Editing Cabibbo–Kobayashi–Maskawa matrix (section)

===Wolfenstein parameters===
A third parameterization of the CKM matrix was introduced by [[Lincoln Wolfenstein]] with the four real parameters {{mvar|λ}}, {{mvar|A}}, {{mvar|ρ}}, and {{mvar|η}}, which would all 'vanish' (would be zero) if there were no coupling.<ref>
{{cite journal
 |first=L. |last=Wolfenstein  |author-link=Lincoln Wolfenstein
 |year=1983
 |title=Parametrization of the Kobayashi-Maskawa Matrix
 |journal=[[Physical Review Letters]]
 |volume=51  |pages=1945–1947  |issue=21
 |doi=10.1103/PhysRevLett.51.1945  |bibcode=1983PhRvL..51.1945W
}}
</ref> The four Wolfenstein parameters have the property that all are of order 1 and are related to the 'standard' parameterization:
:{|
|-
| <math> \lambda = s_{12} ~, </math>
| <math> \lambda = s_{12} ~,</math>
|-
| <math> A \lambda^2 = s_{23} ~, </math>
| <math> A = \frac{s_{23} }{\; s_{12}^2 \;} ~,</math>
|-
| <math> A \lambda^3 ( \rho  - i \eta ) = s_{13} e^{-i\delta} ~, \quad </math>
| <math>  \rho = \operatorname\mathcal{R_e} \left\{ \frac{\; s_{13} \, e^{-i\delta} \;}{ s_{12} \, s_{23} } \right\} ~, \quad  \eta  = - \operatorname\mathcal{I_m} \left\{ \frac{\; s_{13} \, e^{-i\delta} \;}{ s_{12} \, s_{23} } \right\} ~. </math>
|}

Although the Wolfenstein parameterization of the CKM matrix can be as exact as desired when carried to high order, it is mainly used for generating convenient approximations to the standard parameterization. The approximation to order {{mvar|λ}}{{sup|3}}, good to better than 0.3% accuracy, is:
::<math>\begin{bmatrix} 1 - \tfrac{1}{2}\lambda^2 & \lambda & A\lambda^3(\rho-i\eta) \\
 -\lambda & 1-\tfrac{1}{2}\lambda^2 & A\lambda^2 \\
 A\lambda^3(1-\rho-i\eta) & -A\lambda^2 & 1  \end{bmatrix} + O(\lambda^4) ~. </math>

Rates of [[CP violation]] correspond to the parameters {{mvar|ρ}} and {{mvar|η}}.

Using the values of the previous section for the CKM matrix, as of 2008 the best determination of the Wolfenstein parameter values is:<ref name="PDG2023">{{cite journal |last1=R.L. Workman et al. (Particle Data Group) |title=Review of Particle Physics (and 2023 update) |journal=Progress of Theoretical and Experimental Physics |date=August 2022 |volume=2022 |issue=8 |pages=083C01 |doi=10.1093/ptep/ptac097 |url=https://pdg.lbl.gov/ |access-date=12 September 2023 |ref=PDG2023|doi-access=free |hdl=20.500.11850/571164 |hdl-access=free }}</ref>
:{{mvar|λ}} =.22500 ± 0.0067, &nbsp; {{mvar|A}} = {{val|0.826|+0.018|-0.015}}, &nbsp; {{mvar|ρ}} = 0.159±0.010, &nbsp; and &nbsp; {{mvar|η}} = 0.348±0.010.