Minimally allowed neutrinoless double beta decay rates within an anarchical framework

Abstract

Neutrinoless double beta decay $(\ensuremath{\beta}\ensuremath{\beta}0\ensuremath{\nu})$ is the only realistic probe of the Majorana nature of the neutrino. In the standard picture, its rate is proportional to ${m}_{ee}$, the $e\mathrm{\text{\ensuremath{-}}}e$ 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. $\ensuremath{\beta}\ensuremath{\beta}0\ensuremath{\nu}$ bounds below ${m}_{ee}\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}$ should indicate symmetry in the lepton sector, new light degrees of freedom, or the Dirac nature of the neutrino.