Neutrino Oscillations and Collider Test of the R-parity Violating Minimal Supergravity Model

We study the R-parity violating minimal supergravity models accounting forthe observed neutrino masses and mixing, which can be tested in future colliderexperiments. The bi-large mixing can be explained by allowing five dominanttri-linear couplings $ \lambda'_{1,2,3}$ and $\lambda_{1,2}$. The desired ratioof the atmospheric and solar neutrino mass-squared differences can be obtainedin a very limited parameter space where the tree-level contribution is tuned tobe suppressed. In this allowed region, we quantify the correlation between thethree neutrino mixing angles and the tri-linear R-parity violating couplings.Qualitatively, the relations $| \lambda'_1 | < | \lambda'_2| \sim |\lambda'_3|$, and $|\lambda_1| \sim |\lambda_2|$ are required by the largeatmospheric 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 nextlinear colliders by observing the branching ratios of the lightestsupersymmetric 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 measuredby establishing $Br(e\nu): Br(\mu\nu) : Br(\tau\nu)$ or $Br(\nu e^\pm \tau^\mp): Br(\nu\mu^\pm\tau^\mp) : Br(\nu\tau^\pm\tau^\mp)$, respectively. Theinformation on the couplings $\lambda'_i$ can be drawn by measuring $Br(l_i t\bar{b}) \propto |\lambda'_i|^2$ if the neutralino LSP is heavier than the topquark.Comment: RevTex, 25 pages, 8 eps figure