Enhancingli→3ljwith theZ0-penguin

Abstract

Lepton flavor violation has been observed in neutrino oscillations. For charged lepton flavor violation decays only upper limits are known, but sizable branching ratios are expected in many neutrino mass models. High-scale models, such as the classical supersymmetric seesaw, usually predict that decays ${l}_{i}\ensuremath{\rightarrow}3{l}_{j}$ are roughly a factor $\ensuremath{\alpha}$ smaller than the corresponding decays ${l}_{i}\ensuremath{\rightarrow}{l}_{j}\ensuremath{\gamma}$. Here we demonstrate that the ${Z}^{0}$-penguin diagram can give an enhancement for decays ${l}_{i}\ensuremath{\rightarrow}3{l}_{j}$ in many extensions of the minimal supersymmetric standard model (MSSM). We first discuss why the ${Z}^{0}$-penguin is not dominant in the MSSM with seesaw and show that much larger contributions from the ${Z}^{0}$-penguin are expected in general. We then demonstrate the effect numerically in two example models, namely, the supersymmetric inverse seesaw and $R$-parity violating supersymmetry.