Neutrino mass matrix in the minimal supergravity model: Bi-large mixing with trilinear R-parity violation

We study the neutrino oscillation and the production/decay of the lightest supersymmetric particle (LSP) under the minimal supergravity model (mSUGRA) without R-parity. The supersymmetric model without R-parity can explain the neutrino masses and mixing naturally, and has the virtue that it can be probed by collidcr experiments, by observing the decay of the LSP. In this paper, we show that we can describe the neutrino masses and mixing well under the mSUGRA without R-parity. In general, the 1-loop corrections are important to explain the known structure of neutrino oscillation. In mSUGRA, the neutraliho is LSP in most cases, but there is a small region which makes the scalar tau LSP. We search that region. For each case, we calculate the decay rate and branching ratios; as a result, we can find that it is possible to allow or exclude the model in the small tan β region. Unfortunately, it is impossible to probe the model in the large tan/3 case, because of the interferences among some diagrams of the LSP decay.