Neutrinoless Double Beta Decay, the Inverted Hierarchy and Precision   Determination of theta(12)
  Ruling out the inverted neutrino hierarchy with neutrinoless double beta decay experiments is possible if a limit on the effective mass below the minimal theoretically possible value is reached. We stress that this lower limit depends strongly on the value of the solar neutrino mixing angle: it introduces an uncertainty of a factor of 2 within its current 3 sigma range. If an experiment is not background-free, a factor of two in effective mass corresponds to a combined factor of 16 improvement for the experimental parameters running time, detector mass, background level and energy resolution. Therefore, a more precise determination of theta(12) is crucial for the interpretation of experimental results and the evaluation of the potential and requirements for future experiments. We give the required half-lifes to exclude (and touch) the inverted hierarchy regime for all double beta decay isotopes with a Q-value above 2 MeV. The nuclear matrix elements from 6 different groups and, if available, their errors are used and compared. We carefully put the calculations on equal footing in what regards various convention issues. We also use our compilation of matrix elements to give the reachable values of the effective mass for a given half-life value. 
Alexander Dueck, Werner Rodejohann, Kai Zuber
hep-ph hep-ex nucl-ex nucl-th