Candidates for the leptonic X − particle of interest in these models are the spin 0 supersymmetric partners of the standard-model leptons. Such X − particles (and their antiparticles X $^{+}$) would be produced copiously in the hot early universe and subsequently annihilate. Their annihilations, however, would freezeout at some epoch. The residual X + particles do not affect BBN because they do not bind to the positively-charged nuclei. It is possible, however, that the decay of both X ± particles affect the final light element abundances through elec- tromagnetic and/or hadronic showers. Here, however, we only consider the X -nuclear reactions, and not the effect of subsequent decay. 3 FIG. 1: (color online). Calculated abundances of normal nu- clei (a) and X -nuclei (b) as a function of T 9 (solid lines). The abundance and the lifetime of the X − particle are set to be Y X = n X /n b = 0 . 05 and τ X = ∞ , respectively. The dashed lines correspond to the standard BBN case. The binding energies of nuclei bound to X − particles, i.e., X -nuclei, have been derived by taking account of the modified Coulomb interaction with the nucleus [7] under the assumption that the mass of the X − particle is much heavier than the nucleon mass. We performed the detailed network calculation of the catalyzed BBN [7] taking into account both the recom- bination and ionization of X − particles with nuclei and thermonuclear reactions and β -decay of normal nuclides and X -nuclei. We adopt all of the new reaction rates from the rigorous quantum many-body dynamical cal- culations of Ref. [9]. For the $^{7}$Be$_{X}$ ( p , γ ) $^{8}$B$_{X}$ resonant reaction through an atomic excited state of $^{8}$B$_{X}$ , rates for different masses of X − have been published [9]. For our purposes we adopt their rate for an infinite X − mass. Our results are thus completely different from previous studies without the use of the new cross sections. We adopt the constraint on the primordial $^{6}$Li abun- dance from the observations in MPSs. The primordial abundances of $^{6}$Li and $^{7}$Li could be higher than the ob- served abundances [18] considering the possible effect of stellar depletion of initial surface abundances. The observed abundances should, therefore, be considered a lower limit to the true primordial ones. Since $^{6}$Li is more fragile to nuclear burning than $^{7}$Li [24], its depletion factors could be larger than those for $^{7}$Li. We adopt a conservative limit of a factor of 10 above the mean value of ( $^{6}$Li/H) MPS = (7 . 1 ± 0 . 7) × 10 $^{−}$12 [18], and a 3 σ lower limit to the mean value times a factor of 1 / 3. The limit on the $^{6}$Li/H abundance are thus 1 . 7 × 10 $^{−}$12 ≤ $^{6}$Li/H ≤ 7 . 1 × 10 $^{$^{−}$11}$. Figures 1a and 1b show the results of a catalyzed BBN calculation. For these figures the X − abundance was taken to be 5% of the total baryon abundance, i.e. Y$_{X}$ = n$_{X}$/n$_{b}$ = 0 . 05, where n$_{X}$ and n$_{b}$ are the number densities of the X − particles and baryons, respectively. Figure 1a shows the evolution of normal nuclei while Fig- ure 1b corresponds to X -nuclei. The abundances of the normal nuclei are very simi- lar to the standard BBN abundances until the tempera- ture reaches T 9 ∼ 0 . 5. The X − particles then combine with $^{7}$Be at T 9 ∼ 0 . 5 and subsequently $^{7}$Li at T 9 ∼ 0 . 3. The $^{7}$Be$_{X}$ produced by these X − captures (Fig. 1b) is then destroyed by the $^{7}$Be$_{X}$ ( p , γ ) $^{8}$B$_{X}$ reaction, primarily through the atomic excited state of $^{8}$B$_{X}$ [5], and sec- When the temperature decreases to T 9 ∼ 0 . 1, the X − particles bind to $^{4}$He. Then, the X $^{−}$-catalyzed trans- fer reaction $^{4}$He$_{X}$ ( d , X $^{−}$) operates to produce normal $^{6}$Li and $^{6}$Li$_{X}$ (after the recombination). Because of the small binding energies to the X − (see Table I of Ref. [7]), neu- tral X -nuclei do not form until late times corresponding to T 9 ∼ 0 . 03 (for t$_{X}$ ), T 9 ∼ 0 . 02 (for d$_{X}$ ) and T 9 ∼ 0 . 01 (for p$_{X}$ ). The neutral X -nuclei then mainly react with $^{4}$He nuclei to lose their X − and to produce $^{4}$He$_{X}$ (as a result of the precise calculation [9]) so that abundances of neutral X -nuclei are kept low. Nuclear reactions trig- gered by neutral X -nuclei are thus not important. ondarily through the atomic ground state $^{8}$B $^{∗}$(1 $^{+}$, 0.770 MeV)$_{X}$ composed of the $^{8}$B $^{∗}$(1 $^{+}$, 0.770 MeV) nuclear ex- cited state and an X − particle [6]. We have assumed that $^{8}$B$_{X}$ inter-converts to $^{8}$Be $^{∗}$(2 $^{+}$,3 MeV)$_{X}$ by β -decay with a rate given by the normal $^{8}$B β -decay rate multiplied by a correction term ( Q$_{X}$/Q ) $^{5}$, where Q and Q$_{X}$ are the Q - values of the standard β -decay and that of β -decay for X - nuclei [7]. The produced $^{8}$Be $^{∗}$(2 $^{+}$,3 MeV)$_{X}$ then imme- diately decays to the three-body channel α + α + X − [9].