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 similar to 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 v(H) 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 v(H) decay. We take into account the generation of electrons and positrons, e(+/-)'s, and active neutrinos at the v(H) 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 v(H) mass and the photon temperature. The v(H) decay produces energetic active neutrinos which are not thermalized, and e(+/-)'s which are thermalized. We then derive formulas relevant to the v(H) decay rates and formulas for the baryon-to-photon ratio. and effective neutrino number N-eff. The initial abundance, mass, and lifetime of v(H) are taken as free parameters. We then consistently solve (1) the cosmic thermal history, (2) nonthermal nucleosynthesis induced by the nonthermal photons, (3) the. value, and (4) the N-eff value. We find that an effective Be-7 destruction can occur only if the sterile neutrino decays at photon temperature T = O(1) keV. Amounts of energy injection at the v(H) decay are constrained from limits on primordial D and Li-7 abundances, the N-eff value, and the CBR energy spectrum. We find that Be-7 is photodisintegrated and the Li problem is partially solved for the lifetime 10(4)-10(5) 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 eta value is decreased slightly, while the Neff value is increased by a factor of Delta N-eff less than or similar to 1. In this study, errors in photodisintegration cross sections of Be-7(gamma, alpha)He-3 and Li-7(gamma, alpha)H-3 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 Be-7 and Li-7 photodisintegration. Abundances of sterile neutrino necessary for the Li-7 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.