2018/10/12 by T. Asaka, Asaka, T., M. Tanaka +7 · 3 citations
Engineering · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Phenomenology (hep-ph) #Muon and positron interactions and applications #Neutrino Physics Research #Particle physics theoretical and experimental studies #hep-ex #hep-ph
paper · pdf · doi:10.48550/arxiv.1810.05429
6 pages, 3 figures
arxiv created 2018/10/12 · openalex publication_date 2018/10/12 · arxiv updated 2018/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Electroweak second order shifts of muonium (μ+e- bound state) energy levels are calculated for the first time. Calculation starts from on-shell one-loop elastic μ+ e- scattering amplitudes in the center of mass frame, proceed to renormalization and to derivation of muonium matrix elements by using the momentum space wave functions. This is a reliable method unlike the unjustified four-Fermi approximation in the literature. Corrections of order αGF (with α∼ 1/137 the fine structure constant and GF the Fermi constant) and of order αGF /(mZ aB) (with mZ the Z boson mass and aB the Bohr radius) are derived from three classes of Feynman diagrams, Z self-energy, vertex and box diagrams. The ground state muonium hyperfine splitting is given in terms of the only experimentally unknown parameter, the smallest neutrino mass. It is however found that the neutrino mass dependence is very weak, making its detection difficult.