Primordial lithium abundance in catalyzed big bang nucleosynthesis

There exists a well-known problem with the ${}^7\mathrm{Li}+{}^7\mathrm{Be}$ abundance predicted by standard big bang nucleosynthesis being larger than the value observed in population II stars. The catalysis of big bang nucleosynthesis by metastable, ${\tau }_X\gtrsim {10}^3\sec$, charged particles $X^{-}$ is capable of suppressing the primordial ${}^7\mathrm{Li}+{}^7\mathrm{Be}$ abundance and making it consistent with the observations. We show that to produce the correct abundance, this mechanism of suppression places a requirement on the initial abundance of $X^{-}$ at temperatures of $4\times {10}^8\mathrm{K}$ to be on the order of or larger than 0.02 per baryon, which is within the natural range of abundances in models with metastable electroweak-scale particles. The suppression of ${}^7\mathrm{Li}+{}^7\mathrm{Be}$ is triggered by the formation of (${}^7\mathrm{Be}{X}^{-}$) compound nuclei, with fast depletion of their abundances by catalyzed proton reactions, and in some models by direct capture of $X^{-}$ on ${}^7\mathrm{Be}$. The combination of ${}^7\mathrm{Li}+{}^7\mathrm{Be}$ and ${}^6\mathrm{Li}$ constraints favors the window of lifetimes, $1000\mathrm{s}\lesssim {\tau }_X\le 2000\mathrm{s}$.

Figure 1

Normalized radial wave function for the bound state (${}^7\mathrm{Be}{X}^{-}$) as a function of distance in units of $a_B=1.03\mathrm{fm}$. A. A hydrogenlike profile for a “pointlike” ${}^7\mathrm{Be}$. B. Realistic wave function for the Gaussian charge distribution inside ${}^7\mathrm{Be}$.

Figure 2

Recombination rate $⟨{\sigma }_{\mathrm{rec}}v⟩$ for ${}^7\mathrm{Be}$ and $X^{-}$ in astrophysical units. A: Nonresonant contribution. B: Total recombination rate including $3l$ resonances. C: Total recombination rate, including the $2s$ level, in the assumption of $E_R\sim 10\mathrm{keV}$. Given possible $O(50)\mathrm{keV}$ uncertainty in the position of the $2s$ level, the whole area between curves A and C is representative of the nuclear uncertainty in the recombination rate.

Figure 3

Fraction of ${}^7\mathrm{Be}$ locked in the bound state (${}^7\mathrm{Be}{X}^{-}$) as a function of temperature. Top figure corresponds to a conservative choice of recombination cross section (2.9) and to three different values of $Y_X=n_X/n_B$: 0.1, 0.03 and 0.01. Lower figure corresponds to a recombination cross section enhanced by the $2s$ resonance (2.11) in the assumption that the resonance is just above the threshold, and $Y_X=0.03$, 0.015, 0.005. The long lifetime of $X^{-}$ is assumed.

Figure 4

Effective rate for proton destruction of (${}^7\mathrm{Be}{X}^{-}$), which becomes efficient if the ratio ${\Gamma }_p^{\mathrm{eff}}/H$ is on the order or larger than unity. Even though the rate for $({}^7\mathrm{Be}{X}^{-})+p\to ({}^8\mathrm{B}{X}^{-})+\gamma$ is much faster than the Hubble rate, the reverse rate makes this destruction mechanism inefficient for $T>30\mathrm{keV}$.

Figure 5

Internal conversion of beryllium into lithium in type II models due to $W$-exchange. ${}^7\mathrm{Li}$, being intrinsically more fragile than ${}^7\mathrm{Be}$, is subsequently destroyed.

Figure 6

The abundance of lithium and beryllium in two types of the CBBN models for the sample values of the CBBN input parameters, $Y_X=0.05$ and ${\tau }_X=2000\sec$, and the choice of recombination cross section (2.9). The total lithium abundance is $3.7\times {10}^{-10}$ for type I and $2.3\times {10}^{-10}$ for type II model. The individual abundances of ${}^7\mathrm{Be}$, ${}^7\mathrm{Li}$, (${}^7\mathrm{Be}{X}^{-}$) and the SBBN curve for ${}^7\mathrm{Li}+{}^7\mathrm{Be}$ are also shown. All abundances are given relative to hydrogen.

Figure 7

The abundance of lithium and beryllium in two types of the CBBN models for the sample values of the CBBN input parameters, $Y_X=0.05$ and ${\tau }_X=2000\sec$, and the choice of recombination cross section (2.11). The total lithium abundance is $3.3\times {10}^{-10}$ for type I and $1.5\times {10}^{-10}$ for type II model. The individual abundances of ${}^7\mathrm{Be}$, ${}^7\mathrm{Li}$, (${}^7\mathrm{Be}{X}^{-}$) and the SBBN curve for ${}^7\mathrm{Li}+{}^7\mathrm{Be}$ are also shown. All abundances are given relative to hydrogen.

Figure 8

$\{Y_X,{\tau }_X\}$ parameter space with CBBN lithium abundance. The top panel corresponds to type I models, the lower panel corresponds to type II. Curves A and B are calculated with the use of (2.9, 2.11) correspondingly. The ${}^7\mathrm{Be}+{}^7\mathrm{Li}$ overabundance problem is solved above curves A and B, with $({}^7\mathrm{Li}^{\mathrm{tot}}{)}_{\mathrm{CBBN}}<2.5\times {10}^{-10}$. The domain to the right from the almost vertical line is excluded from the ${}^6\mathrm{Li}$ overproduction at $T_9=0.09$.

Figure 9

If the splitting between $X^{-}$ and $X^0$ is between 0.511 and 0.822 MeV, both the decay of $X^{-}$ to $X^0$ and the $X^0$ capture by ${}^7\mathrm{Be}$ become possible. At the same time the (${}^4\mathrm{He}{X}^{-}$) bound state cannot be formed from $X^0$ and ${}^4\mathrm{He}$ and the ${}^6\mathrm{Li}$ overproduction is automatically avoided if the lifetime of $X^0$ is arbitrarily short.