2019/05/04 by Laurent Nottale, Nottale, Laurent
Computer Science · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Computational Physics and Python Applications #FOS: Physical sciences #General Physics (physics.gen-ph) #Scientific Research and Discoveries #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1905.02551
8 pages, 1 figure, Improved and updated version, account of new experimental results
openalex publication_date 2019/05/04 · arxiv created 2021/04/17 · arxiv updated 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The anomalous magnetic moment of the muon is one of the most precisely measured quantities in physics. Its experimental value exhibits a 4.2 σ discrepancy δaμ=(251 ± 59) × 10-11 with its theoretical value calculated in the standard model framework, while they agree for the electron. The muon theoretical calculation involves a mass-dependent contribution which comes from two-loop vacuum polarization insertions due to electron-positron pairs and depends on the electron to muon mass ratio x=me/mμ. In standard quantum mechanics, mass ratios and inverse Compton length ratios are identical. This is no longer the case in the special scale-relativity framework, in which the Planck length-scale is invariant under dilations. Using the renormalization group approach, we differentiate between the origin of ln x logarithmic contributions which depend on mass, and x linear contributions which we assume to actually depend on inverse Compton lengths. By defining the muon constant ℂμ=ln(m_ℙ/mμ) in terms of the Planck mass m_ℙ, the resulting scale-relativistic correction writes δaμ= -α2 (x ln3 x)/(8 ℂμ2), where α is the fine structure constant. Its numerical value, (230 ± 16) × 10-11, is in excellent agreement with the observed theory-experiment difference.