Work

Relativistic and recoil corrections to vacuum polarization in muonic systems: Three-photon exchange, gauge invariance, and numerical values

Year: 2024

Type: article

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 $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{2}{m}_{r}$, where $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{4}{m}_{r}$ 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 (${\mathrm{NRQED}}_{\ensuremath{\mu}}$), 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.

Source: Physical Review A

DOI: 10.1103/physreva.110.032816

Authors: Gregory S. Adkins, Ulrich D. Jentschura

Institutions: Franklin & Marshall College, Missouri University of Science and Technology

Language: English

Topic: Atomic and Molecular Physics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institute of Standards and Technology

Awards: RUI: Calculation of Higher Order Corrections to Positronium Energy Levels, PURPOSE: THE PURPOSE OF THIS GRANT IS TO ENABLE MORE STRINGENT TESTS OF THE BASIC LAWS OF PHYSICS UNDERLYING METROLOGY, AS WELL AS HIGHER PRECISION IN THE MEASUREMENTS OF FUNDAMENTAL CONSTANTS THAT ARE IMPORTANT FOR CODATA. ACTIVITIES TO BE PERFORMED: THE RESEARCHER PROPOSES TO PERFORM QUANTUM ELECTRODYNAMIC (QED) CALCULATIONS FOR MUONIUM (AN ATOM CONSISTING OF AN ELECTRON ORBITING A MUON) TO COMPUTE THE UNKNOWN RECOIL CORRECTIONS THAT CURRENTLY LIMIT THE ACCURACY FOR THE PREDICTED HYPERFINE SPITTING TO ABOUT 70 HZ, WHICH IS MORE THAN AN ORDER OF MAGNITUDE LARGER THAN THE GOAL OF A NEW EXPERIMENTAL CAMPAIGN UNDERWAY TO REACH 5 HZ.EXPECTED OUTCOMES: SUCCESS IS EXPECTED TO IMPROVE THE PREDICTED VALUE OF THE MUONIUM GROUND STATE HYPERFINE SPLITTING, REDUCING THE UNCERTAINTY TO LESS THAN 10 HZ. TOGETHER WITH THE ANTICIPATED EXPERIMENTAL IMPROVEMENT, THIS CAN BE USED TO OBTAIN A MORE PRECISE DETERMINATION OF THE MUON MASS.INTENDED BENEFICIARIES: INSTITUTIONS OF HIGHER LEARNING WILL BENEFIT FROM PRECISELY TESTING THE BASIC LAWS OF NATURE. METROLOGICAL INSTITUTES WILL BENEFIT FROM THE IMPROVED MEASUREMENTS OF FUNDAMENTAL CONSTANTS THAT ARE INVOLVED IN THE LEAST SQUARES ADJUSTMENTS FOR CODATA RECOMMENDATIONS.SUBRECIPIENT ACTIVITIES: THERE ARE NO SUB-AWARDS IN THIS PROJECT., PM: Precision Low-Energy Quantum Electroynamic Theory and Fundamental Processes