Superallowed $0^{+}\to 0^{+}$ nuclear $\beta$ decays: 2020 critical survey, with implications for $V_{\mathit{ud}}$ and CKM unitarity

A new critical survey of all half-life, decay-energy, and branching-ratio measurements related to 23 superallowed $0^{+}\to 0^{+}\beta$ decays is presented. Included are 222 individual measurements of comparable precision obtained from 174 published references. Compared with our last survey in 2015, we have added results from 28 new publications and eliminated an approximately equal number whose results have been superseded by much more precise modern data. We obtain world-average $ft$ values for each of the 21 transitions that have a complete set of data and then apply radiative and isospin-symmetry-breaking corrections to extract “corrected” $\mathcal{F}t$ values. Fifteen of these $\mathcal{F}t$ values now have a precision of $0.3\%$ or better and all take the same value within statistics, as expected from conservation of the vector current. Their average, $\overline{\mathcal{F}t}$, when combined with the muon lifetime, yields the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix, $V_{\mathit{ud}}=0.97373\pm 0.00031$. This is lower than our 2015 result by one standard deviation and its uncertainty is increased by $50\%$. This is a consequence not of any shifts in the experimental data but of new calculations for the radiative corrections. The lower $V_{\mathit{ud}}$ value now leads to greater tension in the top-row test of unitarity in the CKM matrix. Updates in experimental data have independently led to a factor-of-two tighter limit being set on the possible existence of a scalar interaction. The new limit on Fierz interference is $b_F\le$ 0.0033 at the $90\%$ confidence level.

Figure 1

Calculated and experimental $f{t}^a/f{t}^b$ values for the seven mirror pairs of superallowed transitions that appear in Table 9. The gray band connect calculated results taken from Table 15. The measured results for $A$ = 26, 34, and 38 appear as open circles with error bars.

Figure 2

The calculated correction terms ${\mathrm{\Delta }}_R^V, {\delta }_R^{\prime }, {\delta }_C$, and ${\delta }_{\mathrm{NS}}$ are plotted for each tabulated transition as a function of the atomic number of the daughter nucleus. The lines connecting points serve only to guide the eye. Several representative uncertainties, statistical plus systematic, are shown for each term.

Figure 3

(a) In the top panel are plotted the uncorrected experimental $ft$ values for the 15 precisely known superallowed transitions as a function of the charge on the daughter nucleus. (b) In the bottom panel, the corresponding $\mathcal{F}t$ values are given; they differ from the $ft$ values by the inclusion of the correction terms ${\delta }_R^{\prime }, {\delta }_{\mathrm{NS}}$, and ${\delta }_C$. The horizontal gray band gives one standard deviation around the average $\overline{\mathcal{F}t}$ value. All transitions are labeled by their parent nuclei.

Figure 4

Summary histogram of the fractional uncertainties attributable to each experimental and theoretical input factor that contributes to the final $\mathcal{F}t$ values for the 15 precisely measured superallowed transitions used in the $\mathcal{F}t$-value average. The two bars cut off with jagged lines at about 0.20% actually rise to 0.23% for ${}^{62}\mathrm{Ga}$ and 0.29% for ${}^{74}\mathrm{Rb}$. The bars for ${\delta }_R^{\prime }$ and ${\delta }_C\text{−}{\delta }_{\mathrm{NS}}$ include provision for systematic uncertainty as well as statistical. See text.

Figure 5

Summary histogram of the fractional uncertainties attributable to each experimental and theoretical input factor that contributes to the final $\mathcal{F}t$ values for the eight tabulated superallowed transitions not known precisely enough to contribute to the $\mathcal{F}t$-value average. The three bars cut off with jagged lines at about 4.0% indicate that no useful experimental measurement has been made of those parameters. The bars for ${\delta }_R^{\prime }$ and ${\delta }_C\text{−}{\delta }_{\mathrm{NS}}$ include provision for systematic uncertainty as well as statistical. See text.

Figure 6

Values of $\overline{\mathcal{F}t}$ and $V_{\mathit{ud}}$ as determined from superallowed $0^{+}\to 0^{+} \beta$ decays plotted as a function of analysis date, spanning the past three decades. Only the statistical uncertainties are shown for the $\overline{\mathcal{F}t}$ values. In order, from the earliest date to the most recent, the values are taken from Refs. [4, 204, 205],[5, 6, 7] and this work.

Figure 7

Corrected $\mathcal{F}t$ values from Table 16 plotted as a function of the charge on the daughter nucleus, $Z$. The curved lines represent the approximate loci the $\mathcal{F}t$ values would follow if a scalar current existed with $b_F=\pm 0.002$.

Figure 8

Uncertainty budget for $|V_{\mathit{ud}}{|}^2$ as obtained from superallowed $0^{+}\to 0^{+} \beta$ decay. The contributions are separated into five categories: experiment, the transition-dependent part of the radiative correction (${\delta }_R^{\prime }$), the nuclear-structure-dependent terms ${\delta }_C$ and ${\delta }_{\mathrm{NS}}$, and the transition-independent part of the radiative correction ${\mathrm{\Delta }}_R^V$. The gray bars give the contributions in 2015 [7] while the black bars represent the present survey. The gray and black dashed lines give the corresponding total uncertainties.