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.Comment: 27 pages, 6 figures, 7 table

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

Radiative-nonrecoil corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium

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.Comment: 5 pages, 3 figures; v2: corrected several typos and replaced figure 3, final results and conclusions unchange

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-nonrecoil corrections of order alpha^2 (Z alpha)^5 to the Lamb shift

We present results for the corrections of order alpha^2 (Z alpha)^5 to the Lamb shift. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We confirm results obtained by other groups and improve their precision. Values of the 32 master integrals for this and similar problems are provided.Comment: 8 pages, 4 figures; v2: added two references, changed comparison with previous result, conclusions unchanged, matches published version; v3: corrected typo in Table I, final results and conclusions 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

Universality of Leading Relativistic Corrections to Bound State Gyromagnetic Ratios

We discuss the leading relativistic (nonrecoil and recoil) corrections to bound state $g$-factors of particles with arbitrary spin. These corrections are universal for any spin and depend only on the free particle gyromagnetic ratios. We explain the physical reasons behind this universality.Comment: 10 pp., based on talks given at the Gribov-80 Memorial Workshop, ICTP, Trieste, Italy, May 2010 and at PSAS 2010 workshop, Les Houches, June 2010. To be published in the Gribov-80 Proceedings and in Can. J. Phy

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

Loop-after-loop contribution to the second-order Lamb shift in hydrogenlike low-Z atoms

We present a numerical evaluation of the loop-after-loop contribution to the second-order self-energy for the ground state of hydrogenlike atoms with low nuclear charge numbers Z. The calculation is carried out in the Fried-Yennie gauge and without an expansion in Z \alpha. Our calculation confirms the results of Mallampalli and Sapirstein and disagrees with the calculation by Goidenko and coworkers. A discrepancy between different calculations is investigated. An accurate fitting of the numerical results provides a detailed comparison with analytic calculations based on an expansion in the parameter Z \alpha. We confirm the analytic results of order \alpha^2 (Z\alpha)^5 but disagree with Karshenboim's calculation of the \alpha^2 (Z \alpha)^6 \ln^3(Z \alpha)^{-2} contribution.Comment: RevTex, 19 pages, 4 figure

Bosonization and generalized Mandelstam soliton operators

The generalized massive Thirring model (GMT) with three fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with three interacting soliton species. The generalized Mandelstam soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. In the semi-classical limit one recovers the so-called SU(3) affine Toda model coupled to matter fields (ATM) from which the classical GSG and GMT models were recently derived in the literature. The intermediate ATM like effective action possesses some spinors resembling the higher grading fields of the ATM theory which have non-zero chirality. These fields are shown to disappear from the physical spectrum, thus providing a bag model like confinement mechanism and leading to the appearance of the massive fermions (solitons). The ordinary MT/SG duality turns out to be related to each SU(2) sub-group. The higher rank Lie algebra extension is also discussed.Comment: 22 pages, LaTex. Some misprints were corrected. Published in Eur.Phys J.