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 0νββdecay. 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 outlook the present experimental situation with the 0νββ-decay searches for the SUSY. Upper limits on the R-parity violating 1st generation Yukawa coupling λ′111 are derived from various 0νββ-experiments. The observation of neutrinoless nuclear double beta decay (A,Z) −→ (A,Z+2)+2e (0νββ) would undoubtedly indicate the presence of the new physics beyond the standard model (SM) of electroweak interactions. However, as yet there is no any experimental evidence for this lepton-number violating (∆L = 2)exotic process. On the other hand non-observation of 0νββdecay at certain experimental sensitivity allows one to set limits on some parameters of the new physics. An unprecedented accuracy and precision of the modern 0νββ-decay experiments allows one in certain cases to push these limits far away of the reach of the other accelerator and non-accelerator experiments. A well known example is given by the upper limit on the light effective Majorana neutrino mass 〈mM 〉. From the 0νββ-decay experiments [1] it was found 〈mM 〉 ≤ O(1.1 eV) [2]. Recall that the Majorana neutrino mass term violates the lepton number ∆L = 2. This is exactly that is necessary for 0νββ-decay to proceed via the virtual neutrino exchange between the two neutrons. In this case the 0νββ-decay amplitude is proportional to 〈mM 〉. The Majorana neutrino exchange is not the only possible mechanism of 0νββ-decay. The lepton-number violating quark-lepton interactions of the R-parity non-conserving supersymmetric extensions of the SM (Rp / SUSY) can also induce this process [3]-[6]. R-parity is a discrete multiplicative Z2 symmetry defined as Rp = (−1)3B+L+2S, where S,B and L are the spin, the baryon and the lepton quantum number. The 0νββ-decay proved to be very sensitive probe of the new interactions predicted in the Rp / SUSY [5]-[7]. Searching for tiny effects of the physics beyond the SM in 0νββ-decay requires a reliable treatment of the nuclear structure. In this note we present the results of our calculations within 1 On leave of absence from the Joint Institute for Nuclear Research, Dubna, Russia.