Neutrino masses in SU(2) ⊗ U(1) theories

TLDR

The paper studies SU(2)×U(1) extensions with n isodoublet and m isosinglet neutrinos, outlining the general formalism, parametrization of unitary matrices, and Majorana quantum theory. The study aims to analyze SU(2)×U(1) models with n isodoublet and m isosinglet neutrinos. The authors parametrize the charged‑current interactions with a rectangular matrix K and derive the neutral‑current matrix P = K⁺K. They find that neutrinos can decay into three lighter neutrinos and that neutral‑current mediated oscillations are possible.

Abstract

We analyze SU(2)\ifmmode\times\else\texttimes\fi{}U(1) theories, denoted by ($n, m$), in which there are $n$ neutrinos belonging to isodoublets and $m$ neutrino isosinglets. The charged-current weak interactions are described by a rectangular matrix $K$ which we explicitly parametrize. The neutral-current neutrino interactions are described by a square matrix $P={K}^{+}K$. This has the consequences that neutrinos may decay into three lighter ones and that neutrino oscillations involving neutral-current interactions should exist. The general formalism for the latter situation is given. Associated material on parametrization of unitary matrices and the quantum theory of Majorana particles is also briefly discussed.