Contraction of electroweak model can explain the interactions neutrinos with matter
- PDF / 222,137 Bytes
- 3 Pages / 612 x 792 pts (letter) Page_size
- 108 Downloads / 181 Views
ontraction of Electroweak Model can Explain the Interactions Neutrinos with Matter1 N. A. Gromov Department of Mathematics, Komi Science Center UrD, RAS, Kommunisticheskaya st. 24, Syktyvkar, 167982 Russia email: [email protected] Abstract—The very rare interactions neutrinos with matter and the dependence of the corresponding cross section on neutrinos energy are explained as contraction of the gauge group of the Electroweak Model already at the level of classical gauge fields. Small contraction parameter is connected with the universal Fermi con stant of weak interactions and neutrino energy as ⑀2(s) = G F s. DOI: 10.1134/S1063779612050140 1
1. INTRODUCTION
The modern theory of electroweak interactions – standard Electroweak Model – is gauge theory based on gauge group SU(2) × U(1). In physics it is well known the operation of group contraction [1], which transforms, for example, a simple or semisimple group to a nonsemisimple one. For better uderstanding of a complicated physical system it is useful to investigate its limit cases for limit values of its physical parame ters. For symmetric system similar limit values are often connected with contraction parameters of its symmetry group. In this paper we discuss the modified Electroweak Model with the contracted gauge group SU(2; ⑀) × U(1). We explain at the level of classical fields the vanishingly small interactions neutrinos with matter especially for low energies and the decrease of the neutrinosmatter crosssection when energy tends to zero with the help of contraction of gauge group. We connect dimensionless contraction parameter ε → 0 with neutrinos energy. 2. MODIFICATION OF THE STANDARD ELECTROWEAK MODEL We shall follow the books [2–4] in description of standard Electroweak Model. From the viewpoint of electroweak interactions all known leptons and quarks are divided on three generations. In what follows we shall regarded only first generations of leptons and quarks. We consider a model where the contracted gauge group SU(2; ⑀) × U(1) acts in the boson, lepton and quark sectors. The contracted group SU(2; ⑀) is
obtained [5] by the consistent rescaling of the funda mental representation of SU(2) and the space C2 ⎛ εz ⎛ ⎞ ⎛ εz ⎞ ⑀ ' ⎞ z' ( ε⑀ ) = ⎜ 1 ⎟ = ⎜ α ⑀εβ ⎟ ⎜ ⑀ 1 ⎟ = u ( ε⑀)z ( ε⑀ ), ⎝ z '2 ⎠ ⎝ – ε⑀ β α ⎠ ⎝ z 2 ⎠ detu ( ε⑀ ) = α + ⑀ε β 2
2
2
= 1,
†
u ( ε⑀ )u ( ε⑀) = 1
(1)
in such a way that the hermitian form z†z(⑀) = ⑀|z1|2 + |z2|2 remains invariant, when contraction parameter tends to zero ⑀ → 0 or is equal to the nilpotent unit ⑀ = ι, ι2 = 0. The actions of U(1) and the electromagnetic subgroup U(1)em in the fibered space C2(ι) with the base {z2} and the fiber {z1} are given by the same matri ces as in the space C2. The space C2(⑀) of the fundamental representation of SU(2; ⑀) group can be obtained from C2 by substitut ing z1 by ⑀z1. Substitution z1 → ⑀z1 induces another ones for Lie algebra generators T1 → ⑀T1, T2 → ⑀T2, T3 → T3. As far as the gauge fields take their values in Lie algebra, we can substitute the gauge fields inst
Data Loading...
