Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Cabibbo–Kobayashi–Maskawa matrix
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
==="Standard" parameters=== A "standard" parameterization of the CKM matrix uses three [[Euler angles]] ({{thin space}}{{mvar|θ}}{{sub|12}}, {{mvar|θ}}{{sub|23}}, {{mvar|θ}}{{sub|13}}{{thin space}}) and one CP-violating phase ({{thin space}}{{mvar|δ}}{{sub|13}}{{thin space}}).<ref>{{cite journal |first1=L.L. |last1=Chau |first2=W.-Y. |last2=Keung |year=1984 |title=Comments on the Parametrization of the Kobayashi-Maskawa Matrix |journal=[[Physical Review Letters]] |volume=53 |pages=1802–1805 |doi=10.1103/PhysRevLett.53.1802 |bibcode=1984PhRvL..53.1802C |issue=19}}</ref> {{mvar|θ}}{{sub|12}} is the Cabibbo angle. This is the convention advocated by the [[Particle Data Group]]. Couplings between quark generations {{math|j}} and {{math|k}} vanish if {{nowrap|{{mvar|θ}}{{sub|jk}} {{=}} 0 }}. Cosines and sines of the angles are denoted {{mvar|c}}{{sub|jk}} and {{mvar|s}}{{sub|jk}}, respectively. ::<math> \begin{align} & \begin{bmatrix} 1 & 0 & 0 \\ 0 & c_{23} & s_{23} \\ 0 & -s_{23} & c_{23} \end{bmatrix} \begin{bmatrix} c_{13} & 0 & s_{13}e^{-i\delta_{13}} \\ 0 & 1 & 0 \\ -s_{13}e^{i\delta_{13}} & 0 & c_{13} \end{bmatrix} \begin{bmatrix} c_{12} & s_{12} & 0 \\ -s_{12} & c_{12} & 0 \\ 0 & 0 & 1 \end{bmatrix} \\ & = \begin{bmatrix} c_{12}c_{13} & s_{12} c_{13} & s_{13}e^{-i\delta_{13}} \\ -s_{12}c_{23} - c_{12}s_{23}s_{13}e^{i\delta_{13}} & c_{12}c_{23} - s_{12}s_{23}s_{13}e^{i\delta_{13}} & s_{23}c_{13}\\ s_{12}s_{23} - c_{12}c_{23}s_{13}e^{i\delta_{13}} & -c_{12}s_{23} - s_{12}c_{23}s_{13}e^{i\delta_{13}} & c_{23}c_{13} \end{bmatrix}. \end{align} </math> The 2008 values for the standard parameters were:<ref>Values obtained from values of Wolfenstein parameters in the 2008 ''[[Review of Particle Physics]]''.</ref> :{{mvar|θ}}{{sub|12}} = {{val|13.04|0.05|u=°}}, {{mvar|θ}}{{sub|13}} = {{val|0.201|0.011|u=°}}, {{mvar|θ}}{{sub|23}} = {{val|2.38|0.06|u=°}} and :{{mvar|δ}}{{sub|13}} = {{val|1.20|0.08}} radians = {{val|68.8|4.5|u=°}}.
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)