High-precision half-life measurements for the superallowed $\beta^+$ emitter $^{10}$C

High precision measurements of the $ft$ values for superallowed Fermi beta transitions between 0$^+$ isobaric analogue states allow for stringent tests of the electroweak interaction described by the Standard Model. These transitions provide an experimental probe of the unitary of the Cabibbo-Kobayashi-Maskawa matrix, the Conserved-Vector-Current hypothesis, as well as set limits on the existence of scalar currents in the weak interaction. Half-life measurements for the lightest of the superallowed emitters are of particular interest as the low-Z superallowed decays are most sensitive to a possible scalar current contribution. The half-life of $^{10}$C can be measured by directly counting the $\beta$ particles or by measuring the $\gamma$-ray activity following $\beta$ decay. Previous results for the $^{10}$C half-life measured via these two methods differ at the 1.3$\sigma$ level, motivating further measurements of the $^{10}$C half-life using both techniques. Recent $^{10}$C half-life measurements via both gamma-ray photo-peak and direct beta counting were performed at TRIUMF's Isotope Separator and Accelerator facility. This presentation will highlight the importance of these measurements and half-life results will be presented.