The electroweak mixing angle in unified gauge theories

We study in detail the factors that influence the unification relations among the coupling parameters of strong and electroweak interactions. We find that the factor that decides the unification relations in a theory is the fermion content of the theory. The specific ‘observed’ group of strong and electroweak interactions used and the specific unification group in which these interactions are embedded are largely irrelevant. In particular, we find that the unification value of the electroweak mixing angle is the same for almost all models of interest. We also explicitly illustrate that the canonical value 3/8 of the mixing angle is a characteristic result of the currently popular sequential doublets scheme of fermions. Addition of extra fermion singlets reduces the mixing angle to 1/4. We propose this sequential triplets scheme of fermions as an interesting alternative to the current scheme.     

The electroweak mixing angle in unified gauge theories—the renormalisation effects

A general analysis of the renormalisation corrections to the unification results for the coupling constants of strong and electroweak interactions is attempted. In particular, the effects of introducing an energy scale intermediate between the unification energy and the low-energy regions are studied and found to be important. This analysis is applied to unification schemes of both kinds, namely, unification at superhigh energies, and unification at accessible energies.     

General electroweak mixing models and extended gauge theories

General electroweak mixing schemes containing an arbitrary number of weak bosons and agreeing with the predictions of the standard model for neutrino scattering and polarized electron scattering in the low energy approximation are analyzed using the propagator matrix formalism. The mean charged boson mass is bounded while the mean neutral boson mass is unbounded and determined as a function of the mean charged one. Under a special assumption on the electroweak mixing parameters the four fermion interaction agrees with the one of extended gauge theories and the mean boson masses agree with the boson masses of the standard model.     

Limiting case of modified electroweak model for contracted gauge group

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the free (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to coordinates on the sphere S ³. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group SU(2; j) × U(1) is discussed. Within framework of the limit model Z boson and electromagnetic fields can be regarded as external ones with respect to W-boson fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.     

A precise determination of the electroweak mixing angle from semileptonic neutrino scattering

The cross-section ratio of neutral-current and charged-current semileptonic interactions of muon-neutrinos on isoscalar nuclei has been measured with the result:R ^v =0.3093±0.0031 for hadronic energy larger than 4 GeV. From this ratio we determined the electroweak mixing angle sin² θ _W , wherem _c is the charm-quark mass in GeV/c². Comparison with direct measurements ofm _w andm _z determines the radiative shift of the intermediate boson mass Δr=0.077±0.025(exp.)±0.038(syst.), in agreement with the prediction. Assuming the validity of the electroweak standard theory we determined ?=0.990?0.013(m _c ?1.5)±0.009(exp.)±0.003(theor.).     

Uniqueness of the standard electroweak gauge model

It is proved that the standard SU(2) × U(1) electroweak gauge model is unique against any extension if the effective low-energy neutral-current interaction is to be precisely of the form $\text{(4G}{}_{\mathrm{F}}\text{/}\text{2}\text{) (j}{}_{\mathrm{\mu }}{}^{\mathrm{(3)}}\text{?}\text{sin}{}^2\text{θ}{}_{\mathrm{<mtext>W</mtext>}}\text{j}{}_{\mathrm{\mu }}{}^{\mathrm{<mtext>em</mtext>}}\text{)}{}^2$naturally.     

The electroweak standard model in the axial gauge

We derive the Feynman rules of the standard model in the axial gauge. After this we prove that the fields and do not correspond to physical particles. As a consequence, these fields cannot appear as incoming or outgoing lines in Feynman graphs. We then calculate the contribution of these fields in the case of a particular decay mode of the top quark.Received: 28 January 2004, Revised: 12 February 2004, Published online: 8 April 2004     

Perturbative gauge invariance: the electroweak theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is generalized to massive gauge fields. Applying it to the electroweak theory leads to a complete fixing of couplings of scalar and ghost fields and of the coupling to leptons, in agreement with the standard theory. The W/Z mass ratio is also determined, as well as the chiral character of the fermions. We start directly with massive gauge fields and leptons and, nevertheless, obtain a theory which satisfies perturbative gauge invariance.     

