Many extensions of the leptonic sector of the minimal supersymmetric standard model (MSSM) are known, most of them leading to observable flavor violating effects. It has recently been shown that the 1-loop contributions to lepton flavor violating three-body decays $l_i\to 3l_j$ involving the $Z^0$ boson may be dominant, that is, much more important than the usual photonic penguins. Other processes like $\mu$-$e$ conversion in nuclei and flavor violating $\tau$ decays into mesons are also enhanced by the same effect. This is for instance also the case in the MSSM with trilinear $R$-parity violation. The aim of this work is to derive new bounds on the relevant combinations of $R$-parity violating couplings and to compare them with previous results in the literature. For heavy supersymmetric spectra the limits are improved by several orders of magnitude. For completeness, also constraints coming from flavor violating $Z^0$-decays and tree-level decay channels $l\to l_i{l}_j{l}_k$ are presented for a set of benchmark points.

• Received 3 May 2012

DOI:https://doi.org/10.1103/PhysRevD.86.015003