Re: three kinds of Euler angular unitary matrices
- To: mathgroup at smc.vnet.net
- Subject: [mg117388] Re: three kinds of Euler angular unitary matrices
- From: Roger Bagula <roger.bagula at gmail.com>
- Date: Thu, 17 Mar 2011 06:30:29 -0500 (EST)
- References: <ilq740$bqb$1@smc.vnet.net>
Another approach from physics is the Wolfenstein parametrization
which is also in the above link.
(* normalizing the web CKM (3, 3) to one*)
ckm = {{0.9751068906432654`, 0.22549121655163576`,
0.0034729450574086823`},
{0.22539113167966435`, 0.9742761862059026`, 0.04103479750828703`},
{0.008627315963937418`, 0.040334203404487005`, 1.`}}
(* Wolfenstein Parametrization of CKM matrix*)
m = {{1 - l^2/2, l, A*l^3(r - I*n)},
{-l, 1 - l^2/2, A*l^2},
{A*l^3(1 - r - I*n), A*l^2, 1}}
(* solving for those parameters*)
l = Sqrt[0.22549121655163576*0.22539113167966435]
A = 0.04103479750828703/0.05082372048239745
{n, r} /. Solve[{0.009250932701954831 (-I* n + r) -
0.0034729450574086823 == 0, 0.009250932701954831* (1 - I* n - r) -
0.008627315963937418 == 0}, {n, r}]
The solution angles are:
a0=ArcSin[l]
0.227396
b0=ArcSin[A*l^2]
0.0410463
c0=ArcSin[A*l^3(r-I*n)]
0.00347295
Det[ckm-m]=1.3697829821437137`*^-22