Logarithmic two-loop corrections to the Lamb shift in hydrogen

Higher order $(\alpha/\pi)^2 (Z \alpha)^6$ logarithmic corrections to the hydrogen Lamb shift are calculated. The results obtained show the two-loop contribution has a very peculiar behavior, and significantly alter the theoretical predictions for low lying S-states.Comment: 14 pages, including 2 figures, submitted to Phys. Rev. A, updated with minor change

Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen muH, muonic deuterium muD, the muonic 3He ion, as well as in the muonic 4He ion. Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S-2P Lamb shift of order alpha (Zalpha)^5 mu^3 ln(Zalpha)/(m_mu m_N) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.Comment: 10 pages; svjour style; to appear in the European Physical Journal

Double-Logarithmic Two-Loop Self-Energy Corrections to the Lamb Shift

Self-energy corrections involving logarithms of the parameter Zalpha can often be derived within a simplified approach, avoiding calculational difficulties typical of the problematic non-logarithmic corrections (as customary in bound-state quantum electrodynamics, we denote by Z the nuclear charge number, and by alpha the fine-structure constant). For some logarithmic corrections, it is sufficient to consider internal properties of the electron characterized by form factors. We provide a detailed derivation of related self-energy ``potentials'' that give rise to the logarithmic corrections; these potentials are local in coordinate space. We focus on the double-logarithmic two-loop coefficient B_62 for P states and states with higher angular momenta in hydrogenlike systems. We complement the discussion by a systematic derivation of B_62 based on nonrelativistic quantum electrodynamics (NRQED). In particular, we find that an additional double logarithm generated by the loop-after-loop diagram cancels when the entire gauge-invariant set of two-loop self-energy diagrams is considered. This double logarithm is not contained in the effective-potential approach.Comment: 14 pages, 1 figure; references added and typographical errors corrected; to appear in Phys. Rev.

Some Recent Advances in Bound-State Quantum Electrodynamics

We discuss recent progress in various problems related to bound-state quantum electrodynamics: the bound-electron g factor, two-loop self-energy corrections and the laser-dressed Lamb shift. The progress relies on various advances in the bound-state formalism, including ideas inspired by effective field theories such as Nonrelativistic Quantum Electrodynamics. Radiative corrections in dynamical processes represent a promising field for further investigations.Comment: 12 pages, nrc1 LaTeX styl

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

Leading Chiral Logarithms to the Hyperfine Splitting of the Hydrogen and Muonic Hydrogen

We study the hydrogen and muonic hydrogen within an effective field theory framework. We perform the matching between heavy baryon effective theory coupled to photons and leptons and the relevant effective field theory at atomic scales. This matching can be performed in a perturbative expansion in alpha, 1/m_p and the chiral counting. We then compute the O(m_{l_i}^3 alpha^5/m_p^2 x logarithms) contribution (including the leading chiral logarithms) to the Hyperfine splitting and compare with experiment. They can explain about 2/3 of the difference between experiment and the pure QED prediction when setting the renormalization scale at the rho mass. We give an estimate of the matching coefficient of the spin-dependent proton-lepton operator in heavy baryon effective theory.Comment: 17 pages, LaTeX, minor changes, one reference adde

Two-loop corrections to the decay rate of parapositronium

Order $\alpha^2$ corrections to the decay rate of parapositronium are calculated. A QED scattering calculation of the amplitude for electron-positron annihilation into two photons at threshold is combined with the technique of effective field theory to determine an NRQED Hamiltonian, which is then used in a bound state calculation to determine the decay rate. Our result for the two-loop correction is $5.1243(33)$ in units of $(\alpha/\pi)^2$ times the lowest order rate. This is consistent with but more precise than the result $5.1(3)$ of a previous calculation.Comment: 26 pages, 7 figure

QED theory of the nuclear recoil effect on the atomic g factor

The quantum electrodynamic theory of the nuclear recoil effect on the atomic g factor to all orders in \alpha Z and to first order in m/M is formulated. The complete \alpha Z-dependence formula for the recoil correction to the bound-electron g factor in a hydrogenlike atom is derived. This formula is used to calculate the recoil correction to the bound-electron g factor in the order (\alpha Z)^2 m/M for an arbitrary state of a hydrogenlike atom.Comment: 17 page

Hyperfine structure of the ground state muonic He-3 atom

On the basis of the perturbation theory in the fine structure constant $\alpha$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(\mu\ e \ ^3_2He)$. We obtain total result for the ground state hyperfine splitting $\Delta \nu^{hfs}=4166.471$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections of orders $\alpha^5$ and $\alpha^6$. The remaining difference between our theoretical result and experimental value of the hyperfine splitting lies in the range of theoretical and experimental errors and requires the subsequent investigation of higher order corrections.Comment: Talk on poster section of XXIV spectroscopy congress, 28 February-5 March 2010, Moscow-Troitsk, Russia, 21 pages, LaTeX, 8 figure