New Limits on Fundamental Weak-Interaction Parameters from Superallowed $\beta$ Decay

A new survey of all world data on superallowed $\beta$ decays provides demanding tests of, and tight constraints on, the weak interaction. In confirmation of the conserved vector current hypothesis, the vector coupling constant $G_V$ is demonstrated to be constant to better than three parts in ${10}^4$, and any induced scalar current is limited to $f_S\le 0.0013$ in electron rest-mass units. Any possible fundamental scalar current is similarly limited to $|C_S/C_V|\le 0.0013$. The superallowed data also determine the up-down element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix to be $V_{ud}=0.9738(4)$. With Particle Data Group values for $V_{us}$ and $V_{ub}$, the top-row test of CKM unitarity yields $|V_{ud}{|}^2+|V_{us}{|}^2+|V_{ub}{|}^2=0.9966(14)$; if $V_{us}$ comes instead from two recent results on $K_{e3}$ decay, this sum becomes 0.9996(11). Either unitarity result can be used to constrain the possible existence of right-hand currents.

Figure 1

In the top panel are plotted the experimental $ft$ values corrected only for ${\delta }_R^{\prime }$, those radiative effects that are independent of nuclear structure. In the bottom panel, the corresponding $\mathcal{F}t$ values are given; they differ from the top panel simply by the inclusion of the nuclear-structure-dependent corrections, ${\delta }_{NS}$ and ${\delta }_C$. [See Eq. (1).] Note that the increased uncertainty for ${}^{74}\mathrm{R}\mathrm{b}$ reflects the lack of experimental constraints on the nuclear shell model in this mass region. The horizontal gray band in the bottom panel indicates the average $\overline{\mathcal{F}t}$ value with its uncertainty. The curved lines represent the approximate loci the $\mathcal{F}t$ values would follow if an induced scalar current existed with values of $f_S=\pm 0.002$ in electron rest-mass units or a fundamental scalar current with $C_S/C_V=\pm 0.002$.