Test of physics beyond the standard model in nuclei

The modern theories of Grand Unification (GUT) and SuperSymmetric (SUSY) extensions of Standard Model (SM) suppose that the conservation laws of the SM may be violated to some small degree. The nuclei are well-suited as a laboratory to test fundamental symmetries and fundamental interactions like lepton flavor (LF) and lepton number (LN) conservation. A prominent role between experiments looking for LF and total LN violation play not yet observed processes of neutrinoless double-beta decay (0νββ decay). The GUT and SUSY models offer a variety of mechanisms that allow 0νββ decay to occur. They are based on mixing of Majorana neutrinos and/or R-parity-violation hypothesis. Although the 0νββ-decay has not been seen, it is possible to extract from the lower limits of the lifetime upper limits for the effective electron Majorana neutrino mass, effective right-handed weak-interaction parameters, the effective Majoron coupling constant, R-parity-violating SUSY parameters, etc. A condition for obtaining reliable limits for these fundamental quantities is that the nuclear matrix elements governing this process can be calculated correctly. The nuclear structure wave functions can be tested by calculating the two-neutrino double-beta decay (2νββ decay) for which we have experimental data and not only lower limits as for the 0νββ decay. For open-shell nuclei, the method of choice has been the quasiparticle random-phase approximation (QRPA), which treats Fermion pairs as bosons. It has been found that, by extending the QRPA including fermion commutation relations, better agreement with 2νββ-decay experiments is achieved. This increases also the reliability of conclusions from the upper limits on the 0νββ-decay transition probability. In this work, the limits on the LN-violating parameters extracted from current 0νββ-decay experiments are listed. Studies in respect to future 0νββ-decay experimental projects are also presented.