The $μ^-e^-\to e^-e^-$ process in a muonic atom is one of the promising probes to study the charged lepton flavor violation (CLFV). We have investigated the angular distribution of electrons from the polarized muon of the atomic bound state. The parity violating asymmetric distribution of electrons is analyzed by using lepton wave functions under the Coulomb interaction of a finite nuclear charge distribution. It is found that the asymmetry parameters of electrons are very sensitive to the chiral structure of the CLFV interaction and the contact/photonic interaction. Therefore, together with the atomic number dependence of the decay rate studied in our previous work, the angular distribution of electrons from a polarized muon should be a very useful tool to constrain the model beyond the standard model.
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.
In this paper the longitudinal profile of muon production along the shower axis is studied. The characteristics of this distribution is investigated for different primary masses, zenith angles, primary energies, and different high energy hadronic models. It is found that the shape of this distribution displays universal features similarly to what is known for the electromagnetic profile. The relation between the muon production distribution and the longitudinal electromagnetic evolution is also discussed.
We propose a new process of mu(-) e(-) -> e(-) e(-) in a muonic atom for a quest of charged lepton flavor violation. The Coulomb attraction from the nucleus in a heavy muonic atom leads to significant enhancement in its rate, compared to mu(+) e(-) -> e(+) e(-). The upper limit of the branching ratio is estimated to be of the orders of O[10^(-17)-10^(-18)] for the photonic and the four Fermi interactions from the present experimental constraints. The search for this process could serve complementarily with the other relevant processes to shed lights upon the nature of charged lepton flavor vio…
We calculate cross sections for production of axial-vector $f_1(1285)$ mesons for double-tagged measurements of the $e^+ e^- \to e^+ e^- f_1(1285)$ reaction. Different $γ^* γ^* \to f_1(1285)$ vertices from the literature are used. Both integrated cross section as well as differential distributions are calculated. Predictions for a potential measurement at Belle II are presented. Quite different results are obtained for the different vertices proposed in the literature. Future measurements at $e^+ e^-$ colliders could test and/or constrain the $γ^* γ^* \to f_1 (a_1, f_1')$ vertices and associat…
We constrain the possibility of a new pseudoscalar coupling between the muon and proton using a recent measurement of the 2S hyperfine splitting in muonic hydrogen.
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.
The electromagnetic and the muonic longitudinal profile at production enclosure important information about the primary particle and the hadronic interactions that rule the shower development. In fact, these two profiles provide two different insights of the shower: the electromagnetic component gives a measurement of the energy and the strength of the neutral pion channel; while the muonic profile, being intimately related with the charged mesons decays, can be used as a direct probe for the high energy hadronic interactions. In this work we explore the interplay between the electromagnetic a…
Conserved muonic number may turn out to be a conserved muonic charge, coupled to muonic photons, gamma_mu. Muons and muonic neutrinos would emit gamma_mu's, which might be discovered by analysing the data from the past and future high energy neutrino experiments (like CHARM II, CCFR, CHORUS, NOMAD, etc.). There are two sources of gamma_mu's in these experiments: 1) internal bremsstrahlung in pion and kaon decays into mu and nu_mu, which provide neutrino beams; 2) external bremsstrahlung of muons in the shielding of the neutrino beam. In both cases the gamma_mu's would pass freely through the s…
The contribution of the $α^3$ single electron-loop vacuum-polarization diagrams to the Lamb shift of the muonic hydrogen has been evaluated recently by two independent methods. One uses the exact parametric representation of the vacuum-polarization function while the other relies on the Padé approximation method. High precision of these values offers an opportunity to examine the reliability of the Monte-Carlo integration as well as that of the Padé method. Our examination covers both muonic hydrogen atom and muon $g-2$. We tested them further for the cases involving two-loop vacuum polarizati…
We show that the value of the proton mass depends on each bound state of muonic or electronic hydrogen atom. The charged particle bound to the proton produces magnetic field inside the proton. This makes a change to the amount of chiral condensate inside the proton. The change gives rise to the shift in the value of the proton mass. Numerically, the shift in the $2S$ state of the muonic hydrogen atom can be of the order of $0.1$ meV. The effect may solve the puzzle of the proton radius.
From the comparison between the experimental and theoretical results for the energy difference between 2s1/2 and 2p1/2 states in hydrogen and hydrogen-like ions with different values of Z, we estimate bounds for the presence of an extra fractional dimension. These bounds are higher when we work with muonic hydrogen and muonic deuterium, which open the possibility that future measurements of the Lamb shift in muonic atoms with one electron and higher values of Z may show evidence of the extra dimension.
