Conversion of experimental half-life to effective electron neutrino mass in0νββdecay

Abstract

The Germanium Detector Array (GERDA) collaboration will be searching for neutrinoless double $\ensuremath{\beta}$ decay of $^{76}\mathrm{Ge}$. As a result it will measure the half-life ${T}_{1/2}$ of this rare process; or at least a new value for the lower limit for ${T}_{1/2}$ will be derived. The sensitivity of the GERDA experiment on the effective electron neutrino mass $\ensuremath{\langle}{m}_{\ensuremath{\beta}\ensuremath{\beta}}\ensuremath{\rangle}$ depends on the theoretical value for the nuclear matrix element $\mathcal{M}$ and the kinematical phase space factor $G$.In this Brief Report we focus on existing difficulties in applying the dimensionless values of $\mathcal{M}$ calculated by various theoretical groups, which use different methods and parametrizations. The implicit radius dependencies in $\mathcal{M}$ and $G$ are discussed. Resulting values of the neutrino mass are tabulated for various representative half-lives ${T}_{1/2}$ representing the sensitivity of the various phases of the GERDA experiment.