Pions in nuclei and manifestations of supersymmetry in neutrinoless double beta decay

We examine the pion realization of the short-ranged supersymmetric (SUSY) mechanism of neutrinoless double beta decay (0νββ decay). It originates from the $R$-parity violating quark-lepton interactions of the SUSY extensions of the standard model of the electroweak interactions. We argue that pions are dominant SUSY mediators in 0νββ decay. The corresponding nuclear matrix elements for potentially 0νββ-decaying isotopes are calculated within the proton-neutron renormalized quasiparticle random-phase approximation $(pn$-RQRPA). We define those isotopes which are most sensitive to the SUSY signal and provide an outlook on the present experimental situation with the 0νββ-decay searches for SUSY. Upper limits on the $R$-parity violating first-generation Yukawa coupling ${\lambda }_{111}^{\prime }$ are derived from various 0νββ experiments.