Associated neutrino mixing and neutrino oscillations in left-right electro weak gauge theory

Abstract

The question of the associated neutrino mixing is investigated within the frame work of left-right symmetric gauge theory of electro weak interactions. It is shown that the weak leptonic neutral currents are independent of the mixing angle while the charged counterpart crucially depend on them. As the mass of right handed gauge boson becomes very large, the results reduce to those of the standard model, albeit the arbitrarily small mass for the neutrino. With the associated mixing of neutrinos, the muonness changing neutral weak currents are absent at the tree level. A conditions forvα↔vβ oscillation is derived as\(\frac{{m_{v_\alpha } }}{{m_{v_\beta } }} > \frac{{m_\alpha }}{{m_\beta }}\) where α, β stand fore, μ, τ in that order (α≠β). With three neutrino mixing bySO(3) rotation, the present experimental data on neutrino oscillations are satisfactorily explained with the conclusion thatve oscillates mostly withvτ and vice-versa whilevμ beam suffers very little oscillation. Consequently it is conjectured that most probablyLe andLτ (lepton numbers) are not conserved whileLμ is nearly conserved in weak interaction.