Half-life and Branching ratio measurements of T $=$ 1/2 Mirror Nuclei

The $\beta$-decay transitions between T$=$1/2 isospin doublets in mirror nuclei requires the measurement of decay rate and angular correlation to measure the comparative half-life. The motivation for improving the precision of the \textit{ft} value is to determine the standard-model prediction for the correlation parameters with better precision. We have measured the half-life of $^{21}$Na and $^{37}$K, and the ground-state branching ratio of $^{37}$K to improve the precision of the \textit{ft} value. For $^{37}$K, the \textit{ft} value was limited by 0.6{\%} uncertainty in the half-life and 0.14{\%} uncertainty in the ground-state branching ratio. The precision of the present half-life measurement is nearly an order of magnitude improvement over the previously accepted world average. In case of $^{21}$Na, the \textit{ft} value was limited by 0.13{\%} uncertainty in the half-life. Another motivation for the half-life measurement comes from the fact that the half-life has only been measured thrice nearly 40 years ago. The measurements were carried out at the Cyclotron Institute, Texas A{\&}M University. An overview of both experiments and results will be presented.