On the Statistical Treatment of the Cabibbo Angle Anomaly

Understand

We point out that testing the equality of the Cabibbo angle as extracted from $\Gamma(K\rightarrow \pi l\nu)$, the ratio $\Gamma(K\rightarrow l\nu)/\Gamma(\pi\rightarrow l\nu)$ and nuclear $\beta$ decays is not identical to a test of first row unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.

• The reason is that a CKM unitarity test involves only two parameters, while the degrees of freedom for the assessment of the goodness-of-fit of the universality of the Cabibbo angle entailed by the Standard Model (SM) is equal to the number of measurements minus one.
• Beyond the SM all different processes could in principle give different Cabibbo angles.
• Consequently, the difference between the two tests becomes relevant starting from three observables giving results for the Cabibbo angle that are in tension with each other.