We review a non-standard Big-Bang nucleosynthesis (BBN) scenario within the minimal supersymmetric standard model, and propose an idea to solve both ${}^{7}$Li and ${}^{6}$Li problems. Each problem is a discrepancy between the predicted abundance in the standard BBN and observed one. We focus on the stau, a supersymmetric partner of tau lepton, which is a long-lived charged particle when it is the next lightest supersymmetric particle and is degenerate in mass with the lightest supersymmetric particle. The long-lived stau forms a bound state with a nucleus, and provide non-standard nuclear reactions. One of those, the internal conversion process, accelerates the destruction of ${}^{7}$Be and ${}^{7}$Li, and leads to a solution to the ${}^{7}$Li problem. On the other hand, the bound state of the stau and ${}^{4}$He enhances productions of n, d, t, and ${}^{6}$Li. The over-production of ${}^{6}$Li could solve the ${}^{6}$Li problem. While, the over-productions of d and t could conflict with observations, and the relevant parameter space of the stau is strictly constrained. We therefore need to carefully investigate the stau-${}^{4}$He bound state to find a condition of solving the ${}^{6}$Li problem. The scenario of the long-lived stau simultaneously and successfully fit the abundances of light elements (d, t, ${}^{3}$He, ${}^{4}$He, ${}^{6}$Li, and ${}^{7}$Li) and the neutralino dark matter to the observed ones. Consequently parameter space both of the stau and the neutralino is determined with excellent accuracy.
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