The Abelian Embedding Formulation of the Stueckelberg Model and its Power-counting Renormalizable Extension

We elucidate the geometry of the polynomial formulation of the non-abelian Stueckelberg mechanism. We show that a natural off-shell nilpotent BRST differential exists allowing to implement the constraint on the sigma field by means of BRST techniques. This is achieved by extending the ghost sector by an additional U(1) factor (abelian embedding). An important consequence is that a further BRST-invariant but not gauge-invariant mass term can be written for the non-abelian gauge fields. As all versions of the Stueckelberg theory, also the abelian embedding formulation yields a non power-counting renormalizable theory in D=4. We then derive its natural power-counting renormalizable extension and show that the physical spectrum contains a physical massive scalar particle. Physical unitarity is also established. This model implements the spontaneous symmetry breaking in the abelian embedding formalism.Comment: LATEX, 30 page

Off-shell renormalization in the presence of dimension 6 derivative operators. II. UV coefficients

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 UV 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.Comment: 33 pages; revised version including the derivation of the one-loop beta function

Canonical transformations in gauge theories with non-trivial backgrounds

We show how to implement the background field method by means of canonical transformations and comment on the applications of the method to non-perturbative techniques in non-Abelian gauge theories. We discuss the case of the lattice in some details.Comment: 6 pages. Prepared for the Sixth International Conference on Quarks and Nuclear Physics QNP2012, April 16-20, 2012, Ecole Polytechnique, Palaiseau, Pari

Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory

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.Comment: 37 pages, 3 figures; updated version to match the published on

Off-shell renormalization in Higgs effective field theories

The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential $\sim\left(\Phi^\dagger\Phi-\frac{v^2}2\right)^N$ 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 $N\to\infty$ case.Comment: 33 pages, no figures. v3: complete one-loop off-shell renormalization for a BSM potential involving arbitrary powers of $\left(\phi^\dagger\phi-\frac{v^2}2\right)$ presented; Higgs wavefunction renormalization shown to be SM like; renormalization of the complete set of Higgs self-coupling in the $N\to\infty$ case discussed. v3 matches the published on