Solar neutrino constraints on the BBN production of Li

Abstract

Using the recent WMAP determination of the baryon-to-photon ratio, ${10}^{10}\ensuremath{\eta}=6.14$ to within a few percent, big bang nucleosynthesis (BBN) calculations can make relatively accurate predictions of the abundances of the light element isotopes which can be tested against observational abundance determinations. At this value of $\ensuremath{\eta},$ the ${}^{7}\mathrm{Li}$ abundance is predicted to be significantly higher than that observed in low metallicity halo dwarf stars. Among the possible resolutions to this discrepancy are (1) ${}^{7}\mathrm{Li}$ depletion in the atmosphere of stars, (2) systematic errors originating from the choice of stellar parameters\char22{}most notably the surface temperature, and (3) systematic errors in the nuclear cross sections used in the nucleosynthesis calculations. Here, we explore the last possibility, and focus on possible systematic errors in the ${}^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{7}\mathrm{Be}$ reaction, which is the only important ${}^{7}\mathrm{Li}$ production channel in BBN. The absolute value of the cross section for this key reaction is known relatively poorly both experimentally and theoretically. The agreement between the standard solar model and solar neutrino data thus provides additional constraints on variations in the cross section ${(S}_{34}).$ Using the standard solar model of Bahcall, and recent solar neutrino data, we can exclude systematic ${S}_{34}$ variations of the magnitude needed to resolve the BBN ${}^{7}\mathrm{Li}$ problem at the $\ensuremath{\gtrsim}95%$ C.L., or more strongly, depending on the Li observations used. Additional laboratory data on ${}^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma}{)}^{7}\mathrm{Be}$ will sharpen our understanding of both BBN and solar neutrinos, particularly if care is taken in determining the absolute cross section and its uncertainties. Nevertheless, it is already clear that this ``nuclear fix'' to the ${}^{7}\mathrm{Li}$ BBN problem is unlikely; other possible solutions are briefly discussed.