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

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-β, with M the gauge boson mass, a quartic non-local interaction with coupling λ² and a momentum cut-off Λ. The magnetic moment is written as a series in λ², with n-th coefficients bounded by Cⁿ (m² M²) β²ⁿ (Λ² M²)(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.