Large Cosmological Light Element Bound on R Parity Violating Parameters

Abstract

In R parity violating theories, there does not exist the {\it stable} lightest supersymmetric particle (LSP). The LSP, $χ$, of MSSM decays to lighter ordinary particles with dimension 6 effective R violating interaction terms. Since the lifetime of $χ$ can be sufficiently long for small R-violating couplings, it can affect the standard nucleosynthesis scenario. This constraint gives an upper limit for the lifetime of $χ$ in the small $τ_χ$ region; $\simτ_χ>10^6$ s. This translates to the sum of squared R-violating couplings, for $m_χ=$ 60 GeV in the photino (bino) limit, $(0.12 (0.05)|λ_{i,j,k}|^2+0.31(0.07) |λ^\prime_{i,j\ne 3,k}|^2 +0.04(0.04)|λ^{\prime}_{i,3,k}|^2 +0.23(0.12)|λ_{i,j,k}^{\prime\prime}(i<j,k\ne 3)|^2)> 7.7\times 10^{-24}$.