Sum rules fore + e − annihilation in general electroweak mixing models and extended gauge theories

We derive a lower bound for the integrated cross section for production of weak neutral bosons ine ⁺ e ^? annihilation within general electroweak theories containing an arbitrary number of weak bosons. The low energy parameterC of such theories is expressed in terms of integrals over the weighted cross section fore ⁺ e ^? annihilation at high energies.     

Composite model of gauge bosons in electroweak interactions

We consider a simple Lagrangian which is constructed by only the preon and antipreon fields. By introducing the auxiliary fields φ_μ, φ _μ ^† , and ϕ_μ, it is shown that φ_μ, φ _μ ^† , and ϕ_μ correspond to the electroweak gauge bosonsW _μ ⁺ ,W _μ ⁻ , andW _μ ³ , respectively, which are composite particles of preons and antipreons.     

Polarized bhabha scattering in multiboson electroweak gauge models

The general expression for the differential cross section of the reactione ⁺ e ^?→γ,Z ₁ ⁰ ,Z ₂ ⁰ , ..., →e ⁺ e ^? with an arbitrary initial polarization state is derived in the context of electroweak gauge models with more than one neutral boson. Angular distributions, azimuthal asymmetries in the case of natural polarization, and longitudinal polarization asymmetries for models of the typeSU(2)×U(1)×G (G=?(1),S?(2)) and left-right symmetric models are compared with the standard model results. For the angular distributions withe ^± having equal helicities a～10% deviation from the standard model is predicted already below 50 GeV for models of the first type withZ ₁ ⁰ masses up to 80 GeV. At energies around the firstZ ₁ ⁰ a study of azimuthal and polarization asymmetries yields the possibility of distinguishing between different models.     

Renormalization group analysis of extended electroweak models from the heterotic string

Extended electroweak models need new parameters (including new renormalization-induced gauge-mixing angles) to fix the gauge currents. We present the renormalization group predictions for these parameters in all heterotic string models with one extra, neutral, gauge boson at low energy. The possible matter contents, consistent with perturbative unification and low-energy physics, are determined for any model.     

Constraints on unparticle physics in electroweak gauge boson scattering

The existence of scale invariant physics would lead to new phenomena in particle physics that could be detected at the LHC. In this Letter we exploit the effects of these unparticles in WW→WW$WW\to WW$ scattering. From the requirement of unitarity we derive constraints on unparticle physics. We show that the existence of unparticles would lead to deviations in differential cross sections which can be measured. These deviations are sensitive on the scale dimension and on the spin characteristics of the unparticles.     

Comment on triple gauge boson interactionsin the non-commutative electroweak sector

In this comment we present an analysis of electroweak neutral triple gauge boson couplings projected out of the gauge sector of the extended non-commutative standard model. A brief overview of the current experimental situation is given.Received: 31 July 2003, Published online: 20 November 2003     

Non-abelian gauge structure in neutrino mixing

We discuss the existence of a non-abelian gauge structure associated with flavor mixing. In the specific case of two flavor mixing of Dirac neutrino fields, we show that this reformulation allows to define flavor neutrino states which preserve the Poincaré structure. Phenomenological consequences of our analysis are explored.     

Indications for an extra neutral gauge boson in electroweak precision data

A new analysis of the hadronic peak cross section at LEP 1 implies a small amount of missing invisible width in Z decays, while the effective weak charge in atomic parity violation has been determined recently to 0.6% accuracy, indicating a significantly negative S parameter. As a consequence, the data are described well if the presence of an extra Z' boson, such as predicted in grand unified theories, is assumed. Moreover, the data are now rich enough to study an arbitrary extra Z' boson and to determine its couplings in a model independent way. An excellent fit to the data is obtained in this case, suggestive of a family nonuniversal Z' similar to those predicted in a class of superstring theories.     

Spontaneous generation of torsion coupling of electroweak massive gauge bosons

We derive the coupling to torsion of massive electroweak vector bosons generated by the Higgs mechanism.