Collider Signatures of Neutrino Masses and Mixing from R-parity Violation

$R$-parity violation in the supersymmetric standard model can be the source of neutrino masses and mixing. We analyze the neutrino mass matrix coming from either bilinear or trilinear R-parity violation and its collider signatures, assuming that the atmospheric and solar neutrino data are explained by three active neutrino oscillations. Taking the gauge mediated supersymmetry breaking mechanism, we show that the lightest neutralino decays well inside the detector and the model could be tested by observing its branching ratios in future colliders. In the bilinear model where only the small solar neutrino mixing angle can be accommodated, the relation ${10}^{3}\mathrm{BR}(\ensuremath{\nu}{e}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}})\ensuremath{\sim}\mathrm{BR}(\ensuremath{\nu}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}})\ensuremath{\approx}\mathrm{BR}(\ensuremath{\nu}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}})$ serves as a robust test of the model. The large mixing angle solution can be realized in the trilinear model which predicts $\mathrm{BR}(\ensuremath{\nu}{e}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}})\ensuremath{\sim}\mathrm{BR}(\ensuremath{\nu}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}})\ensuremath{\sim}\mathrm{BR}(\ensuremath{\nu}{\ensuremath{\tau}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\tau}}^{\ensuremath{\mp}}).$ In either case, the relation $\mathrm{BR}(\mathrm{ejj})\ensuremath{\ll}\mathrm{BR}(\ensuremath{\mu}jj)\ensuremath{\sim}\mathrm{BR}(\ensuremath{\tau}jj)$ should hold to be consistent with the atmospheric neutrino and CHOOZ experiments.