Neutrino oscillations and collider test of the R-parity violating minimal supergravity model

We study the R-parity violating minimal supergravity models accounting for the observed neutrino masses and mixing, which can be tested in future collider experiments. The bi-large mixing can be explained by allowing five dominant tri-linear couplings lambda'(1,2,3) and lambda(1,2). The desired ratio of the atmospheric and solar neutrino mass-squared differences can be obtained in a very limited parameter space where the tree-level contribution is tuned to be suppressed. In this allowed region, we quantify the correlation between the three neutrino mixing angles and the tri-linear R-parity violating couplings. Qualitatively, the relations \lambda(1)'\ < \lambda(2)'\ similar to\lambda(3)'\, and \lambda(1)\ similar to \lambda(2)\ are required by the large atmospheric neutrino mixing angle theta(23) and the small angle theta(13), and the large solar neutrino mixing angle theta(12), respectively. Such a prediction on the couplings can be tested in the next linear colliders by observing the branching ratios of the lightest supersymmetric particle (LSP). For the stau or the neutralino LSP, the ratio \lambda(1)\(2) :\lambda(2)\(2) :\lambda(1)\(2)+ \lambda(2)\(2) can be measured by establishing Br(e nu):Br(mu nu):Br(tau nu) or Br(nu e(+/-)tau(-/+)):Br(nu mu(+/-)tau(-/+)): Br(nu tau(+/-)tau(-/+)), respectively. The information on the couplings lambda(i)' can be drawn by measuring Br(l(i)t<(b)over bar>) proportional to \lambda(i)'\(2) the neutralino LSP is heavier than the top quark.