Non-perturbative RG for the Weak interaction corrections to the magnetic moment

Abstract

We analyze, by rigorous Renormalization Group (RG) methods, a Fermi model for Weak forces with a single family of leptons, one massless and the other with mass $m=M{e}^{-\beta }$, with $M$ the gauge boson mass, a quartic non-local interaction with coupling ${\lambda }^2$ and a momentum cut-off $\Lambda$. The magnetic moment is written as a series in ${\lambda }^2$, with $n$-th coefficients bounded by $C^n(\frac{m^2}{M^2}){\beta }^{2n}(\frac{{\Lambda }^2}{M^2}{)}^{(1+0^{+})(n-1)}$ if $C$ a constant; this implies convergence and provides non-perturbative bounds on the higher orders contribution. The fact that the magnetic moment is associated to a dimensionally irrelevant quantity requires the implementation of cancellations in the multiscale analysis.

9 pages, 8 Figures