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

A new critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed $0^{+}\to 0^{+}\beta$ decays. Compared with our last review, there are numerous improvements: First, we have added 27 recently published measurements and eliminated 9 references, either because they have been superseded by much more precise modern results or because there are now reasons to consider them fatally flawed; of particular importance, the new data include a number of high-precision Penning-trap measurements of decay energies. Second, we have used the recently improved isospin symmetry-breaking corrections, which were motivated by these new Penning-trap results. Third, our calculation of the statistical rate function $f$ now accounts for possible excitation in the daughter atom, a small effect but one that merits inclusion at the present level of experimental precision. Finally, we have re-examined the systematic uncertainty associated with the isospin symmetry-breaking corrections by evaluating the radial-overlap correction using Hartree-Fock radial wave functions and comparing the results with our earlier calculations, which used Saxon-Woods wave functions; the provision for systematic uncertainty has been changed as a consequence. The new “corrected” $\mathcal{F}t$ values are impressively constant and their average, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, $V_{\mathit{ud}}=0.97425\pm 0.00022$. The unitarity test on the top row of the matrix becomes $\left|V_{\mathit{ud}}\right|{}^2+\left|V_{\mathit{us}}\right|{}^2+\left|V_{\mathit{ub}}\right|{}^2=0.99995\pm 0.00061$. Both $V_{\mathit{ud}}$ and the unitarity sum have significantly reduced uncertainties compared with our previous survey, although the new value of $V_{\mathit{ud}}$ is statistically consistent with the old one. From these data we also set limits on the possible existence of scalar interactions, right-hand currents, and extra $Z$ bosons. Finally, we discuss the priorities for future theoretical and experimental work with the goal of making the CKM unitarity test even more definitive.