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 $^1H$, $D$, $^3H$+$^3He$, $^4He$,
and $^7Li$+$^7Be$ in the first minutes of cosmic time. The neutron
mean life $\tau_n$ has two roles in modern BBN calculations: (1) it normalizes
the matrix element for weak $n p$ 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 $\tau_n$ measurements and BBN, and
present a study of the sensitivity of the light element abundances to the
modern neutron lifetime measurements. We find that $\tau_n$ uncertainties
dominate the predicted $^4He$ error budget, but these theory errors
remain smaller than the uncertainties in $^4He$ observations, even with
the dispersion in recent neutron lifetime measurements. For the other
light-element predictions, $\tau_n$ 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 $\tau_n(\rm
BBN+CMB) = 870 16 \ sec$, which is consistent with experimental mean
life determinations. We go on to show that if future astronomical and
cosmological helium observations can reach an uncertainty of $\sigma_\rm
obs(Y_p) = 0.001$ in the $^4He$ mass fraction $Y_p$, this could begin to
discriminate between the mean life determinations.
Description
The Neutron Mean Life and Big Bang Nucleosynthesis
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