Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values

Abstract

For an accurate theoretical description of muonic bound systems, it is crucial to consistently treat relativistic and recoil corrections to vacuum polarization. The one-loop vacuum-polarization effect is by far the dominant quantum electrodynamic (QED) energy correction for bound muons, being of order $\alpha (Z\alpha {)}^2{m}_r$, where $\alpha$ is the fine-structure constant, $Z$ is the nuclear charge number, and $m_r$ is the reduced mass. Gauge invariance of the relativistic and recoil corrections to vacuum polarization of order $\alpha (Z\alpha {)}^4{m}_r$ is investigated with respect to nonretarded and standard, renormalized variants of Coulomb gauge. The invariance is shown after including three-photon exchange diagrams. Our derivation is based on an adapted form of Nonrelativistic Quantum Electrodynamics for bound muon systems (NRQED${}_{\mu }$), which is a version of NRQED where the hard scale is set at the muon mass instead of the electron mass. Updated values for the gauge-independent corrections for one-muon ions with nuclear charge numbers $Z=1,2,6$ are presented.

15 pages, 1 figure

References in corpus (4)

• The NRQED lagrangian at order 1/M^4
• The proton structure in and out of muonic hydrogen
• Comprehensive theory of the Lamb shift in light muonic atoms
• Dimensional Regularization and Two-Loop Vacuum Polarization Operator: Master Integrals, Analytic Results and Energy Shifts

Cited by in corpus (4)

• High precision X-ray spectroscopy of kaonic neon
• 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
• Laser Excitation of Muonic 1S Hydrogen Hyperfine Transition: Effects of Multi-pass Cell Interference