The X^- Solution to the ^6Li and ^7Li Big Bang Nucleosynthesis Problems

The $^6$Li abundance observed in metal poor halo stars appears to exhibit a plateau as a function of metallicity similar to that for $^7$Li, suggesting a big bang origin. However, the inferred primordial abundance of $^6$Li is $\sim$1000 times larger than that predicted by standard big bang nucleosynthesis for the baryon-to-photon ratio inferred from the WMAP data. Also, the inferred $^7$Li primordial abundance is 3 times smaller than the big bang prediction. We here describe in detail a possible simultaneous solution to both the problems of underproduction of $^6$Li and overproduction of $^7$Li in big bang nucleosynthesis. This solution involves a hypothetical massive, negatively-charged leptonic particle that would bind to the light nuclei produced in big bang nucleosynthesis, but would decay long before it could be detected. We consider only the $X$-nuclear reactions and assume that the effect of decay products is negligible, as would be the case if lifetime were large or the mass difference between the charged particle and its daughter were small. An interesting feature of this paradigm is that, because the particle remains bound to the existing nuclei after the cessation of the usual big bang nuclear reactions, a second longer epoch of nucleosynthesis can occur among $X$-nuclei. We confirm that reactions in which the hypothetical particle is transferred can occur that greatly enhance the production of $^6$Li while depleting $^7$Li. We also identify a new reaction that destroys large amounts of $^7$Be, and hence reduces the ultimate $^7$Li abundance. Thus, big-bang nucleosynthesis in the presence of these hypothetical particles, together with or without an event of stellar processing, can simultaneously solve the two Li abundance problems.