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 $f\bar{f}$ 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 $e^+e^-$ collisions at $\sqrt{s}=500 GeV$, the expected energy of the next $e^+e^-$ 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