Lessons after the evidence for neutrinoless double beta decay — the next step

This paper describes the lessons we have to draw after the observation of neutrinoless ββ decay by the enriched ⁷⁶Ge experiment, for present and future experiments so as (a) to fulfill the task to confirm the present result (b) to deliver additional information on the main contributions of effective neutrino mass and right-handed weak currents etc. to the 0νββ amplitude. It is shown that presently running and planned experiments are probably not sensitive enough to check the evidence on a reasonable time scale. It is further demonstrated that, the only way to get more information on the individual contributions of m, η, λ etc. to the 0νββ amplitude is to go to completely different types of experiments, rather than those under construction and preparation at present, e.g. to mixed-mode β⁺/EC decay experiments, such as ¹²⁴Xe decay. It is pointed out that the sometimes observed "tension" between the result of 0νββ decay and cosmological experiments like WMAP, SDSS etc. does not exist and is an artificial product of improper analysis of the latter. (author)