Grand unified theory constrained supersymmetry and neutrinoless doubleβdecay

We analyze the contributions to the neutrinoless double $\beta$ decay $(0\mathrm{}\nu \beta \beta$ 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 $0\nu \beta \beta$-decay transitions. In this context, the questions of reliability of the calculated relevant nuclear matrix elements within the renormalized quasiparticle random phase approximation for several medium and heavy open-shell nuclei are addressed. The importance of gluino and neutralino contributions to $0\nu \beta \beta$ decay is also analyzed. We review the present experiments and deduce limits on the trilinear R-parity breaking parameter ${\lambda }_{111}^{\prime }$ from the nonobservability of $0\nu \beta \beta$ decay for different GUT constrained supersymmetry scenarios. In addition, a detailed study of limits on the MSSM parameter space coming from the $\overrightarrow{B}{X}_s\gamma$ processes by using the recent CLEO and OPAL results is performed. Some studies in respect to the future $0\nu \beta \beta$-decay project GENIUS are also presented.