Improving the ft value of 37K via a precision measurement of the branching ratio

The TRIUMF Neutral Atom Trap collaboration is searching for new physics via precision measurements of the isobaric analogue $\beta^+$ decay of $^{37}$K. The recent 0.3$\%$ measurement of the $\beta$ asymmetry parameter, $A_\beta$, was combined with the present $ft$ value to improve the value of $V_{ud}$ for this decay as well as to search for right-handed currents. Presently, uncertainties in $A_\beta$ remain the limiting factor in these standard model tests, however, the next $A_\beta$ measurement will reach $\leq0.1\%$ precision; at that point, uncertainties in the $ft$ value will no longer be negligible. This motivated us to improve the $ft$ value to ensure its precision does not limit our search for new physics. The current uncertainty in the $ft$ value is dominated by the branching ratio. This talk will describe how, using the fast-tape-transport system at the Cyclotron Institute and the world's most precisely calibrated HPGe, we measured the branching ratio to be 97.81(2)$\%$. This $5\times$ more precise result leads to, $ft=4585(4)$s, which is precise enough that $A_\beta$ would have to be measured to 0.07$\%$ before the $ft$ value limited searches for new physics.