Scale-relativistic corrections to the muon anomalous magnetic moment

Abstract

The anomalous magnetic moment of the muon is one of the most precisely measured quantities in physics. Its experimental value exhibits a $4.2\sigma$ discrepancy $\delta a_{\mu }=(251\pm 59)\times 10^{-11}$ 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 $x=m_e/m_{\mu }$. 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 ${\mathbb{C}}_{\mu }=\ln (m_{\mathbb{P}}/m_{\mu })$ in terms of the Planck mass $m_{\mathbb{P}}$, the resulting scale-relativistic correction writes $\delta a_{\mu }=-{\alpha }^2(x{\ln }^{3}x)/(8{\mathbb{C}}_{\mu }^2)$, where $\alpha$ is the fine structure constant. Its numerical value, $(230\pm 16)\times 10^{-11}$, is in excellent agreement with the observed theory-experiment difference.

8 pages, 1 figure, Improved and updated version, account of new experimental results

References in corpus (1)

• Turbulence and Scale Relativity