The detection of ultralight dark matter through interactions with nucleons, electrons, and photons has been explored in depth. In this work we propose to use precision muon experiments, specifically muon g-2 and electric dipole moment measurements, to detect ultralight dark matter that couples predominantly to muons. We set direct, terrestrial limits on DM-muon interactions using existing g-2 data, and show that a time-resolved reanalysis of ongoing and upcoming precession experiments will be sensitive to dark matter signals. Intriguingly, we also find that the current muon g-2 anomaly can be …
Currently, both the g factor measurement of the muon as well as the Lamb shift 2S-2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. W…
We explore the possibility that a new interaction between muons and protons is responsible for the discrepancy between the CODATA value of the proton radius and the value deduced from the measurement of the Lamb shift in muonic hydrogen. We show that a new force carrier with roughly MeV mass can account for the observed energy shift as well as the discrepancy in the muon anomalous magnetic moment. However, measurements in other systems constrain the couplings to electrons and neutrons to be suppressed relative to the couplings to muons and protons, which seems challenging from a theoretical po…
The objective of this work is to report on the modifications in air shower development due to muon bremsstrahlung and muonic pair production. In order to do that we have implemented new muon bremsstrahlung and muonic pair production procedures in the AIRES air shower simulation system, and have used it to simulate ultra high energy showers in different conditions. The influence of the mentioned processes in the global development of the air shower is important for primary particles of large zenith angles, while they do not introduce significant changes in the position of the shower maximum.
The sixth-order electron-loop vacuum-polarization contribution to the $2P_{1/2} - 2S_{1/2}$ Lamb shift of the muonic hydrogen ($μ^{-} p^+$ bound state) has been evaluated numerically. Our result is 0.007608(1) meV. This eliminates the largest uncertainty in the theoretical calculation. Combined with the proposed precision measurement of the Lamb shift it will lead to a very precise determination of the proton charge radius.
Leading order ($α^4$) finite size corrections in muonic deuterium are evaluated within a few body formalism for the $μ^- p n$ system in muonic deuterium and found to be sensitive to the input of the deuteron wave function. We show that this sensitivity, taken along with the precise deuteron charge radius determined from muonic atom spectroscopy can be used to determine the elusive deuteron D-state probability, $P_D$, for a given model of the nucleon-nucleon (NN) potential. The radius calculated with a $P_D$ of 4.3\% in the chiral NN models and about 5.7\% in the high precision NN potentials is…
The recoil, vacuum polarization and electron vertex corrections of first and second orders in the fine structure constant $α$ and the ratio of electron to muon and electron to α-particle masses are calculated in the hyperfine splitting of the $1s^{(e)}_{1/2}2s^{(μ)}_{1/2}$ state of muonic helium atom (μe ^4_2He) on the basis of a perturbation theory. We obtain total result for the muonically excited state hyperfine splitting $Δν^{hfs}=4295.66$ MHz which improves previous calculations due to the account of new corrections and more accurate treatment of the electron vertex contribution.
The complete contribution of diagrams with the light-by-light scattering to the Lamb shift is found for muonic hydrogen, deuterium and helium ion. The results are obtained in the static muon approximation and a part of the paper is devoted to the verification of this approximation and analysis of its uncertainty.
Weak interaction contributions to hyperfine splitting and Lamb shift in light electronic and muonic atoms are calculated. We notice that correction to hyperfine splitting turns into zero for deuterium. Weak correction to the Lamb shift in hydrogen is additionally suppressed in comparison with other cases by a small factor $(1-4\sin^2θ_W)$.
In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The coupling of mesons with the muon is via two-photon intermediate state. The parametrization of the transition form factor of two photons into PS and AV mesons, based on the experimental data on the transition form factors and QCD asymptotics, is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are …
Using the nonobservance of missing mass events in the leptonic kaon decay $K \to μX$, we place a strong constraint on exotic parity-violating gauge interactions of the right-handed muon. By way of illustration, we apply it to an explanation of the proton size anomaly that invokes such a new force; scenarios in which the gauge boson decays invisibly or is long-lived are constrained.
