Distinguishing the neutrinoless double beta decay mechanisms

Many new neutrinoless double beta decay (0nbb) experiments are planned or in preparation. If the 0nbb-decay will be detected, the key issue will be what is the dominant mechanism of this process. By measuring only transitions to the ground state one can not distinguish among many of the 0nbb-decay mechanisms (the light and heavy Majorana neutrino exchange mechanisms, the trilinear R-parity breaking mechanisms etc.). We show that if the ratio of the 0nbb-decay half-lifes for transitions to the 0^+ first excited and ground states is determined both theoretically and experimentally, it might be possible to determine, which 0nbb-decay mechanisms is dominant. For that purpose the corresponding nuclear matrix elements have to be evaluated with high reliability. The present work is giving strong motivations for experimental studies of the 0nbb-decay transitions to the first excited 0^+ states of the final nuclei.