Dominance of Pion Exchange inR-Parity-Violating Supersymmetric Contributions to Neutrinoless Double Beta Decay

We present a new contribution of the $R$-parity-violating $\left(R{}_p\right)$ supersymmetry (SUSY) to neutrinoless double beta decay $\left(0\nu \beta \beta \right)$ via the pion exchange between decaying neutrons. The pion coupling to the final state electrons is induced by the $R{}_p$ SUSY interactions. We have found this pion-exchange mechanism to dominate over the conventional two-nucleon one. The latter corresponds to direct interaction between quarks from two decaying neutrons without any light hadronic mediator like $\pi$ meson. The constraints on the certain $R{}_p$ SUSY parameters are extracted from the current experimental $0\nu \beta \beta$-decay half-life limit. These constraints are significantly stronger than those previously known or expected from the ongoing accelerator experiments.