The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms

Abstract

Corrections to energy levels in light muonic atoms are investigated in order ${\alpha }^2(Z\alpha {)}^{4}m$. We pay attention to corrections which are specific for muonic atoms and include the electron vacuum polarization loop. In particular, we calculate relativistic and relativistic-recoil two-loop electron vacuum polarization contributions. The results are obtained for the levels with $n=1,2$ and in particular for the Lamb shift ($2p_{1/2}-2s_{1/2}$) and fine-structure intervals ($2p_{3/2}-2p_{1/2}$) in muonic hydrogen, deuterium, and muonic helium ions.

Accepted by Phys.Rev.D; cross refs are added in v.2

References in corpus (4)

• High-precision determination of the electric and magnetic form factors of the proton
• Theory of the 2S-2P Lamb shift and 2S hyperfine splitting in muonic hydrogen
• Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\mathbf{n}=2$ Lamb shift and hyperfine structure
• Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z

Cited by in corpus (24)

• Model independent extraction of the proton magnetic radius from electron scattering
• Theory of the n=2 levels in muonic deuterium
• The proton structure in and out of muonic hydrogen
• Comprehensive theory of the Lamb shift in light muonic atoms
• Theory of the Lamb shift and Fine Structure in muonic ${}^4\mathrm{He}$ ions and the muonic ${}^3\mathrm{He}{-}^4\mathrm{He}$ Isotope Shift
• The Lamb shift in muonic hydrogen and the proton radius from effective field theories
• Hyperfine structure of S-states in muonic deuterium
• Lamb shift in muonic ions of lithium, beryllium and boron
• Radiative nonrecoil nuclear finite size corrections of order $\alpha (Z\alpha {)}^5$ to the hyperfine splitting of S-states in muonic hydrogen
• Theory of the n=2 levels in muonic helium-3 ions
• Experiments towards resolving the proton charge radius puzzle
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• Hyperfine structure of S-states in muonic ions of lithium, beryllium and boron
• Light-by-light-scattering contributions to the Lamb shift in light muonic atoms
• Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory
• Hyperfine structure of P states in muonic ions of lithium, beryllium and boron
• Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values
• Relativistic two fermion treatment of hyperfine transitions
• Relativistic recoil effects in a muonic atom within a Grotch-type approach: General approach
• Relativistic recoil effects for energy levels in a muonic atom within a Grotch-type approach: An application to the one-loop electronic vacuum polarization
• Relativistic recoil effects to energy levels in a muonic atom: a Grotch-type calculation of the second-order vacuum-polarization contributions
• Irreducible Three-Loop Vacuum-Polarization Correction in Muonic Bound Systems
• Reexamination of vacuum-polarization corrections to the self-energy in muonic bound systems
• Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles