NEW CORRECTIONS OF ORDER α3(Zα)4\alpha^3(Z\alpha)^4 AND α2(Zα)6\alpha^2(Z\alpha)^6 TO THE LAMB SHIFT

Two corrections to the Lamb shift, induced by the polarization operator insertions in the external photon lines are calculated.Comment: 4 pages, revtex, no figure

Improved Theory of the Muonium Hyperfine Structure

Terms contributing to the hyperfine structure of the muonium ground state at the level of few tenths of kHz have been evaluated. The $\alpha^2 (Z\alpha)$ radiative correction has been calculated numerically to the precision of 0.02 kHz. Leading $\ln (Z\alpha )$ terms of order $\alpha^{4-n} (Z\alpha)^n , n=1,2,3,$ and some relativistic corrections have been evaluated analytically. The theoretical uncertainty is now reduced to 0.17 kHz. At present, however, it is not possible to test QED to this precision because of the 1.34 kHz uncertainty due to the muon mass.Comment: 11 pages + 2 figures (included), RevTeX 3.0, CLNS 94/127

Radiative Corrections to the Muonium Hyperfine Structure. I. The α2(Zα)\alpha^2 (Z\alpha) Correction

This is the first of a series of papers on a systematic application of the NRQED bound state theory of Caswell and Lepage to higher-order radiative corrections to the hyperfine structure of the muonium ground state. This paper describes the calculation of the $\alpha^2 (Z\alpha)$ radiative correction. Our result for the complete $\alpha^2 (Z\alpha)$ correction is 0.424(4) kHz, which reduces the theoretical uncertainty significantly. The remaining uncertainty is dominated by that of the numerical evaluation of the nonlogarithmic part of the $\alpha (Z\alpha )^2$ term and logarithmic terms of order $\alpha^4$.Comment: 56 pages, Rev.tex V3.0 and epsf.tex. 12 postscript files are called in the text. Version accepted by Phys. Rev. D. A new table is adde

Radiative Correction to the Nuclear-Size Effect and Hydrogen-Deuterium Isotopic Shift

The radiative correction to the nuclear charge radius contribution to the Lamb shift of order $\alpha(Z\alpha)^5m_r^3$ is calculated. In view of the recent high precision experimental data, this theoretical correction produces a significant contribution to the hydrogen-deuterium isotopic shift.Comment: 5 pages, REVTEX, replaced with the final version, to be published in Phys.Rev. A, two references adde

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.Comment: 15 pages, 11 figure

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.Comment: Revtex, 19 pages, 3 tables; two references added, no other change

One more hard three-loop correction to parapositronium energy levels

A hard three-loop correction to parapositronium energy levels of order $m\alpha^7$ is calculated. This nonlogarithmic contribution is due to the insertions of one-loop photon propagator in the fermion lines in the diagrams with virtual two-photon annihilation. We obtained $\Delta E=0.03297(2)(m\alpha^7/\pi^3)$ for this energy shift.Comment: Version to be published in Phys. Rev.D, results unchange

Two-Loop Effects and Current Status of the 4He+ Lamb Shift

We report on recent progress in the treatment of two-loop binding corrections to the Lamb shift, with a special emphasis on S and P states. We use these and other results in order to infer an updated theoretical value of the Lamb shift in 4He+.Comment: 11 pages, nrc1 style; paper presented at PSAS (2006), Venic

Lamb shift in muonic deuterium atom

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.Comment: 24 pages, 11 figures. arXiv admin note: text overlap with arXiv:hep-ph/061229

The second-order electron self-energy in hydrogen-like ions

A calculation of the simplest part of the second-order electron self-energy (loop after loop irreducible contribution) for hydrogen-like ions with nuclear charge numbers $3 \leq Z \leq 92$ is presented. This serves as a test for the more complicated second-order self-energy parts (loop inside loop and crossed loop contributions) for heavy one-electron ions. Our results are in strong disagreement with recent calculations of Mallampalli and Sapirstein for low $Z$ values but are compatible with the two known terms of the analytical $Z\alpha$-expansion.Comment: 13 LaTex pages, 2 figure