Towards reliable nuclear matrix elements for neutrinoless ββ decay

The calculated nuclear matrix elements for the neutrinoless double-beta (0νββ) decay suffer from several limitations. Predicted matrix-element values depend on the many-body method used to calculate them and, in addition, they may need to be "quenched", albeit by an unknown amount due to the relatively high momentum transferred in the decay. These uncertainties are hard to figure out from theoretical calculations alone because of the unique character of 0νββ decay, not clearly related to other nuclear structure observables. We present recent progress in the determination of the nuclear matrix elements. First, we report improved shell model calculations in an extended configuration space of two harmonic oscillator shells. Second, we note the relation between the 0νββ decay and double Gamow-Teller transitions that can in principle be measured in double charge-exchange reactions. These new insights pave the way for a more reliable estimation of the value of the nuclear matrix elements. (author)