Determinations of $|V_{ud}|$ and $|V_{us}|$ along with their implications for the unitarity test $|V_{ud}{|}^2+|V_{us}{|}^2+|V_{ub}{|}^2=1$ are discussed. The leading two-loop radiative corrections to neutron $\beta$ decay are evaluated and used to derive a refined relationship $|V_{ud}{|}^2{\tau }_n(1+3g_A^2)=4908(4)\mathrm{s}$. Employing $|V_{ud}|=0.9740(5)$ from superallowed nuclear decays and the measured neutron lifetime ${\tau }_n=885.7(7)\mathrm{s}$ leads to the precise prediction $g_A=1.2703(8)$ which is compared with current direct experimental values. Various extractions of $|V_{us}|$ are described and updated. The long accepted Particle Data Group value of $|V_{us}|$ from fitted $K_{e3}$ decay rates suggests a deviation from CKM unitarity but it is contradicted by more recent experimental results which confirm unitarity with good precision. An outlook for possible future advances is given.

• Received 29 June 2004

DOI:https://doi.org/10.1103/PhysRevD.70.093006