Large Cosmological Light Element Bound on R Parity Violating Parameters

In R parity violating theories, there does not exist the {\it stable} lightest supersymmetric particle (LSP). The LSP, $\chi$, of MSSM decays to lighter ordinary particles with dimension 6 effective R violating interaction terms. Since the lifetime of $\chi$ 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 $\chi$ in the small $\tau_\chi$ region; $\sim\tau_\chi>10^6$ s. This translates to the sum of squared R-violating couplings, for $m_\chi=$ 60 GeV in the photino (bino) limit, $(0.12 (0.05)|\lambda_{i,j,k}|^2+0.31(0.07) |\lambda^\prime_{i,j\ne 3,k}|^2 +0.04(0.04)|\lambda^{\prime}_{i,3,k}|^2 +0.23(0.12)|\lambda_{i,j,k}^{\prime\prime}(i<j,k\ne 3)|^2)> 7.7\times 10^{-24}$.