Branching ratio for the superallowed beta-decay of $^{10}$C

Superallowed $\beta$ decays play a key role in testing the Standard Model of Particle Physics. These decays occur between nuclear analog states having spin-parity of $0^+$ and isospin $T=1$. Currently, and in the foreseeable future, they offer the most accurate value for the $V_{ud}$ matrix element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Each superallowed transition is characterized with an ${\mathcal F}t$ value combining both experimental and theoretical quantities. We have just made a preliminary new measurement of the $^{10}$C branching ratio, which currently is the least precisely known quantity for any of the ``traditional nine'' superallowed transitions. Furthermore, $^{10}$C is the only case that appears to have its corrected ${\mathcal F}t$ value outside the world average value, which could be explained with the existence of a scalar current. We performed the branching-ratio measurement with a $\beta$-$\gamma$ coincidence setup using a scintillator for $\beta$ and an HPGe with $\pm$0.15\% calibrated relative efficiency for $\gamma$ detection. Since the branching ratio is obtained from the ratio of intensities of 718 keV and 1022 keV $\gamma$ lines, most systematic uncertainties cancel out. I will show an overview of the experiment and preliminary results.