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Register a new userPrecision measurement of the Lamb shift in Muonium
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We report a new measurement of the $n=2$ Lamb shift in Muonium using microwave spectroscopy. Our result of $1047.2(2.3)_textrm{stat}(1.1)_textrm{syst}$ MHz comprises an order of magnitude improvement upon the previous best measurement. This value matches the theoretical calculation within one standard deviation allowing us to set limits on CPT violation in the muonic sector, as well as on new physics coupled to muons and electrons which could provide an explanation of the muon $g-2$ anomaly.
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Electroweak second order shifts of muonium ($mu^+e^-$ bound state) energy levels are calculated for the first time. Calculation starts from on-shell one-loop elastic $mu^+ e^-$ scattering amplitudes in the center of mass frame, proceed to renormalization and to derivation of muonium matrix elements by using the momentum space wave functions. This is a reliable method unlike the unjustified four-Fermi approximation in the literature. Corrections of order $alpha G_F$ (with $alpha sim 1/137$ the fine structure constant and $G_F$ the Fermi constant) and of order $alpha G_F /(m_Z a_B)$ (with $m_Z$ the Z boson mass and $a_B$ the Bohr radius) are derived from three classes of Feynman diagrams, Z self-energy, vertex and box diagrams. The ground state muonium hyperfine splitting is given in terms of the only experimentally unknown parameter, the smallest neutrino mass. It is however found that the neutrino mass dependence is very weak, making its detection difficult.
Emission of muonium ($mu^{+}e^{-}$) atoms from silica aerogel into vacuum was observed. Characteristics of muonium emission were established from silica aerogel samples with densities in the range from 29 mg cm$^{-3}$ to 178 mg cm$^{-3}$. Spectra of muonium decay times correlated with distances from the aerogel surfaces, which are sensitive to the speed distributions, follow general features expected from a diffusion process, while small deviations from a simple room-temperature thermal diffusion model are identified. The parameters of the diffusion process are deduced from the observed yields.
We present a precise calculation of the Lamb shift $(2P_{1/2}-2S_{1/2})$ in muonic ions $(mu ^6_3Li)^{2+},~(mu ^7_3Li)^{2+}$, $(mu ^9_4Be)^{3+},~(mu ^{10}_4Be)^{3+}$, $(mu ^{10}_5B)^{4+},~(mu ^{11}_5B)^{4+}$. The contributions of orders $alpha^3divalpha^6$ to the vacuum polarization, nuclear structure and recoil, relativistic effects are taken into account. Our numerical results are consistent with previous calculations and improve them due to account of new corrections. The obtained results can be used for the comparison with future experimental data, and extraction more accurate values of nuclear charge radii.
We consider corrections to the Lamb shift of p-wave atomic states due to the finite nuclear size (FNS). In other words, these are radiative corrections to the atomic isotop shift related to FNS. It is shown that the structure of the corrections is qualitatively different from that for s-wave states. The perturbation theory expansion for the relative correction for a $p_{1/2}$-state starts from $alphaln(1/Zalpha)$-term, while for $s_{1/2}$-states it starts from $Zalpha^2$ term. Here $alpha$ is the fine structure constant and $Z$ is the nuclear charge. In the present work we calculate the $alpha$-terms for $2p$-states, the result for $2p_{1/2}$-state reads $(8alpha/9pi)[ln(1/(Zalpha)^2)+0.710]$. Even more interesting are $p_{3/2}$-states. In this case the ``correction is by several orders of magnitude larger than the ``leading FNS shift.
The measurement of the 2P^{F=2}_{3/2} to 2S^{F=1}_{1/2} transition in muonic hydrogen by Pohl et al. and subsequent analysis has led to the conclusion that the rms radius of the proton differs from the accepted (CODATA) value by approximately 4%, corresponding to a 4.9 sigma discrepancy. We investigate the finite-size effects - in particular the dependence on the shape of the proton electric form-factor - relevant to this transition using bound-state QED with nonperturbative, relativistic Dirac wave-functions for a wide range of idealised charge-distributions and a parameterization of experimental data in order to comment on the extent to which the perturbation-theory analysis which leads to the above conclusion can be confirmed. We find no statistically significant dependence of this correction on the shape of the proton form-factor.
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