Symplectic Symmetry of the Neutrino Mass and the See-Saw Mechanism
A.B. Balantekin (Wisconsin U., Madison, Max-Planck-Institute,, Heidelberg), N. Ozturk (U. Wisconsin)
TL;DR
This paper explores the algebraic structure underlying the neutrino mass Hamiltonian, revealing its formulation within an Sp(4) algebra and connecting the see-saw mechanism to an embedded SU(2) symmetry.
Contribution
It introduces an algebraic framework for neutrino masses, unifying the see-saw mechanism within the Sp(4) algebraic structure and linking it to the Pauli-Gursey transformation.
Findings
Neutrino mass Hamiltonian can be expressed using Sp(4) generators.
The see-saw mechanism corresponds to an SU(2) subgroup within Sp(4).
The Pauli-Gursey transformation is an SU(2) rotation embedded in Sp(4).
Abstract
We investigate the algebraic structure of the most general neutrino mass Hamiltonian and place the see-saw mechanism in an algebraic framework. We show that this Hamiltonian can be written in terms of the generators of an Sp(4) algebra. The Pauli-Gursey transformation is an SU(2) rotation which is embedded in this Sp(4) group. This SU(2) also generates the see-saw mechanism.
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