$A_{\beta}[E_{\beta}]$ in $^{37}$K decay: new physics with opposite $\beta$ helicity
By extending our analysis and simulations of our $^{37}$K $\beta$-decay data set to allow the $\beta$ asymmetry with respect to nuclear spin to vary with $\beta$ energy $E_{\beta}$, we have gained sensitivity to new physics that depends on a helicity factor for the $\beta$, $m_\beta/E_\beta$. In particular, we constrain Lorentz scalar and tensor quark-lepton interaction strengths at a sensitivity complementary to the similar Fierz interference term in neutron $\beta$ decay. Our result for that new physics is a Fierz interference term $b$ = 0.033 $\pm$ 0.084 (stat) $\pm$ 0.039 (syst), consistent with the standard model electroweak interaction value $b=0$. We consider presently achieved complementarity to $\beta$-decay and particle physics experiments, along with projectable technical improvements to our method.