We review important reactions in the big bang nucleosynthesis (BBN) model involving a long-lived negatively charged massive particle, $X^-$, which is much heavier than nucleons. This model can explain the observed $^7$Li abundances of metal-poor stars, and predicts a primordial $^9$Be abundance that is larger than the standard BBN prediction. In the BBN epoch, nuclei recombine with the $X^-$ particle. Because of the heavy $X^-$ mass, the atomic size of bound states $A_X$ is as small as the nuclear size. The nonresonant recombination rates are then dominated by the $d$-wave $rightarrow$ 2P transition for $^7$Li and $^{7,9}$Be. The $^7$Be destruction occurs via a recombination with the $X^-$ followed by a proton capture, and the primordial $^7$Li abundance is reduced. Also, the $^9$Be production occurs via the recombination of $^7$Li and $X^-$ followed by deuteron capture. The initial abundance and the lifetime of the $X^-$ particles are constrained from a BBN reaction network calculation. We estimate that the derived parameter region for the $^7$Li reduction is allowed in supersymmetric or Kaluza-Klein (KK) models. We find that either the selectron, smuon, KK electron or KK muon could be candidates for the $X^-$ with $m_Xsim {mathcal O}(1)$ TeV, while the stau and KK tau cannot.
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