| Summary: | Abstract The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ∼Φ†Φ−υ22N $$ \sim {\left({\Phi}^{\dagger}\Phi -\frac{\upupsilon^2}{2}\right)}^N $$ with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.
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