209 research outputs found

### 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

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