Critical view on double-beta decay matrix elements within Quasi Random Phase Approximation-based methods

Abstract

A systematic study of the two-neutrino and neutrinoless double-beta decay matrix elements (ME) for the nuclei with A=76, 82, 96, 100, 116, 128, 130 and 136 is done. The calculations are performed with four different quasi random phase approximation (QRPA)-based methods, i.e. the proton–neutron QRPA (pnQRPA), the renormalized proton–neutron QRPA (pnRQRPA), the full-RQRPA and the second-QRPA (SQRPA). First we checked the conservation of the Ikeda sum rule (ISR) and found that it is fulfilled with a good accuracy for the SQRPA, while for the pnRQRPA and full-RQRPA the deviations are up to 17%. Then, we studied the dependence of the ME on the single-particle (s.p.) basis. For that we performed the calculations using the same set of parameters and two different s.p. basis. For the two-neutrino decay mode the ME manifest generally the largest sensitivity to the choice of the basis when they are calculated with the pnQRPA, while the smallest sensitivity is got with the SQRPA. For all the methods the largest differences between the results were found for 128,130Te and 136Xe. For the neutrinoless decay mode the ME display generally a stronger dependence on the basis than for the two-neutrino decay mode, when they are calculated with the pnQRPA, RQRPA and full-RQRPA, while for SQRPA differences in the results are within 30%. A better stability against the change of the s.p. basis used and a good fulfillment of the ISR allow to reduce the uncertainties in the values of the neutrinoless ME predicted by the QRPA-based methods to about 50% from their magnitude. Further, we fixed the values of g pp from the two-neutrino calculations and according to recent experimental data, and then we used them to compute the ME for the neutrinoless decay mode. Taking the most recent experimental limits for the neutrinoless half-lives, we deduce new upper limits for the neutrino mass parameter. Finally, there are estimated, for each nucleus, scales for the neutrinoless double-beta decay half-lives that the experiments should reach for exploring neutrino masses around 0.1 eV. This might guide the experimentalists in planning their setups.