Electron-muon Mass Research Articles

Three Particle Muon-Electron Bound Systems in Quantum Electrodynamics

The muonic 2P-2S Lamb shift in muon-electron atoms and ions of helium, lithium, beryllium, and boron with the electron in the ground state was calculated by the perturbation theory using the fine structure constant and the electron-muon mass ratio. The corrections of first- and second-orders of perturbation theory on the Coulomb interaction and nucleus recoil were taken into account. The obtained analytical results were validated numerically using calculations within the variational method.

Ground-state hyperfine structure of light muon-electron ions

The ground state hyperfine splitting of light muon-electron ions of lithium, beryllium, boron and helium is calculated on the basis of analytical perturbation theory in terms of small parameters of the fine structure constant and electron-muon mass ratio. The corrections of vacuum polarization, nuclear structure and recoil effects and electron vertex corrections are taken into account. The dependence of the corrections on the nucleus charge Z is studied. The obtained total values of hyperfine splitting intervals can be used for comparison with future experimental data.

Low-lying electron energy levels in three-particle electron-muon ions of Li, Be, and B

The electron Lamb shift $(2P-2S)$ and the energy interval $(2S-1S)$ in muon-electron ions of lithium, beryllium, and boron have been calculated within the framework of the perturbation theory method for the fine structure constant and the electron-muon mass ratio. The corrections of the first and second orders of the perturbation theory, which include the effects of vacuum polarization, nuclear structure and recoil, are taken into account. The obtained analytical results in perturbation theory are compared with the results of calculations within the variational approach. The obtained values for the Lamb shift $(2P-2S)$ and the interval $(2S-1S)$ can be used for comparison with future experimental data and verification of quantum electrodynamics.

Hyperfine splitting in muonium: Accuracy of the theoretical prediction

In the last twenty years, the theory of hyperfine splitting in muonium developed without any experimental input. Finally, this situation is changing and a new experiment on measuring hyperfine splitting in muonium is now in progress at J-PARC. The goal of the MuSEUM experiment is to improve by an order of magnitude experimental accuracy of the hyperfine splitting and muon-electron mass ratio. Uncertainty of the theoretical prediction for hyperfine splitting will be crucial for comparison between the forthcoming experimental data and the theory in search of a possible new physics. In the current literature estimates of the error bars of the theoretical prediction differ roughly by a factor of two. We explain the origin of this discrepancy and obtain the theoretical prediction for the muonium hyperfine splitting ΔνHFSth(Mu)=4463302872(515)Hz,δ=1.2×10−7.

High precision measurement of muonium hyperfine structure

MuSEUM (Muonium Spectroscopy Experiment Using Microwave) collaboration aims to measure the muonium hyperfine structure (MuHFS,vhfs) with a few ppb (parts per billion). MuHFS spectroscopy is a stringent test of the bound-state QED. From this measurement, the muon-proton magnetic moment ratio (μμ/μP) and the muon-electron mass ratio (mμ/me) can also be determined by applying a high magnetic field. In the previous MuHFS measurement carried out at Los Alamos Meson Physics Facility (LAMPF), the main uncertainty was caused by the lack of the statistics. MuSEUM collaboration uses the high intense pulsed muon beam at Japan Proton Accelerator Research Complex (J-PARC) to improve the statistical uncertainty. We are also developing our own experimental setups for the improvement of the systematic uncertainties. From June 2016, MuSEUM collaboration have carried out the MuHFS measurement in an extremely low magnetic field within 100 nT and now we are preparing for the measurement in a 1.7 T high magnetic field.

Hard three-loop corrections to hyperfine splitting in positronium and muonium

We consider hard three-loop corrections to hyperfine splitting in muonium and positronium generated by the diagrams with closed electron loops. There are six gauge-invariant sets of such diagrams that generate corrections of order $m\alpha^7$. The contributions of these diagrams are calculated for an arbitrary electron-muon mass ratio without expansion in the small mass ratio. We obtain the formulae for contributions to hyperfine splitting that in the case of small mass ratio describe corrections for muonium and in the case of equal masses describe corrections for positronium. First few terms of the expansion of hard corrections in the small mass ratio were earlier calculated for muonium analytically. We check numerically that the new results coincide with the sum of the known terms of the expansion in the case of small mass ratio. In the case of equal masses we obtain hard nonlogarithmic corrections of order $m\alpha^7$ to hyperfine splitting in positronium.

