Primordial Lithium Abundance in Catalyzed Big Bang Nucleosynthesis

TL;DR

The paper addresses the primordial lithium problem by exploring catalyzed BBN (CBBN) with metastable charged particles $X^-$ that bind to $^7$Be, forming $(^7BeX^-)$ bound states and opening new destruction channels. It develops a detailed, largely model-independent framework to compute bound-state formation, recombination rates (including near-threshold resonances and potential $2s$-state contributions), and the subsequent catalytic channels (proton- and neutron-induced destruction, internal conversion, and energy injection from $X^-$ annihilation). The authors show that, for $Y_X$ of order a few percent and lifetimes around $10^3$ s, substantial suppression of $^7$Li+$^7$Be is possible, particularly in Type II models with fast internal conversion, but the viable parameter space is constrained by the $^6$Li bound and nuclear-structure uncertainties in the recombination rate. Overall, CBBN offers a physically motivated mechanism to alleviate the lithium discrepancy, but its viability hinges on precise nuclear calculations of bound-state properties and the balance between hadronic energy release and non-thermal effects.

Abstract

There exists a well known problem with the Li7+Be7 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, τ_X \ge 10^3 sec, charged particles X^- is capable of suppressing the primordial Li7+Be7, 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 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 Li7+Be7, is triggered by the formation of (Be7X^-), compound nuclei, with fast depletion of their abundances by catalyzed proton reactions, and in some models by direct capture of X^- on Be7. The combination of Li7+Be7 and Li6 constraints favours the window of lifetimes, 1000s \la tau_X \leq 2000 s.

Figures (9)

• Figure 1: Normalized radial wavefunction for the bound state ($^7$Be$X^-$) as a function of distance in units of $a_B = 1.03$ fm. A. A hydrogen-like profile for a "point-like" $^7$Be. B. Realistic wavefunction for the Gaussian charge distribution inside $^7$Be.
• Figure 2: Recombination rate $\langle \sigma_{rec}v\rangle$ for $^7$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 $E_R \sim 10$ keV. Given possible $O(50)$ 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 $^7$Be locked in the bound state ($^7$Be$X^-$) as a function of temperature. Top figure corresponds to a conservative choice of recombination cross section (\ref{['sigma_tot']}) and to three different values of $Y_X=n_X/n_B$: 0.1, 0.03 and 0.01. Lower figure corresponds to recombination cross section enhanced by the $2s$ resonance (\ref{['addon']}) and $Y_X=0.03,~0.015,~0.005$. The long lifetime of $X^-$ is assumed.
• Figure 4: Effective rate for proton destruction of ($^7$Be$X^-$), that becomes efficient if the ratio $\Gamma_{p}^{\rm eff}/H$ is on the order or larger than unity. Even though the rate for $({\rm ^7Be} X^-) + p \to (^8{\rm B}X^-) + \gamma$ is much faster than Hubble rate, the reverse rate makes this destruction mechanism inefficient for $T>30$keV.
• Figure 5: Internal conversion of beryllium into lithium in type II models due to $W$-exchange. $^7$Li, being intrinsically more fragile than $^7$Be , is subsequently destroyed.