Superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear $\ensuremath{\beta}$ decays: 2014 critical survey, with precise results for ${V}_{ud}$ and CKM unitarity

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Superallowed $0^{+} \to 0^{+}$ nuclear $β$ decays: 2014 critical survey, with precise results for $V_{u d}$ and CKM unitarity

J. C. Hardy and I. S. Towner

Phys. Rev. C 91, 025501 – Published 12 February 2015

An article within the collection: Physical Review C 50^th Anniversary Milestones

Abstract

A new critical survey is presented of all half-life, decay-energy, and branching-ratio measurements related to 20 superallowed $0^{+} \to 0^{+} β$ decays. Included are 222 individual measurements of comparable precision obtained from 177 published references. Compared with our last review in 2008, we have added results from 24 new publications and eliminated 9 references, the results from which having been superseded by much more precise modern data. We obtain world-average $f t$ values for each of the 18 transitions that have a complete set of data, then apply radiative and isospin-symmetry-breaking corrections to extract “corrected” $F t$ values. Fourteen of these $F t$ values now have a precision of order 0.1% or better. In the process of obtaining these results we carefully evaluate the available calculations of the isospin-symmetry-breaking corrections by testing the extent to which they lead to $F t$ values consistent with conservation of the vector current. Only one set of calculations satisfactorily meets this condition. The resultant average $F t$ value, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix, $V_{u d} = 0.974 17 \pm 0.000 21 .$ The unitarity test on the top row of the matrix becomes $| V_{u d} |^{2} + | V_{u s} |^{2} + {| V_{u b} |}^{2} = 0.999 78 \pm 0.000 55$ if the Particle Data Group (PDG) recommended value for $V_{u s}$ is used. However, recent lattice QCD calculations, not included yet in the PDG evaluation, have introduced some inconsistency into kaon-decay measurements of $V_{u s}$ and $V_{u s} / V_{u d} .$ We examine the impact of these new results on the unitarity test and conclude that there is no evidence of any statistically significant violation of unitarity. Finally, from the $F t$ -value data we also set limits on the possible existence of scalar interactions.