Renormalization group equation for weakly power-counting renormalizable theories

We study the renormalization group flow inweak power-counting (WPC) renormalizable theories. The latter are theories which, after being formulated in terms of certain variables, display only a finite number of independent divergent amplitudes order by order in the loop expansion. Using as a toolbox the well-known SU(2) non-linear sigma model, we prove that for such theories a renormalization group equation holds that does not violate the WPC condition; that is, the sliding of the scaleμ for physical amplitudes can be reabsorbed by a suitable set of finite counterterms arising at the loop order prescribed by theWPC itself. We explore in some detail the consequences of this result; in particular, we prove that it holds in the framework of a recently introduced beyond the Standard Model scenario in which one considers nonlinear Stückelberg-like symmetry breaking contributions to the fermion and gauge boson mass generation mechanism.