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Non-perturbative RG for the Weak interaction corrections to the magnetic moment (2406.14755v1)

Published 20 Jun 2024 in hep-th

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 $\lambda2$ and a momentum cut-off $\Lambda$. The magnetic moment is written as a series in $\lambda2$, with $n$-th coefficients bounded by $Cn ({m2\over M2}) \beta{2n } ({\Lambda2\over M2}){(1+0+)(n-1)}$ 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.

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