O(5)xU(1) electroweak gauge theory and the neutrino oscillations in matter

A study is made of the group O(5) x U(1). The group is economical in the number of gauge bosons, which we associate with each of its generators, and is anomaly-free. The left-handed leptons L/sub L//sup T/ = (v/sub e/, e, μ, v/sub μ/)/sub L/ are assigned to the four-dimensional spinorial representations of O(5). The right-handed particles are taken to be the singlets of the group. The theory has three sets of gauge bosons: (1) analogues of the GWS model, (2) additional charged gauge bosons, and (3) a set of three additional neutral gauge bosons as compared to the GWS model. We introduce neutrino mixing the additional charged gauge bosons. We develop a theory of neutrino oscillations in matter in such a way that in the absence of matter the scattering length reduces to the usual scattering length in vacuum. Even if the neutrino masses are equal or the neutrinos are massless, we still have neutrino oscillations in matter, a result already noted by Wolfenstein