3b. What is
the CKM matrix?

guided tour

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The weak interaction is the only one in which a quark can change into another type (flavor) of quark or a lepton into another type of lepton. In this transformation, a quark is allowed only to change charge by a unit amount e (the charge of the electron). Because quarks can change flavor by weak interactions, only the lightest quarks and leptons are included in the stable matter of the world around us - all heavier ones decay to one or another of the lighter ones. If we look at all the ways in which one quark can turn into another quark with a charge change of e, that's just all quarks with charge +2/3e (u, c, or t) paired with quarks with charge -1/3e (d, s, or b). That's nine possible pairings. Each of these pairings has its own weak charge associated with it, which is related to a physical constant which we call a "coupling constant" which contains real and imaginary parts - it is complex. The set of coupling constants can be represented by a matrix with 3 rows and 3 columns:

It has a name - the Cabibbo-Kobayashi-Maskawa or CKM matrix. In contrast with electric charge, which seems to come in a well-defined universal unit, each of these nine coupling constants is different. The triumph of the Standard Model is that it predicts a set of relationships between the nine elements of the CKM matrix and it predicts that they include properties that result in CP violation. The CP violation is related to the fact that the matrix elements include imaginary numbers. If we look at enough decays that involve the different matrix elements, we can see whether the relationships are true.