Light-by-light scattering nonlogarithmic corrections to hyperfine splitting in muonium

We consider three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These diagrams produce both recoil and nonrecoil contributions to hyperfine splitting. Recoil corrections are enhanced by large logarithms of the muon-electron mass ratio. Both nonrecoil and logarithmically enhanced radiative-recoil corrections where calculated some time ago. Here we calculate nonlogarithmic radiative-recoil corrections generated by the insertions of the light-by-light scattering block.

Light-by-light scattering single-logarithmic corrections to hyperfine splitting in muonium

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These corrections are enhanced by the large logarithms of the electron-muon mass ratio. We present the results of an analytic calculation of the single-logarithmic radiative-recoil corrections of order ${\ensuremath{\alpha}}^{2}(Z\ensuremath{\alpha})(m/M){E}_{F}$ to hyperfine splitting in muonium generated by these diagrams.

Radiative recoil corrections to hyperfine splitting: Polarization insertions in the electron factor

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the electron factor. The contribution generated by electron polarization insertions is a cubic polynomial in the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared terms are well known for some time. We calculated all single-logarithmic and nonlogarithmic radiative-recoil corrections of order $\alpha^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.

Radiative-recoil corrections to hyperfine splitting: Polarization insertions in the muon factor

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of a one-loop polarization operator in the muon factor. The contribution produced by electron polarization insertions is enhanced by the large logarithm of the electron-muon mass ratio. We obtained all single-logarithmic and nonlogarithmic radiative-recoil corrections of order ${\ensuremath{\alpha}}^{3}(m/M){E}_{F}$ generated by the diagrams with electron and muon polarization insertions.

Three-loop radiative-recoil corrections to hyperfine splitting in muonium

We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium. These corrections are enhanced by the large logarithm of the electron–muon mass ratio. The leading logarithm-cubed and logarithm-squared contributions were obtained a long time ago. We calculate the single-logarithmic and nonlogarithmic contributions of order α3(m/M)EF generated by gauge invariant sets of diagrams with one- and two-loop polarization insertions in diagrams with two exchanged photons and radiative photons, and by diagrams with one-loop radiative photon insertions both in the electron and muon lines. The results of this paper constitute a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz. They improve the theory of hyperfine splitting, and affect the value of the electron–muon mass ratio extracted from experimental data on the muonium hyperfine splitting.PACS Nos.: 12.20.Ds, 31.30.Jv, 32.10.Fn, 36.10.Dr

Three-loop radiative-recoil corrections to hyperfine splitting in muonium

We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The current paper therefore concludes calculation of all three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with closed fermion loop insertions in the exchanged photons. The new results obtained here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from experimental data on the muonium hyperfine splitting.

Two-loop polarization contributions to radiative-recoil corrections to hyperfine splitting in muonium

We calculate radiative-recoil corrections of order $\alpha^2(Z\alpha)(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.

New value of m(mu)/m(e) from muonium hyperfine splitting.

The complete contribution to the muonium hyperfine splitting of relative order alpha(3)(m(e)/m(mu))lnalpha is calculated. The result is much smaller than suggested by a previous estimate and leads to a 2sigma upward shift of the most precise value for the muon-electron mass ratio. Analogous contributions are calculated for the positronium hyperfine splitting, where a discrepancy with experiment remains.

Pulsed laser spectroscopy in muonium and deuterium

The 1s–2s energy interval in the muonium (μ+e−) atom has been measured by Doppler free two photon laser spectroscopy. A value of 2455528941.0(9.8) MHz has been obtained in good agreement with quantum electrodynamics (QED). The muon-electron mass ratio can be extracted and is found to be 206.76838(17). The measurement may also be interpreted as a determination of the muon-electron charge ratio as -1- 1.1(2.1)· 10−9. Corresponding measurements in deuterium using the same experimental setup confirmed the validity of the applied analysis procedure.

Second order in mass ratio radiative-recoil corrections to hyperfine splitting in muonium

Radiative-recoil corrections to hyperfine splitting in muonium of orders $\alpha(Z\alpha)(m/M)^2E_F$ and $(Z^2\alpha)(Z\alpha)(m/M)^2E_F$ are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression $[(-6 \ln2- \frac{3}{4})\alpha (Z\alpha) - \frac{17}{12} (Z^2 \alpha) (Z\alpha)](\frac{m}{M})^2 E_F$ is obtained. Numerically the correction is equal to $-0.0351\:\mbox{kHz}$ and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.

