We show that the Li problems can be solved in the next-to-minimal supersymmetric standard model where the slepton as the next-to-lightest supersymmetric (SUSY) particle is very long lived. Such a long-lived slepton induces exotic nuclear reactions in big-bang nucleosynthesis, and destroys and produces the ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ nuclei via bound state formation. We study cases where the lightest SUSY particle is singlino-like neutralino and bino-like neutralino to present allowed regions in the parameter space, which is consistent with the observations on the dark matter and the Higgs mass.

• Received 13 March 2014

DOI:https://doi.org/10.1103/PhysRevD.90.035003