Measurement of the Beta-Neutrino Correlation of $^{21}$Na Using Shakeoff Electrons

We have measured the \mbox{$\beta - \nu$} correlation coefficient, $a_{\beta\nu}$, in $^{21}$Na using a laser-trapped sample. We measure the energy spectrum of the recoil nuclei by measuring their time-of-flight in coincidence with the atomic electrons shaken off in beta decay. High detection efficiency of these low-energy electrons allows good counting statistics, even with low trap density. Low trap density suppresses photoassociation to molecular sodium, which can cause a large systematic error in the beta decay correlation. Our measurement, $a_{\beta\nu} = 0.5502(60)$ with a 1\% fractional uncertainty, agrees with the Standard Model prediction $a_{\beta\nu} = 0.553(2)$, but disagrees with our previous measurement which was susceptible to error introduced by molecular sodium. We summarize precise measurements of $a_{\beta\nu}$ and their consequences for searches for Beyond Standard Model scalar and tensor current couplings. We will make a few remarks about the future of precision measurements of beta decay using optical traps.