In this work we investigate the possibility to observe $C\!P$-violation in $η$ decays containing muons at the proposed REDTOP experiment. Employing the SMEFT to parametrize the new-physics $C\!P$-violating effects, we find that a single operator exists for which is possible to observe $C\!P$-violation at REDTOP in $η\toμ^+μ^-$ decays, while evading bounds from the neutron electric dipole moment and $D^-\toμ\barν$
A bound-state field theory approach to muonic hydrogen is set up using a variant of the Furry representation in which the lowest-order Hamiltonian describes a muon in the presence of a point Coulomb field, but the origin of the binding field is taken to be three charged quarks in the proton which are modeled as Dirac particles that move freely within a spherical well. Bound-state field theory techniques are used to evaluate one- and two-photon effects. Particular attention is paid to two-photon exchange diagrams, which include the effect of proton polarizability. In addition the modification o…
The recent discrepancy between proton charge radius measurements extracted from electron-proton versus muon-proton systems is suggestive of a new force that differentiates between lepton species. We identify a class of models with gauged right-handed muon number, which contains new vector and scalar force carriers at the 100 MeV scale or lighter, that is consistent with observations. Such forces would lead to an enhancement by several orders-of-magnitude of the parity-violating asymmetries in the scattering of low-energy muons on nuclei. The relatively large size of such asymmetries, O(10^{-4}…
Bound muons (also pions, kaons, etc) increase the fission barrier and produce some stabilizing effects for highly charged nuclei. If the binding energy of the muon exceeds $mc^2$, it becomes stable. The $1s$ state of a muon inside an exotic nucleus with atomic number $A= 5Z/2$ and such large charge $Z$ that the $1s$ energy $E$ is in the range $0\le E<-mc^2$ is considered.
We consider one-loop light-by-light-scattering contributions to the Lamb shift of the $1s, 2s, 2p$ states in light muonic hydrogen like atoms at $Z\leq10$. The contributions are of the order $α^5m_μ$ (with diverse dependence on the nuclear charge $Z$). Those include the contributions of the so-called Wichmann-Kroll potential ($α(Zα)^4m_μ$), the virtual Delbrück scattering ($α^2(Zα)^3m_μ$), etc. The results are obtained in a nonrelativistic approximation. For the calculation of the virtual-Delbrück-scattering contribution, we have constructed an effective potential in the coordinate space which…
ALPs (Axion Like Particle) beyond the standard model are solutions to several important problems of modern physics. One way to detect these particles is to detect the new interactions they meditate. Many experiments have been performed to search for these new interactions in ranges from $\simμ$m to astrophysical range. At present, nearly all known experiments searching for the ALP-meditated long range new interactions use sources or probes containing protons, neutrons and electrons. Constraints for other fermions such as muons are scarce, though muons might be the most suspicious particles whi…
We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic deuterium (mu d) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure and recoil effects are calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.
On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $α(Z α)^5$ to the Lamb shift in muonic hydrogen and helium. To construct the interaction potential of particles, which gives the necessary contributions to the energy spectrum, we use the method of projection operators to states with a definite spin. Separate analytic expressions for the contributions of the muon self-energy, the muon vertex operator and the amplitude with spanning photon are obtained. We present also numerical results for these contributions using m…
The calculation of hadronic polarizability contribution of the nucleus to hyperfine structure of muonic hydrogen and helium is carried out within the unitary isobar model and experimental data on the polarized structure functions of deep inelastic lepton-proton and lepton-deuteron scattering. The calculation of virtual absorption cross sections of transversely and longitudinally polarized photons by nucleons in the resonance region is performed in the framework of the program MAID.
We calculate hyperfine structure intervals $ΔE^{hfs}(2P_{1/2})$ and $ΔE^{hfs}(2P_{3/2})$ for P-states in muonic ions of lithium, beryllium and boron. To construct the particle interaction operator in momentum space we use the tensor method of projection operators on states with definite quantum numbers of total atomic momentum F and total muon momentum j. We take into account vacuum polarization, relativistic, quadruple and structure corrections of orders $α^4$, $α^5$ and $α^6$. The obtained numerical values of hyperfine splittings can be used for a comparison with future experimental data of …
The steady advance in core-collapse supernova simulations requires a more precise description of neutrino processes in hot and dense matter. In this work, we study the rates of charged-current (CC) weak processes with (anti)muons in supernova matter. At the relativistic mean field level, we derive results for the rates of CC neutrino-nucleon reactions, taking into account full kinematics, weak magnetism and pseudoscalar terms, and $q^2$-dependent nucleon form factors in the hadronic current. In addition to muonic semileptonic processes we also consider purely leptonic processes. In particular,…
We illustrate how to apply modern effective field theory techniques and dimensional regularization to factorise the various scales which appear in QED bound states at finite temperature. We focus here on the muonic hydrogen atom. Vacuum polarization effects make the physics of this atom at finite temperature very close to that of heavy quarkonium states. We comment on the implications of our results for these states in the quark gluon plasma. In particular, we estimate the effects of a finite charm quark mass in the dissociation temperature of bottomonium.
