The evaluation of Vud and its impact on the unitarity of the Cabibbo–Kobayashi–Maskawa quark-mixing matrix

Abstract

The determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element Vud is reviewed. Data from 0+ → 0+ superallowed beta decay in nuclei, neutron decay, beta decay of odd-mass mirror nuclei and pion beta decay are considered. Theoretical radiative and isospin-symmetry breaking corrections are applied. The most precise result comes from the nuclear 0+ → 0+ decays, which yield a recommended value of |Vud| = 0.974 25(22). We further summarize the data leading to the CKM matrix element Vus: Kℓ3 decays, Kℓ2 decays, hyperon decays and hadronic tau decay. Again SU(3)-symmetry breaking corrections (from lattice QCD) and radiative corrections are applied. We adopt values from Kℓ3 decay of |Vus| = 0.2246(12) and from Kℓ2 decay of |Vus/Vud| = 0.2319(14). From the three data just cited, a least squares fit determines two CKM matrix elements: |Vud| = 0.974 25(22) and |Vus| = 0.225 21(94). Data leading to the third member of the top row of the CKM matrix, Vub, are summarized as well but, being of order 10−3, that matrix element contributes negligibly to the unitarity sum, |Vud|2 + |Vus|2 + |Vub|2. We find this sum to be 0.999 90(60) showing unitarity to be satisfied to a precision of 0.06%. We discuss the constraints this result places on selected extensions to the standard model.