Novel constraints on $\Delta L=1$ interactions from neutrino masses
  We reanalyze the constraints imposed on lepton-number violating interactions by radiative contributions to neutrino masses at the one- and two-loop level in supersymmetric models without R-parity. The interactions considered are the $\Delta L=1$ superpotential operators $\lambda_{ijk} L_i L_j E^c_k$ and $\lambda^\prime_{ijk} L_i Q_j D^c_k$, and the $\Delta L=1$ soft terms $A_{ijk} \tilde{L}_i \tilde{L}_j \tilde{E}^c_k$ and $A_{ijk}^\prime \tilde{L}_i \tilde{Q}_j \tilde{D}^c_k$. It is shown how the constraints on the couplings $\lambda_{ijk}$ and $\lambda^\prime_{ijk}$ coming from the one-loop analysis can be evaded. In such a case, the two-loop contributions to neutrino masses become important. The combined one- and two-loop analysis yields constraints on the couplings $\lambda_{i33}$ and $\lambda^\prime_{i33}$ that are rather difficult to escape. The two-loop analysis yields also new constraints on $A_{i33}$ and $A^\prime_{i33}$, which are not bounded at the one-loop level. More freedom remains for couplings $\lambda_{ijk}$, $\lambda^\prime_{ijk}$, and $A_{ijk}$, $A^\prime_{ijk}$, when $j$ and $k$ are first- or second-generation indices. 
Francesca Borzumati and Jae Sik Lee