Limiting case of modified electroweak model for contracted gauge group
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ELEMENTARY PARTICLES AND FIELDS Theory
Limiting Case of Modified Electroweak Model for Contracted Gauge Group* N. A. Gromov** Department of Mathematics, Komi Science Center UrD, RAS, Syktyvkar Received July 19, 2010
Abstract—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 S3 . 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. DOI: 10.1134/S1063778811060147
1. INTRODUCTION The standard Electroweak Model based on gauge group SU (2) × U (1) gives a good description of electroweak processes. The massive vector bosons predicted by the model were experimentally observed and have the masses mW = 80 GeV for charged W boson and mZ = 91 GeV for neutral Z boson. At the same time the existence of the scalar field (Higgs boson) has not been experimentally verified up to now. One expects that the future experiments on LHC will give definite answer. The scalar field arises in the standard Electroweak Model as a result of spontaneous symmetry breaking by Higgs mechanism [1], which includes three steps: 1) the potential of the self-acting ¯ + λ(φφ) ¯ 2 scalar field of the special form V (φ) = μ2 φφ is introduced by hand in the Lagrangian; 2) its minimal values are considered for imaginary mass μ2 < 0 and are interpreted as degenerate vacuum; 3) one of the gauge equivalent vacuum is fixed and then all fields are regarded in the neighbourhood of this vacuum. Sufficiently artificial Higgs mechanism with its imaginary bare mass is a naive relativistic analog of the phenomenological description of superconductivity [2]. Therefore there is a serious doubt whether electroweak symmetry is broken by such a Higgs mechanism, or by something else. The emergence of ∗ **
The text was submitted by the author in English. E-mail: [email protected]
large number of Higgsless models [3–8] was stimulated by difficulties with Higgs boson. These models are mainly based on extra dimensions of different types or larger gauge groups. A finite Electroweak Model without a Higgs particle which is used a regularized quantum field theory [9, 10] was developed in [8]. The simple mechanism for generation of the vector boson masses in Electroweak Model was suggested in [11–13]. It is based on the fact that the quadratic form φ† φ = ρ2 in the matter field space Φ2
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