Neutron Lifetime and Axial Coupling Connection

Abstract

Experimental studies of neutron decay, $n\to pe\bar{\nu }$, exhibit two anomalies. The first is a 8.6(2.1)s, roughly $4\sigma$ difference between the average beam measured neutron lifetime, ${\tau }_n^{\text{beam}}=888.0(2.0)$s, and the more precise average trapped ultra cold neutron determination, ${\tau }_n^{\text{trap}}=879.4(6)$s. The second is a $5\sigma$ difference between the pre2002 average axial coupling, $g_A$, as measured in neutron decay asymmetries $g_A^{\text{pre2002}}=1.2637(21)$, and the more recent, post2002, average $g_A^{\text{post2002}}=1.2755(11)$, where, following the UCNA collaboration division, experiments are classified by the date of their most recent result. In this study, we correlate those ${\tau }_n$ and $g_A$ values using a (slightly) updated relation ${\tau }_n(1+3g_A^2)=5172.0(1.1)$s. Consistency with that relation and better precision suggest ${\tau }_n^{\text{favored}}=879.4(6)$s and $g_A^{\text{favored}}=1.2755(11)$ as preferred values for those parameters. Comparisons of $g_A^{\text{favored}}$ with recent lattice QCD and muonic hydrogen capture results are made. A general constraint on exotic neutron decay branching ratios, $<0.27\%$, is discussed and applied to a recently proposed solution to the neutron lifetime puzzle.