3,151 research outputs found
The Equivalence Theorem and Effective Lagrangians
We point out that the equivalence theorem, which relates the amplitude for a
process with external longitudinally polarized vector bosons to the amplitude
in which the longitudinal vector bosons are replaced by the corresponding
pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a
more general formulation of this theorem also holds for effective interactions.
The generalized theorem can be utilized to determine the high-energy behaviour
of scattering processes just by power counting and to simplify the calculation
of the corresponding amplitudes. We apply this method to the phenomenologically
most interesting terms describing effective interactions of the electroweak
vector and Higgs bosons in order to examine their effects on vector-boson
scattering and on vector-boson-pair production in annihilation. The
use of the equivalence theorem in the literature is examined.Comment: 20 pages LaTeX, BI-TP 94/1
On Non-Standard Couplings among the Electroweak Vector Bosons
Application of a Stueckelberg transformation allows one to connect various
Lagrangians which have been independently proposed for non-standard couplings.
We discuss the reduction of the number of independent parameters in the
Lagrangian and compare symmetry arguments with dimensional arguments.Comment: 11 pages LaTeX 2.0
Effective Lagrangians with Higher Order Derivatives
The problems that are connected with Lagrangians which depend on higher order
derivatives (namely additional degrees of freedom, unbound energy from below,
etc.) are absent if effective Lagrangians are considered because the equations
of motion may be used to eliminate all higher order time derivatives from the
effective interaction term. The application of the equations of motion can be
realized by performing field transformations that involve derivatives of the
fields. Using the Hamiltonian formalism for higher order Lagrangians
(Ostrogradsky formalism), Lagrangians that are related by such transformations
are shown to be physically equivalent (at the classical and at the quantum
level). The equivalence of Hamiltonian and Lagrangian path integral
quantization (Matthews's theorem) is proven for effective higher order
Lagrangians. Effective interactions of massive vector fields involving higher
order derivatives are examined within gauge noninvariant models as well as
within (linearly or nonlinearly realized) spontaneously broken gauge theories.
The Stueckelberg formalism, which relates gauge noninvariant to gauge invariant
Lagrangians, becomes reformulated within the Ostrogradsky formalism.Comment: 17 pages LaTeX, BI-TP 93/2
Equivalence of Hamiltonian and Lagrangian Path Integral Quantization: Effective Gauge Theories
The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev--Popov)
path integral quantization (Matthews's theorem) is proven for gauge theories
with arbitrary effective interaction terms. Effective gauge-boson
self-interactions and effective interactions with scalar and fermion fields are
considered. This result becomes extended to effective gauge theories with
higher derivatives of the fields.Comment: 14 pages LaTeX, BI-TP 93/40, August 199
Bounds on Bess Model Parameters from Vector-Boson Production in e+e- Collisions
The BESS model is the Higgs-less alternative to the standard model of
electroweak interaction, based on nonlinearly realized spontaneous symmetry
breaking. Since it is nonrenormalizable, new couplings (not existing in the SM)
are induced at each loop order. On the basis of the one loop induced
vector-boson self-couplings we study the two- and three-vector-boson-production
processes in collisions at , the expected energy of
the next linear collider (NLC). Assuming that NLC results will agree
with the SM predictions within given accuracy we identify the bounds for the
free parameters of the BESS model.Comment: December 1992, 8 pages LaTeX, 6 figures (not included but available
on request), BI-TP 92/59, LMU-92/1
High-Energy Vector-Boson Scattering with Non-Standard Interactions and the Role of a Scalar Sector
The high-energy behavior of vector-boson scattering amplitudes is examined
within an effective theory for non-standard self-interactions of electroweak
vector-bosons. Irrespectively of whether this theory is brought into a gauge
invariant form by including non-standard interactions of a Higgs particle I
find that terms that grow particularly strongly with increasing scattering
energy are absent. Different theories are compared concerning their high-energy
behavior and the appearance of divergences at the one-loop level.Comment: 21 pages LaTeX, condensed version of BI-TP 93/5
Deriving Non-decoupling Effects of Heavy Fields from the Path Integral: a Heavy Higgs Field in an SU(2) Gauge Theory
We describe a method to remove non-decoupling heavy fields from a quantized
field theory and to construct a low-energy one-loop effective Lagrangian by
integrating out the heavy degrees of freedom in the path integral. We apply
this method to the Higgs boson in a spontaneously broken SU(2) gauge theory
(gauged linear sigma-model). In this context, the background-field method is
generalized to the non-linear representation of the Higgs sector by applying (a
generalization of) the Stueckelberg formalism. The (background) gauge-invariant
renormalization is discussed. At one loop the log M_H-terms of the heavy-Higgs
limit of this model coincide with the UV-divergent terms of the corresponding
gauged non-linear sigma-model, but vertex functions differ in addition by
finite (constant) terms in both models. These terms are also derived by our
method. Diagrammatic calculations of some vertex functions are presented as
consistency check.Comment: 33 Pages LaTeX, 6 figures uuencoded postscrip
Perturbative Hamiltonian constraints for higher order theories
We present a method for constructing a consistent low energy canonical
formalism for higher order time-derivative theories, extending the Dirac method
to include perturbative Hamiltonian constraints. We apply it to two
paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan
scalar field. We also compare the results, both at the classical and quantum
level, with the ones corresponding to a direct perturbative construction
applied to the exact higher order theory. This comparison highligths the
soundness of the present formalism.Comment: 26 pages, 4 figures; review section shortened and appendices change
Production of Three Vector Bosons in e+e- Annihilation as a Test of W+-, Z, gamma Self-Interactions
We study the vector-boson production processes e+e- --> WWZ and e+e-
-->WWgamma which are directly affected by the trilinear and quadrilinear self
couplings of the W, Z and gamma. Our analysis is based upon a single-parameter
effective-Lagrangian model for these self interactions which contains the
standard model as a special case. Consequences for the phenomenology at an e+e-
collider of 500 GeV (NLC) are discussed, and fits of the free parameter around
its standard model value are carried out.Comment: BI-TP 92/30, July 1992 (Enlarged Version October 1992) One section
added to the old version. Figures (unchanged) no more included but available
by reques
Physical Unitarity for Massive Non-abelian Gauge Theories in the Landau Gauge: Stueckelberg and Higgs
We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge
with a mass term a la Stueckelberg. We assume that the theory
(non-renormalizable) makes sense in some subtraction scheme (in particular the
Slavnov-Taylor identities should be respected!) and we devote the paper to the
study of the space of the unphysical modes. We find that the theory is unitary
only under the hypothesis that the 1-PI two-point function of the vector mesons
has no poles (at p^2=0). This normalization condition might be rather crucial
in the very definition of the theory. With all these provisos the theory is
unitary. The proof of unitarity is given both in a form that allows a direct
transcription in terms of Feynman amplitudes (cutting rules) and in the
operatorial form. The same arguments and conclusions apply verbatim to the case
of non-abelian gauge theories where the mass of the vector meson is generated
via Higgs mechanism. To the best of our knowledge, there is no mention in the
literature on the necessary condition implied by physical unitarity.Comment: References added. 22 pages. Final version to appear in the journa
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