Superallowed0+→0+nuclearβdecays: A critical survey with tests of the conserved vector current hypothesis and the standard model

A complete and critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed $0^{+}\to 0^{+}$ decays; no measurements are ignored, although some are rejected for cause and others updated. A new calculation of the statistical rate function f is described and experimental $ft$ values determined. The associated theoretical corrections needed to convert these results into “corrected” $\mathcal{F}t$ values are discussed, and careful attention is paid to the origin and magnitude of their uncertainties. As an exacting confirmation of the conserved vector current hypothesis, the corrected $\mathcal{F}t$ values are seen to be constant to three parts in ${10}^4$. These data are also used to set a new limit on any possible scalar interaction (assuming maximum parity violation) of $C_S/C_V=-(0.00005\pm 0.00130)$. The average $\mathcal{F}t$ value obtained from the survey, when combined with the muon liftime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, $V_{ud}=0.9738\pm 0.0004$, and the unitarity test on the top row of the matrix becomes $\left|V_{ud}\right|{}^2+\left|V_{us}\right|{}^2+\left|V_{ub}\right|{}^2=0.9966\pm 0.0014$ using the Particle Data Group's currently recommended values for $V_{us}$ and $V_{ub}$. If $V_{us}$ comes instead from two recent results on $K_{e3}$ decay, the unitarity sum becomes 0.9996(11). Either result can be expressed in terms of the possible existence of right-hand currents. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test more definitive.