by the $^{7}$Li( p , α ) $^{4}$He and $^{7}$Li( X $^{−}$, γ ) $^{7}$Li$_{X}$ ( p ,2 α ) X − reac- tions [5, 7] or a further conversion of $^{7}$Li$_{X}$ by the weak interaction [12] shifts the contours of the $^{7}$Li abundance toward smaller values of Y$_{X}$ . In this case the parame- ter region which solves both the $^{6}$Li and $^{7}$Li problems is Y$_{X}$ ≈ 0 . 04 − 0 . 2 and τ$_{X}$ ≈ (1 . 4 − 2 . 6) × 10 3 s. We now consider a model in which the present cold dark matter (DM) was produced by the decay of X ± particles, i.e., Y DM ≥ Y$_{X}$ . The WMAP-CMB con- straint on the cosmological density parameter of cold DM Ω CDM = 0 . 2 then corresponds to m DM Y DM ≤ 4 . 5 GeV. The constraints on Y$_{X}$ required to resolve the $^{6}$Li and $^{7}$Li problems then imply a range for the the dark- matter mass m DM . In the case where the reactions $^{7}$Be$_{X}$ + p → $^{8}$B $^{∗}$a X → $^{8}$B$_{X}$ + γ [5] and $^{7}$Be$_{X}$ + p → $^{8}$B $^{∗}$(1 $^{+}$, 0.770 MeV)$_{X}$ → $^{8}$B$_{X}$ + γ [6] destroy $^{7}$Be$_{X}$ , the DM mass is thus constrained to be m DM ≤ 4 . 5 GeV. On the other hand, when the $^{7}$Be$_{X}$ → $^{7}$Li+ X 0 reaction [5, 12] is in- cluded, the allowed mass range increases to m DM ≤ 20 − 110GeV. Comparing this result to the allowed parameter region for the DM mass of 40 GeV < m DM < 200 GeV [14], im- plies that only an X − particle which decay via the weak interaction can have existed with sufficient abundance to reduce $^{7}$Li produced from BBN. On the other hand, if the X − particles do not decay via the weak interaction they are excluded. In summary, we have re-investigated BBN in the pres- ence of negatively-charged massive particles X − by solv- ing the rate equations with an improved nuclear reaction network code [7]. We have adopted the newest quantum many-body dynamical calculations [9]. With the new rates, we find that, contrary to the speculation in pre- vious studies, the neutral X -nuclei, i.e., p$_{X}$ , d$_{X}$ and t$_{X}$ , do not significantly affect the BBN abundances. Further- more, based upon constraints for the mass of DM parti- cles from the possible CDMS-II events we conclude that only X − particles which decay into the DM via the weak interaction can simultaneously reduce $^{7}$Li to the desired level while producing enough $^{6}$Li in the early universe. Finally, we note that in this revised catalyzed BBN model there is no signature in the abundances of nuclei heavier than Be. Thus, if one were to find a primor- dial plateau abundance of Be or B, it would require an origin other than this catalyzed BBN model. There are three physical processes by which enhanced abundances of nuclei heavier than Be could have been formed. The first is the cosmological cosmic ray nucleosynthesis in- duced by supernova explosions during an early epoch of structure formation [46]. This model can resolve the $^{6}$Li problem and leave possible abundance plateaus of $^{9}$Be and B [47, 48]. The second is the BBN model including a long-lived strongly interacting massive particle. Signa- tures of such particles are possibly left on the primordial abundances of Be and B which may be found in future astronomical observations of MPSs [49]. The third is the inhomogeneous BBN model which can lead to a high pri- mordial abundance of $^{9}$Be [50]. If the X − particle decays via the weak interaction, $^{7}$Be$_{X}$ converts to $^{7}$Li by a weak charged current tran- sition from X − to X $^{0}$, i.e. $^{7}$Be$_{X}$ → $^{7}$Li+ X 0 [5, 12]. This case is shown in Fig. 6 of Ref. [7]. The results from that study do not change by the implementation of the new cross sections adopted here. The larger destruction rate associated with the $^{7}$Be$_{X}$ → $^{7}$Li+ X 0 decay followed For τ$_{X}$ > ∼ 10 4 s and Y$_{X}$ > ∼ 0 . 3, the calculated abun- dance of $^{7}$Li increases slightly due to the $^{4}$He$_{X}$ ( t , X $^{−}$) $^{7}$Li and $^{4}$He$_{X}$ ( $^{3}$He, X $^{−}$) $^{7}$Be reactions which produce some amount of $^{7}$Li. However, this parameter region is not allowed due to an extreme overproduction of $^{6}$Li. The gray region in Fig. 2 is the parameter region excluded by the overproduction of $^{6}$Li. The thick dashed curves are for d ( $^{7}$Li)=1, 2 and 3. The dashed curve for d ( $^{7}$Li)=2 intersects the contours of d ( $^{6}$Li) for Y$_{X}$ > ∼ 1 and τ$_{X}$ ≈ (1 − 2) × 10 $^{$^{−}$3}$. In the region above this curve the $^{7}$Li abundance is lower than $^{7}$Li/H ≈ 2 . 5 × 10 $^{$^{−}$10}$. The updated parameter region for a simultaneous solution to the $^{6}$Li and $^{7}$Li abundances in BBN with negatively charged particle is: Y$_{X}$ > ∼ 1 and τ$_{X}$ ≈ (1 − 2) × 10 3 s. Figure 2 shows the contours of d ( $^{6}$Li) (solid curves) and d ( $^{7}$Li) (dashed curves) in the parameter plane of the abundance Y$_{X}$ and the lifetime τ$_{X}$ of the X − parti- cles. d ( $^{A}$Li)=$^{A}$Li $^{Calc}$/ $^{A}$Li Obs is the ratio of the calculated abundance to the observed abundance. The solid curves labeled d ( $^{6}$Li)=10 and 0.2 correspond to upper and lower limits on the abundance constraint (1 . 7 × 10 $^{−}$12 ≤ $^{6}$Li/H ≤ 7 . 1 × 10 $^{$^{−}$11}$). Above the d ( $^{6}$Li)=0.2 line, $^{6}$Li is pro- duced at the observed level in MPSs. FIG. 2: (color online). Contours of constant lithium isotopic abundances relative to observed values in MPSs, i.e., d ( $^{6}$Li) = $^{6}$Li$^{Calc}$/$^{6}$LiObs (solid curves) and d ( $^{7}$Li) = $^{7}$Li$^{Calc}$/$^{7}$LiObs (dashed curves). The adopted observational abundances are $^{7}$Li/H= (1 . 23 +0 . 68 $_{−}$0 . $_{32}$) × 10 $_{−}$10 [16] and $^{6}$Li/H= (7 . 1 ± 0 . 7) × 10 $_{−}$12 [18]. Thin solid and dashed lines around the lines of d ( 6 , $^{7}$Li) = 1 correspond to the 1 σ uncertainties in the observa- tional constraint. The gray region is observationally excluded by the overproduction of $^{6}$Li. 4