Precision Measurement of the $\beta$ Asymmetry in Spin-Polarized ${}^{37}\mathrm{K}$ Decay

Using Triumf’s neutral atom trap, Trinat, for nuclear $\beta$ decay, we have measured the $\beta$ asymmetry with respect to the initial nuclear spin in ${}^{37}\mathrm{K}$ to be $A_{\beta }=-0.5707{(13)}_{\mathrm{syst}}{(13)}_{\mathrm{stat}}{(5)}_{\mathrm{pol}}$, a 0.3% measurement. This is the best relative accuracy of any $\beta$-asymmetry measurement in a nucleus or the neutron, and is in agreement with the standard model prediction $-0.5706(7)$. We compare constraints on physics beyond the standard model with other $\beta$-decay measurements, and improve the value of $V_{\mathrm{ud}}$ measured in this mirror nucleus by a factor of 4.

Figure 1

The Trinat detection chamber. To polarize the atoms along the $\beta$-detection ($\widehat{z}$) axis, optical pumping light is brought in at a 19° angle with respect to the $\widehat{z}$ axis and reflected off thin mirrors mounted within a $\beta$ collimator on the front face of the reentrant flanges. Thin Be foils behind the mirrors separate the Si strip and scintillator $\beta$ detectors from the $1\times {10}^{-9}\mathrm{Torr}$ vacuum of the chamber. Magnetic field coils provide the Helmholtz (optical pumping, 2 Gauss) and anti-Helmholtz (MOT) fields. Glassy carbon and titanium electrostatic hoops produce a uniform electric field of 150 to $535\mathrm{V}/\mathrm{cm}$ in the $\widehat{x}$ direction to guide shakeoff electrons and ions towards microchannel plate detectors.

Figure 2

Scintillator spectrum in coincidence with its DSSSD and the electron MCP, showing a very clean selection of $\beta$-decay events originating from the trapping region. The Geant4 comparison shows residuals consistent with statistics. The vertical dashed blue line shows the energy threshold used to exclude Compton-scattered annihilation radiation.

Figure 3

Top: The physics superratio of a subset of the data (points) fit to a Geant4 simulation (filled band, with the width indicating its statistical uncertainty) where the only free parameter was the value of $\rho$. Bottom: Difference between the data and Geant4, and the small size of the recoil-$\mathrm{order}+\text{radiative}$ corrections (ROC).

Figure 4

Shakeoff electron TOF spectrum with respect to the ${\beta }^{+}$, showing all data at an electric field of $150\mathrm{V}/\mathrm{cm}$. This spectrum constrains the production of metastable ${\mathrm{Ar}}^{-}$ with $\tau =260(25)\mathrm{ns}$ [37] to be less than 4%, while the TOF cut eliminates any possible contribution. Overlaid is a simulation (dotted line) of the TOF from atoms that escaped the trap before decaying from an electrostatic hoop, where the only free parameter is the normalization fixed to times $\ge 43\mathrm{ns}$. While this simulation reproduces the longer TOF very well, it does not explain all of the background (red hatched area) under the main peak of good events within our TOF cuts (dashed vertical lines).

Figure 5

Constraints on manifest L-R symmetric models from nuclear and neutron [39] $\beta$ decay: CKM unitarity [16]; the ratio of ${\beta }^{+}$ polarization to $A_{\beta }$ of ${}^{12}\mathrm{N}$ and ${}^{107}\mathrm{In}$ [2, 40]; $A_{\beta }$ of mixed $\mathrm{GT}/\mathrm{F}$ ${}^{19}\mathrm{Ne}$ [14, 41, 42, 43]; the ${\beta }^{+}$ polarization of ${}^{10}\mathrm{C}$ compared to ${}^{14}\mathrm{O}$ [44]; and the weighted average of $A_{\beta }$ from three recent pure-GT cases [45, 46, 47].

Figure 6

Measurements of $V_{\mathrm{ud}}$ comparing the values from the neutron [39], ${}^{24}\mathrm{Al}$ [51], and the $T=1/2$ mirror nuclei: ${}^{19}\mathrm{Ne}$ [42], ${}^{21}\mathrm{Na}$ [52], ${}^{35}\mathrm{Ar}$ [43], the previous value for ${}^{37}\mathrm{K}$ [12], and the present work. The averages (uncertainties) in $V_{\mathrm{ud}}$ determined from $0^{+}\to 0^{+}$ [16] and mirror transitions are shown as the solid (dashed) lines.