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, $\chi$, 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, $(0.12(0.05)|{\lambda }_{i,j,k}{|}^2+0.31(0.07)|{\lambda }_{i,j\ne 3,k}^{\prime }{|}^2+0.04(0.04)|{\lambda }_{i,3,k}^{\prime }{|}^2+0.23(0.12)|{\lambda }_{i,j,k}^{\prime \prime }(i<j,k\ne 3){|}^2)>7.7\times 10^{-24}$.

15 pages plus 9 figures