Effects of Long-lived 10 MeV Scale Sterile Neutrino on Primordial Elemental Abundances and Effective Neutrino Number

The primordial lithium abundance inferred from observations of metal-poor stars is ~3 times smaller than the theoretical value in standard big bang nucleosynthesis (BBN) model. We assume a simple model including a sterile neutrino nu_H with mass of O(10) MeV which decays long after BBN. We then investigate cosmological effects of a sterile neutrino decay. We formulate the injection spectrum of nonthermal photons induced by electrons and positrons generated at the nu_H decay, as a function of the nu_H mass and the photon temperature. We then consistently solve (1) the cosmic thermal history, (2) nonthermal nucleosynthesis induced by the nonthermal photons, (3) the baryon-to-photon ratio eta, and (4) the effective neutrino number N_eff. Amounts of energy injection at the nu_H decay are constrained from limits on primordial D and 7Li abundances, the N_eff value, and the cosmic microwave background energy spectrum. We find that 7Be 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 over-destruction. In the parameter region, the eta value is decreased slightly, while the N_eff value is increased by a factor of <~ 1. In this study, errors in photodisintegration cross sections of 7Be(g, a)3He and 7Li(g, a)3H that have propagated through literatures are corrected. It is then found that the new photodisintegration rates are 2.3 to 2.5 times smaller than the old rates, so that efficiencies of 7Be and 7Li photodisintegration are significantly smaller.