Effect of quark-mass variation on big bang nucleosynthesis

We calculate the effect of variation in the light-current quark mass, $m_q$, on standard big bang nucleosynthesis. A change in $m_q$ at during the era of nucleosynthesis affects nuclear reaction rates, and hence primordial abundances, via changes the binding energies of light nuclei. It is found that a relative variation of $\delta m_q/m_q = 0.016 \pm 0.005$ provides better agreement between observed primordial abundances and those predicted by theory. This is largely due to resolution of the existing discrepancies for 7Li. However this method ignores possible changes in the position of resonances in nuclear reactions. The predicted 7Li abundance has a strong dependence on the cross-section of the resonant reactions 3He(d,p)4He and t(d,n)4He. We show that changes in $m_q$ at the time of BBN could shift the position of these resonances away from the Gamow window and lead to an increased production of 7Li, exacerbating the lithium problem.