Novel constraints on $\mathrm{\Delta }L=1$ 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 $\mathrm{\Delta }L=1$ superpotential operators ${\lambda }_{ijk}{L}_i{L}_j{E}_k^c$ and ${\lambda }_{ijk}^{\mathrm{\prime }}{L}_i{Q}_j{D}_k^c$, and the $\mathrm{\Delta }L=1$ soft terms $A_{ijk} \tilde{L}_i \tilde{L}j \tilde{E}^c_k$and$A{ijk}^\prime \tilde{L}i \tilde{Q}j \tilde{D}^c_k$\mathrm{.}Itisshownhowtheconstraintsonthecouplings$\lambda{ijk}$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 ${\lambda }_{i33}^{\mathrm{\prime }}$ that are rather difficult to escape. The two-loop analysis yields also new constraints on $A_{i33}$ and $A_{i33}^{\mathrm{\prime }}$, which are not bounded at the one-loop level. More freedom remains for couplings ${\lambda }_{ijk}$, ${\lambda }_{ijk}^{\mathrm{\prime }}$, and $A_{ijk}$, $A_{ijk}^{\mathrm{\prime }}$, when $j$ and $k$ are first- or second-generation indices.