Positron - neutrino correlations in $^{32}$Ar and $^{33}$Ar decays: Probes of scalar weak currents and nuclear isospin mixing

The positron-neutrino correlation in the $0^+ \to 0^+ \beta$-decay of $^{32}$Ar was measured at ISOLDE by analyzing the effect of lepton recoil on the shape of the narrow proton group following the superallowed decay. Our result is consistent with the Standard Model prediction; for vanishing Fierz interference we find $a=0.9989 \pm 0.0052 \pm 0.0036$. Our result leads to improved constraints on scalar weak interactions. The positron-neutrino correlation in $^{33}$Ar decay was measured in the same experiment; for vanishing Fierz interference we find $a=0.944 \pm 0.002 \pm 0.003$. The $^{32}$Ar and $^{33}$Ar correlations, in combination with precision measurements of the half-lives, superallowed branching ratios and beta endpoint energies, will determine the isospin impurities of the superallowed transitions. These will provide useful tests of isospin-violation corrections used in deducing $|V_{\rm ud}|$ which currently indicates non-unitarity of the KM matrix.