Effects of long-lived 10 MeV-scale sterile neutrinos on primordial elemental abundances and the effective neutrino number

The primordial lithium abundance inferred from spectroscopic observations of metal-poor stars is ~3 times smaller than the theoretical prediction in the standard big bang nucleosynthesis (BBN) model. We assume a simple model composed of standard model particles and a sterile neutrino νH with mass of O(10) MeV which decays long after BBN. We then investigate cosmological effects of a sterile neutrino decay, and check if a sterile neutrino can reduce the primordial lithium abundance. We formulate the injection spectrum of nonthermal photon induced by the νH decay. We take into account the generation of electrons and positrons, e^±'s, and active neutrinos at the νH decay, the primary photon production via the inverse Compton scattering of cosmic background radiation (CBR) by energetic e^±, and electromagnetic cascade showers induced by the primary photons. The steady state injection spectrum is then derived as a function of the νH mass and the photon temperature. The νH decay produces energetic active neutrinos which are not thermalized, and e^±'s which are thermalized. We then derive formulas relevant to the νH decay rates and formulas for the baryon-to-photon ratio η and effective neutrino number Neff. The initial abundance, mass, and lifetime of νH are taken as free parameters. We then consistently solve (1) the cosmic thermal history, (2) nonthermal nucleosynthesis induced by the nonthermal photons, (3) the η value, and (4) the Neff value. We find that an effective ⁷Be destruction can occur only if the sterile neutrino decays at photon temperature T=O(1) keV. Amounts of energy injection at the νH decay are constrained from limits on primordial D and ⁷Li abundances, the Neff value, and the CBR energy spectrum. We find that ⁷Be is photodisintegrated and the Li problem is partially solved for the lifetime 10⁴--10⁵ s and the mass 14 MeV. ⁷Be destruction by more than a factor of 3 is not possible because of an associated D overdestruction. In the parameter region, the η value is decreased slightly, while the Neff value is increased by a factor of ΔNeff1. In this study, errors in photodisintegration cross sections of ⁷Be(γ,α)³He and ⁷Li(γ,α)³H that have propagated through the literature are corrected, and new functions are derived based on recent nuclear experiments. It is found that the new photodisintegration rates are 2.3 to 2.5 times smaller than the old rates. The correct cross sections thus indicate significantly smaller efficiencies of ⁷Be and ⁷Li photodisintegration. Abundances of sterile neutrino necessary for the ⁷Li reduction are much smaller than thermal freeze-out abundances. The relic sterile neutrino, therefore, must be diluted between the freeze-out and BBN epochs by some mechanism.