contribution to the anomalous magnetic moment of a muon from the channels of annihilation of an electron-positron pair to a pair of charged pi-mesons with radiative correction connected with the final state, as well as corrections to the lowest order kernel. The result with point-like pi-meson assumptions is $a_{point}=a_{point}^{(1)}+Δa_{point}$, $a_{point}^{(1)}=7.0866 \cdot 10^{-9}; Δa_{point}= -2.4 \cdot 10^{-10} .$ Taking into account the pion form factor in the frames of the Nambu-Jona-Lasinio (NJL) approach leads to $a_{NJL}=a_{NJL}^{(1)}+Δa_{NJ…
