The Neutron Mean Life and Big Bang Nucleosynthesis

Abstract

We explore the effect of neutron lifetime and its uncertainty on standard big bang nucleosynthesis (BBN). BBN describes the cosmic production of the light nuclides, (Formula presented.), D, (Formula presented.) + (Formula presented.), (Formula presented.), and (Formula presented.) + (Formula presented.), in the first minutes of cosmic time. The neutron mean life (Formula presented.) has two roles in modern BBN calculations: (1) it normalizes the matrix element for weak (Formula presented.) interconversions, and (2) it sets the rate of free neutron decay after the weak interactions freeze-out. We review the history of the interplay between (Formula presented.) measurements and BBN, and present a study of the sensitivity of the light element abundances to the modern neutron lifetime measurements. We find that (Formula presented.) uncertainties dominate the predicted (Formula presented.) error budget, but these theory errors remain smaller than the uncertainties in (Formula presented.) observations, even with the dispersion in recent neutron lifetime measurements. For the other light element predictions, (Formula presented.) contributes negligibly to their error budget. Turning the problem around, we combine present BBN and cosmic microwave background (CMB) determinations of the cosmic baryon density to predict a “cosmologically preferred” mean life of (Formula presented.), which is consistent with experimental mean life determinations. We show that if future astronomical and cosmological helium observations can reach an uncertainty of (Formula presented.) in the (Formula presented.) mass fraction (Formula presented.), this could begin to discriminate between the mean life determinations.