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.