Nonperturbative RG for the weak interaction corrections to the magnetic moment

We analyze, by rigorous renormalization group methods, a Fermi model for weak forces with a single family of leptons, one massless and the other with mass m = Me-beta, with M the gauge boson mass, a quartic nonlocal interaction with coupling lambda 2, and a momentum cutoff Lambda. The magnetic moment is written as a series in lambda 2, with n-th coefficients bounded by Cn(m2 M2)beta 2n(M Lambda 2 2)(1+0+)(n-1) if C is a constant; this implies convergence and provides nonperturbative bounds on the higher order contributions. The fact that the magnetic moment is associated with a dimensionally irrelevant quantity requires the implementation of cancellations in the multiscale analysis.