Novel constraints on $\Delta L=1$ interactions from neutrino masses

Abstract

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

Comments: 19 pages, 4 figures, and 2 tables. Version to appear in Phys. Rev. D