Abstract
The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the Slavnov-Taylor identity to all orders in the loop expansion by homotopy techniques and a suitable choice of invariant field coordinates (named bleached variables) for the linearly realized gauge group. This allows one to disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from those associated with the gauge-fixing and (generalized) non-polynomial field redefinitions (that do appear already at one loop). The tools presented can be easily generalized to the non-Abelian case.
Highlights
Whenever physics beyond the Standard Model (BSM) appears at an energy scale Λ much higher than the electroweak scale v, it can be described, in the low energy regime, by an effective field theory (EFT)
In this paper we have addressed some aspects of the off-shell renormalization of an Abelian spontaneously broken gauge theory supplemented by dimension 6 derivative-dependent operators
In the ordinary formalism the classification of UV. Divergences for this model is very complicated already at one loop, due to the presence of an infinite set of divergent amplitudes with an arbitrary number of external σ-legs; and one cannot disentangle contributions from generalized field redefinitions from genuine physical effects arising from the renormalization of higher dimensional operators
Summary
Whenever physics beyond the Standard Model (BSM) appears at an energy scale Λ much higher than the electroweak scale v, it can be described, in the low energy regime, by an effective field theory (EFT). The present paper is devoted to the study of the off-shell renormalization of an Abelian Higgs-Kibble model supplemented by the dimension 6 operator φ†φ(Dμφ)†Dμφ The latter has been chosen as a non-trivial test of the formalism we are going to develop since it generates interaction vertices with two derivatives, leading to a maximal violation of the power-counting already at one loop This is achieved by combining the bleaching of the field coordinates (an operatorial-valued finite gauge transformation leading to invariant variables) with homotopy techniques designed to deal with the non gauge-invariant contributions to the 1-PI amplitudes.
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