We analyze the contributions to the neutrinoless double β decay (0νββ-decay) coming from the Grand Unified Theory (GUT) constrained Minimal Supersymmetric Standard Model (MSSM) with trilinear R-parity breaking. We discuss the importance of two-nucleon and pion-exchange realizations of the quark-level 0νββ-decay transitions. In this context, the questions of reliability of the calculated relevant nuclear matrix elements within the Renormalized Quasiparticle Random Phase Approximation (pn-RQRPA) for several medium and heavy open-shell nuclei are addressed. The importance of gluino and neutralino contributions to 0νββ-decay is also analyzed. We review the present experiments and deduce limits on the trilinear R-parity breaking parameter λ ′ 111 from the non-observability of 0νββ-decay for different GUT constrained SUSY scenarios. In addition, a detailed study of limits on the MSSM parameter space coming from the B → X s γ processes by using the recent CLEO and OPAL results is performed. Some studies in respect to the future 0νββ-decay project GENIUS are also presented.12.60. Jv,11.30.Er,23.40.Bw Typeset using REVT E X 1 .

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The neutrinoless double beta decay (0νββ-decay) transition to the first excited 0 + collective final state is examined for A=76, 82, 100 and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized Quasiparticle Random Phase Approximation. Transitions to the first excited twoquadrupole phonon 0 + state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the 0νββ-decay experiments. The half-life of 0νββ-decay to the first excited state 0 + 1 is by a factor of 10 to 100 larger than that of the transition to the ground state, 0 + g.s. .

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The first, to our knowledge, calculation of neutrinoless double beta decay (0νββ-decay ) matrix elements within the self-consistent renormalized Quasiparticle Random Phase Approximation (SRQRPA) is presented. The contribution from the momentum-dependent induced nucleon currents to 0νββ-decay amplitude is taken into account. A detailed nuclear structure study includes the discussion of the sensitivity of the obtained SRQRPA results for 0νββ-decay of 76 Ge to the parameters of nuclear Hamiltonian, two-nucleon short-range correlations and the truncation of the model space. A comparison with the standard and renormalized QRPA results is presented. We have found a considerable reduction of the SRQRPA nuclear matrix elements, resulting in less stringent limits for the effective neutrino mass. PACS numbers:23.40. Hc, 21.60.Jz, 27.50.+e, 27.60.+j The neutrino mass and mixing of neutrinos are the main subject of the elementary 1

The validity of the commonly assumed closure approximation has been tested by explicit calculations of the Ov PP-decay matrix elements of Ge Se performed in the context of quasiparticle random-phase approximation with a realistic model space. The closure approximation seems to work well for those matrix elements not very suppressed. Our results indicate that unlike the 2v decay, the Ov PP-decay matrix elements are not greatly suppressed but are comparable to those of shell model calculations. They are dominated by multipoles other than 0+ and 1+.Although at present there exist no data which contradict the standard model of the electroweak [SU (2) xU(1)] and the strong SU3(3), interactions there is a general belief that the standard model with its 23 unspecified parameters cannot be the ultimate fundamental theory of nature. Therefore during the last years various extensions of the standard model have been considered. Among them the most popular have been various unification schemes of the electroweak and strong forces, including the grand unified theories (GUT's) with their supersymmetric extensions and, more recently, superstring and superstring-inspired models.An interesting feature of such extensions of the standard model is that the neutrino turns out quite naturally to be a massive majorana particle, i.e. , loosely speaking identical with its own antiparticle. In such a situation the neutrinoless double P decay' (Ov PP decay) becomes possible. Thus if such a process is eventually detected it would indicate physics beyond the standard model. ' ' But, even if one is not able to observe the neutrinoless double P decay, an upper limit on its transition probability or a lower bound on its lifetime can provide rather stringent restrictions on the parameters of these models.For the extraction of these constraints from the data a reliable calculation of the nuclear matrix elements involved is quite crucial. Since the natural final states of Ov PP decay, i.e. , the double isobaric analog (DIA) and the double Gamow-Teller (DGT) states, cannot be reached due to the limited available energy, the populated states (ground state or low-lying excited states ) are very weak. Thus the transition probability depends on fine details of nuclear structure. Thus one may have to worry about problems which are normally assumed not be be critical." In this class of problems one may include the validity of closure approximation, the short-range correlations between the nucleons, and the role of the weak magnetism term of the weak hadronic current.The closure approximation in the usual two neutrino double P decay has to be circumvented. It has, however, been assumed to be good in Ov PP decay since in this case the propagator is expected to be dominated by the virtual neutrino momentum.Nevertheless, some groups ' have not used closure in the sense that they explicitly used the intermediate nuclear states. They did not, however, use the exact energy-dependent transition operator.In this Rapid Communication we are going to employ a method...

1W, 128 and 130 systems is examined in the context of the QRPA formalism without invoking the closure approximation. All possible nuclear matrix elements are calculated including the nucleon recoil contributions as well as those resulting from the exchange of heavy intermediate Majorana neutrinos. Using the hest presently available experimental limit TEP(Ov) > 1.1 x 1@' y the following limits on the lepton violating parameters are extracted: I(my)l<2.0eV. (1/M,)p126.7X 10'GeV. As3.3XlO-" and n s 4 . 2 ~ 10-8.