Neutrinoless Double-βDecay and Its Relation to Pion Double Charge Exchange

A two-delta ($\Delta \Delta$) process and a new two-nucleon ($\mathrm{NN}$) process are proposed for neutrinoless $\left(0_{\nu }\right)\beta \beta$ decay. The conventional $\mathrm{NN}$ mechanism is also examined. The $N\Delta$ interaction and the integration over virtual neutrino momenta lead to the dominance of the $\Delta \Delta$ process. This dominance enables one to relate $0_{\nu }\beta \beta$ decay rates and forward-angle double-charge-exchange cross sections for $0^{+}$ (g.s.) → $0^{+}$ (g.s.) transitions, and to use this relation to obtain limits on lepton-number nonconservation from experimental double-charge-exchange cross sections in a nearly nuclear-structure-model-independent way.