Abstract
The 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 , 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 -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.
Highlights
We discuss how to extract the dependence of the βfunction coefficients on the non-renormalizable coupling g in one loop approximation, as well as the cohomological techniques required to efficiently separate the mixing of contributions associated to different higherdimensional operators in a spontaneously broken effective field theory
In this paper we continue the study of the off-shell renormalization of the Abelian Higgs-Kibble model supplemented by the maximally power counting violating dimension 6 operator φ†φ(Dμφ)† Dμφ
We will show here how to evaluate the one-loop divergent coefficients associated to all dimension 6 operators which are radiatively generated, and without limiting ourselves to: (i) on-shell quantities that are customarily assumed in the Standard Model Effective Field Theories (SMEFT) literature, where the cancellations between one-loop anomalous dimensions of dimension 6 operators were originally discovered [1,2,3]; and (ii) the linearized approximation in the higher dimensional couplings
Summary
In this paper we continue the study of the off-shell renormalization of the Abelian Higgs-Kibble model supplemented by the maximally power counting violating dimension 6 operator φ†φ(Dμφ)† Dμφ. To systematically compute the (one-loop) UV coefficients in spontaneously broken effective field theories possessing (dimension 6) derivative operators, it is convenient to first renormalize an associated auxiliary model, the so-called X theory, which is obtained by describing the scalar physical degree of freedom in terms of the gauge-invariant field coordinate vX2. We hasten to emphasize that since we are working off-shell the effects of generalized field redefinitions, that are present already at one-loop order, and are not even polynomial for the model at hand [17], need to be correctly accounted for This is automatically done through the cohomologically trivial invariants of the X -theory. The paper ends with two appendices: Appendix A contains the list of all the independent invariants needed for renormalizing the theory, while the relevant X -theory divergent one-loop amplitudes up to dimension 6 are given in Appendix B
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