Irreducible Three-Loop Vacuum-Polarization Correction in Muonic Bound Systems

Abstract

Three-loop electronic vacuum-polarization corrections due to irreducible diagrams are evaluated for two-body muonic ions with nuclear charge numbers 1 <= Z <= 6. The corrections are of order alpha^3 (Zalpha)^2 m_r, where alpha is the fine-structure constant and m_r is the reduced mass. Numerically, the energy corrections are found to be of the same order-of-magnitude as the largest of the order alpha^2 (Zalpha)^6 m_r corrections, and are thus phenomenologically interesting. Our method of calculation eliminates numerical uncertainty encountered in other approaches.

arXiv comment7 pages; RevTeX

References in corpus (15)

• Lamb Shift in Light Muonic Atoms - Revisited
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Analytical on-shell QED results: 3-loop vacuum polarization, 4-loop beta-function and the muon anomaly
• Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
• Lamb Shift in Muonic Hydrogen. II. Analysis of the Discrepancy of Theory and Experiment
• Comprehensive theory of the Lamb shift in light muonic atoms
• The ${\alpha }^2(Z\alpha {)}^{4}m$ contributions to the Lamb shift and the fine structure in light muonic atoms
• Second-order corrections to the wave function at origin in muonic hydrogen and pionium
• Accuracy of Calculations Involving ${\alpha }^3$ Vacuum-Polarization Diagrams: Muonic Hydrogen Lamb Shift and Muon $g-2$
• Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil
• Towards Precision Muonic X-Ray Measurements of Charge Radii of Light Nuclei
• Dimensional Regularization and Two-Loop Vacuum Polarization Operator: Master Integrals, Analytic Results and Energy Shifts
• MMC Array to Study X-ray Transitions in Muonic Atoms
• Energy interval 3S-1S in muonic hydrogen
• Reexamination of vacuum-polarization corrections to the self-energy in muonic bound systems

Cited by in corpus (1)

• Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles