U_{uL}^{†} M_{u} U_{u R} = diag (m_{u}, m_{c}, m_{t}), U_{d L}^{†} M_{d} U_{d R} = diag (m_{d}, m_{s}, m_{b}) .

The neutral currents remain flavour diagonal because the same unitary matrix occurs on both sides of each bilinear. The charged current contains the mismatch

V_{CKM} = U_{uL}^{†} U_{d L},

and becomes

L_{W} = \frac{g}{2} [W_{μ}^{+} \overline{u}_{i L} γ^{μ} (V_{CKM})_{ij} d_{j L} + W_{μ}^{-} \overline{d}_{i L} γ^{μ} (V_{CKM}^{†})_{ij} u_{j L}] .

A general unitary

3

3

matrix has nine real parameters. Independent rephasings of the six quark fields remove five phases because one common baryon-number phase changes nothing. The Cabibbo-Kobayashi-Maskawa matrix therefore has four physical parameters: three mixing angles and one CP-violating phase.

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