https://doi.org/10.1140/epjc/s10052-014-3049-2
Regular Article - Theoretical Physics
Renormalization group equation for weakly power-counting renormalizable theories
1
Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133, Milan, Italy
2
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler, Villa Tambosi, Strada delle Tabarelle 286, 38123, Villazzano (Trento), Italy
3
INFN, Sezione di Milano, via Celoria 16, 20133, Milan, Italy
* e-mail: binosi@ectstar.eu
Received:
17
July
2014
Accepted:
21
August
2014
Published online:
23
September
2014
We study the renormalization group flow in weak 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 scale 
for physical amplitudes can be reabsorbed by a suitable set of finite counterterms arising at the loop order prescribed by the WPC 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 non-linear Stückelberg-like symmetry breaking contributions to the fermion and gauge boson mass generation mechanism.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