One-logarithmic recoil correction in muonium hyperfine splitting.

A source of recoil corrections to muonium hyperfine splitting which are linear in the logarithm of the electron-muon mass ratio is detected. The contribution is induced by the simultaneous insertion of muon and electron polarization loops in the external photon lines. This contribution is calculated analytically and is given by the numerical result \ensuremath{\delta}E=(${\mathrm{\ensuremath{\alpha}}}^{2}$Z\ensuremath{\alpha}/\ensuremath{\pi})${\mathit{E}}_{\mathit{F}}${0.6455[m/M]ln[M/m] +0.9212[m/M]}=0.011 37 kHz.

Mass-gap equations within the QED framework: I

The author introduces a substructure into the fermion lines of QED Feynman diagrams and find a substantial modification of the running coupling alpha (q2) at energies larger than the substructure mass scale ( Lambda ). The Feldman-Landau ghost vanishes if the number of light charged lepton states has an upper bound. Estimates of this bound are given; an ultraviolet fixed point appears. He applies these results to the radiative generation of charged lepton masses. This mechanism for the generation of fermion masses is analogous to the Schwinger mechanism in the boson sector or to the energy-gap generation in a superconductor. The masses arise non-perturbatively from the self-interaction of radial excitations of a massless bound state with the photon. Correspondingly, the bare masses are assumed to be zero. The coefficients of the resulting mass-gap equations depend on the magnitude of the ultraviolet fixed point. Only the case of asymptotic freedom can give rise to the right behaviour of the coefficients. The masses, obtained numerically, are indeed of the observed order of magnitude. In addition, the mass ratios of the first few states become largely similar to the observed values. That asymptotic freedom behaviour may be due to some kind of grand unification at energies Lambda approximately=1015 GeV; the properties of the heavy hypercolour states are of substantial significance for the whole light mass spectrum. The nondiagonal mass matrix elements are estimated and the effect of diagonalization of the mass matrix is analysed. It does not account for the large electron-muon mass ratio. He discovers that the diagonalization can lead to negative mass roots which sets an upper and physically relevant bound on alpha u, the value of alpha (q2) at q2 approximately= Lambda 2. The paper constitutes a nice example for the case where the desert hypothesis within the standard model does not hold.

Mass-gap equations within the QED framework: II. Closed sets of mass equations

The QED Dyson-Schwinger equation for the inverse fermion propagator is examined for composite fermions. The photon couples to the constituent scalar of the fermions constituting the radial excitations of a hypercolour composite. A set of nonlinear mass-gap equations for the individual states is found. After having estimated the contribution of the intermediate states lying above the compositeness scale Lambda , this set is solved for a number of states below Lambda ranging from 10 to 14. Though the most elementary estimate is chosen, the results are seen to confirm those of part I: the mass spectra exhibit both the observed large mass ratios and the electron mass scale if the running coupling vanishes at hypercolour energies. In the case of a sharp cutoff, the precise values of the fine-structure constant and the electron-muon mass ratio can be reproduced; fourteen states below Lambda are predicted for Lambda approximately=1015 GeV. The muon-tau mass ratio comes out to be too large and, therefore, nonsharp cutoffs are studied. The complete solution of the mass equations is presented. This reveals a pronounced decrease of the muon-tau mass ratio. The effect is independent of the kind of non-sharp cutoff chosen and persists when extending the mass loop integration to larger values of q2 or when varying the number of states below Lambda while keeping alpha at 1/137 and m1/m0 at 207. Extending the loop integration to still larger values of q2, distinctive effects of 'spectral inversion' are found, in particular, the effect mL/m tau >tau /mmu (mL denotes the fourth charged lepton mass). These results suggest the existence of 11-12 charged lepton states below Lambda approximately=1015 GeV and 40 GeV<mL<50 GeV. Sequential Dirac neutrinos should exist above MZ/2.

Electron-muon mass ratio and the masses of their neutrinos

In this note, we arrange equal mass for all the four leptons,e,μ, and their neutrinos through their coupling to a Higg's quartet. In addition, the electron and muon are coupled to the left handed and right handed Higgs doublets. This is a pseudo scalar coupling. This enables these charged leptons to attain different masses. Their masses are arranged to be proportional to their neutrino mass. The mass of the electron or muon neutrino turns out to be 6.3 eV.