Playing with Neutrino Masses

TL;DR

This paper explores constraints on neutrino mass observables derived from six hypothetical, ad hoc assumptions about the complex neutrino mass parameters, highlighting the lack of theoretical justification for these hypotheses.

Contribution

It systematically examines how six simple, unmotivated hypotheses about neutrino masses impose constraints on key neutrino observables.

Findings

Constraints on neutrino mass sum, effective mass, and neutrinoless double beta decay parameter.

Highlights the speculative nature of assumptions without theoretical basis.

Provides a framework for testing hypotheses against experimental data.

Abstract

Most of what is known about neutrino masses and mixings results from studies of oscillation phenomena. We focus on those neutrino properties that are not amenable to such studies: $\Sigma $, the sum of the absolute values of the neutrino masses; $m_\beta $, the effective mass of the electron neutrino; and $m_{\beta\beta} $, the parameter governing neutrinoless double beta decay. Each of these is the subject of ongoing experimental or observational studies. Here we deduce constraints on these observables resulting from any one of six {\it ad hoc\} hypotheses that involve the three complex mass parameters $m_i$: (1) Their product or (2) sum vanishes; (3) Their absolute values, like those of charged leptons or quarks of either charge, do not form a triangle; (4) The $e$-$e$ entry of the neutrino mass matrix vanishes; (5) Both the $\mu$-$\mu$ and $\tau$-$\tau$ entries vanish; (6) All three diagonal entries are equal in magnitude. The title of this note reflects the lack of any theoretical basis for any of these simple assertions.