  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 $C^n ({m^2\over M^2}) \beta^{2n } ({\Lambda^2\over
M^2})^{(1+0^+)(n-1)}$ 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.
