Off-shell renormalization in the presence of dimension 6 derivative operators. II. Ultraviolet coefficients
AbstractThe full off-shell one loop renormalization for all divergent amplitudes up to dimension 6 in the Abelian Higgs-Kibble model, supplemented with a maximally power counting violating higher-dimensional gauge-invariant derivative interaction $$\sim g ~ \phi ^\dagger \phi (D^\mu \phi )^\dagger D_\mu \phi $$ ∼ g ϕ † ϕ ( D μ ϕ ) † D μ ϕ , is presented. This allows one to perform the complete renormalization of radiatively generated dimension 6 operators in the model at hand. We describe in details the technical tools required in order to disentangle the contribution to ultraviolet divergences parameterized by (generalized) non-polynomial field redefinitions. We also discuss how to extract the dependence of the $$\beta $$ β -function coefficients on the non-renormalizable coupling g in one loop approximation, as well as the cohomological techniques (contractible pairs) required to efficiently separate the mixing of contributions associated to different higher-dimensional operators in a spontaneously broken effective field theory.