The Kobayashi–Maskawa matrix, which delineates what combinations of quark fields are operative in the charge changing weak interaction, was introduced in Chapter 9. Its elements Vij have occurred repeatedly in the preceding chapters and are crucial in providing quantitative results from the theory. We here address the issue of measuring these matrix elements and of summarizing the present knowledge of them.

In the SM the weak currents are all expressed as KM matrix elements multiplying currents built up from the quark fields which, for brevity, we denote by u, d, …, ū, d̄, … In some cases the latter currents can be identified as the conserved Noether currents corresponding to symmetries of the strong interactions, for example, isotopic spin invariance. In that case, as explained in Appendix 3, the matrix elements (at least the forward ones) of the conserved currents are known exactly. Thus the weak transition amplitude appears as a Vij multiplied by a known matrix element, thereby allowing the measurement of that particular Vij. To the extent that the symmetry is not perfect and that one is seeking very precise knowledge of the Vij, one must attempt to correct for the symmetry breaking. This is a highly technical procedure for which the reader should consult Leutwyler and Roos (1984) and Donoghue, Holstein and Klimt (1987), and the major review article by Paschos and Türke (1988). We shall only deal with the case of perfect symmetry and will illustrate the approach in β-decay type reactions.