Minimally Allowed Neutrinoless Double Beta Decay Rates Within an Anarchical Framework

TL;DR

This paper investigates the minimal possible rates of neutrinoless double beta decay within an anarchical neutrino mass framework, finding that the effective mass parameter $m_{ee}$ is constrained between 0.01 and 0.4 eV at 90% confidence, with implications for neutrino nature and underlying symmetries.

Contribution

It introduces a statistical analysis of neutrino mass matrices under anarchy, constraining $m_{ee}$ and exploring the impact of different measure choices on decay rate predictions.

Findings

$m_{ee}$ constrained between 0.01-0.4 eV at 90% confidence

Singular measures allow arbitrarily small $m_{ee}$ values

Bounds below 5e-3 eV suggest new physics or neutrino Dirac nature

Abstract

Neutrinoless double beta decay is the only realistic probe of the Majorana nature of the neutrino. In the standard picture, its rate is proportional to $m_{ee}$, the e-e element of the Majorana neutrino mass matrix in the flavor basis. I explore minimally allowed $m_{ee}$ values within the framework of mass matrix anarchy where neutrino parameters are defined statistically at low energies. Distributions of mixing angles are well defined by the Haar integration measure, but masses are dependent on arbitrary weighting functions and boundary conditions. I survey the integration measure parameter space and find that for sufficiently convergent weightings, $m_{ee}$ is constrained between (0.01-0.4) eV at 90% confidence. Constraints from neutrino mixing data lower these bounds. Singular integration measures allow for arbitrarily small $m_{ee}$ values with the remaining elements ill-defined, but this condition constrains the flavor structure of the model's ultraviolet completion. Bounds below $m_{ee} \sim 5\times10^{-3}$ eV should indicate symmetry in the lepton sector, new light degrees of freedom or the Dirac nature of the neutrino.