arXiv subjects
Publications and source records attributed to Valery A. Shelyuto.
We calculate radiative-recoil contribution of order $Z^2α(Zα)^5(m/M)^2m$ to the Lamb shift in muonium. This correction is due to insertion of radiative photons in the heavy line in the two-photon exchange diagrams. Our calculations are inspired by a new round of precise $1S-2S$ and $2S-2P$ experiments currently in progress.
We calculate hard spin-independent contributions to energy levels in muonium and positronium which are due to radiatively corrected electron factor insertion in two-photon exchange diagrams. Calculation of these corrections is motivated by the new round of precise measurements of spin-independent transition frequencies in muonium and positronium.
Hard spin-independent three-loop radiative contributions to energy levels in positronium generated by the two-photon-exchange diagrams with one-loop radiative insertions in the fermion lines and exchanged photons are calculated. This is a next step in calculations of all corrections of order $mα^7$ inspired by the new generation of precise $1S-2S$ and $2S-2P$ measurements in positronium.
We calculate hard spin-independent three-loop radiative corrections to energy levels in muonium and positronium which are due to radiative insertions in two-photon exchange diagrams. These corrections could be relevant for the new generation of precise $1S-2S$ and $2S-2P$ measurements in muonium and positronium.
We return to the problem of evaluation of the light-by-light contribution to the energy levels of the hydrogen atom. We find an additional contribution directly related to the Delbrück scattering amplitude. The new correction is larger than the previously included light-by-light terms at order~$α^2 (Zα)^6\ln(Zα)\, m_e$. We consider the effective potential in position space using an effective field theory approach and evaluate light-by-light corrections to the energy levels of states with non-zero orbital momentum as well as to the weighted difference of $s$ states. We also determine the large distance asymptotic behaviour of the effective potential induced by the light-by-light scattering in muonic atoms.
We consider the $1s$ Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the bound-state QED. The dominant QED contribution to the uncertainty originates from $α^8m$ external-field contributions (i.e., the contributions at the non-recoil limit). We discuss the two- and three-loop cases and in particular, we revisit calculations of the coefficients $B_{61}, B_{60}, C_{50}$ in standard notation. We have found a missing logarithmic contribution of order $α^2(Zα)^6m$. We have also obtained leading pure self-energy logarithmic contributions of order $α^2(Zα)^8m$ and $α^2(Zα)^9m$ and estimated the subleading terms of order $α^2(Zα)^7m$, $α^2(Zα)^8m$, and $α^2(Zα)^9m$. The determination of those higher-order contributions enabled us to improve the overall accuracy of the evaluation of the two-loop self-energy of the electron. We investigated the asymptotic behavior of the integrand related to the next-to-leading three-loop term (order $α^3(Zα)^5m$, coefficient $C_{50}$ in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the $1s$ Lamb shift for the total three loop next-to-leading term is $(-3.3\pm10.5)(α^3/π^3)(Zα)^5m$. Altogether, we have completed the evaluation of the logarithmic contributions to the $1s$ Lamb shift of order $α^8m$ and reduced the overall $α^8m$ uncertainty by approximately a factor of three for H, D, and He$^+$ as compared with the most recent CODATA compilation.
We consider one-loop light-by-light-scattering contributions to the Lamb shift of the $1s, 2s, 2p$ states in light muonic hydrogen like atoms at $Z\leq10$. The contributions are of the order $α^5m_μ$ (with diverse dependence on the nuclear charge $Z$). Those include the contributions of the so-called Wichmann-Kroll potential ($α(Zα)^4m_μ$), the virtual Delbrück scattering ($α^2(Zα)^3m_μ$), etc. The results are obtained in a nonrelativistic approximation. For the calculation of the virtual-Delbrück-scattering contribution, we have constructed an effective potential in the coordinate space which may be applied to other calculations in muonic atoms.
A hard three-loop correction to parapositronium energy levels of order $mα^7$ 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 $ΔE=0.03297(2)(mα^7/π^3)$ for this energy shift.
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 $mα^7$. 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 $mα^7$ to hyperfine splitting in positronium.
The Lamb shift in muonic hydrogen was measured some time ago to a high accuracy. The theoretical prediction of this value is very sensitive to the proton-finite-size effects. The proton radius extracted from muonic hydrogen is in contradiction with the results extracted from elastic electron-proton scattering. That creates a certain problem for the interpretation of the results from the muonic hydrogen Lamb shift. For the latter we need also to take into account the two-photon-exchange contribution with the proton finite size involved. The only way to describe it relies on the data from the scattering, which may produce an internal inconsistency of theory. Recently the leading proton-finite-size contribution to the two-photon exchange was found within the external field approximation. The recoil part of the two-photon-exchange has not been considered. Here we revisit calculation of the external-field part and take the recoil correction to the finite-size effects into account.
The muon and tauon light-by-light scattering contributions to hyperfine splitting in muonium are calculated. These results conclude calculation of all hard three-loop contributions to hyperfine splitting containing graphs with closed fermion loops. We discuss the special role that the lepton anomalous magnetic moments play in these calculations. The full result for all three-loop radiative-recoil corrections to hyperfine splitting generated by the graphs with closed lepton loops is presented.
We consider hard three-loop nonlogarithmic corrections of order $mα^7$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams. The total result for all these diagrams is $ΔE=-1.2917(1)mα^7/π^3=-5.672$ kHz.
Three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant sets of diagrams with muon and tauon loop light-by-light scattering blocks are calculated. These results complete calculations of all light-by-light scattering contributions 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.
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 $α^2(Zα)(m/M)E_F$ to hyperfine splitting in muonium generated by these diagrams.
We calculate corrections of order $α^3(Zα)E_F$ to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with polarization insertions in the light by light scattering diagrams. This nonrecoil contribution turns out to be -2.63 Hz. The total contribution of all known corrections of order $α^3(Zα)E_F$ is equal to -4.28 Hz.
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 $α^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order $α^3(m/M)E_F$ generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining the new contributions with our older results we present complete result for all three-loop radiative-recoil corrections generated by the diagrams with electron and muon polarization loops.