# Kobayashi Maskawa Matrix Error ?

1. Jan 11, 2012

### Anne-Sylvie

Hello everyone,

I'm studying some lectures on electroweak interactions and I was reading the paper from Kobayashi and Maskawa, particulary the matrix :

But these matrix have to be unitary... And my professor said that it was not the case. When I compute the product of this matrix and its conjugate transpose, I actually don't find the identity matrix but I don't rely on my computation...

Is there REALLY an error in the paper ?
(I computed for many values of θ1, θ2 and θ3 numerically the product and I never have the identity.)

2. Jan 11, 2012

### Bill_K

If you look at the Wikipedia page on the CKM Matrix, they show that the "standard" parametrization can be factored into three Euler-angle rotations. This makes it obvious that the result is unitary. And although they don't do it, the "original" KM parametrization can be factored in a similar manner.

(If only I knew how to write a matrix!) But anyway, it's a rotation by θ3 in the 23 plane, followed by a rotation by θ1 in the 12 plane, followed by a rotation by θ2 again in the 23 plane. The matrix is correct as you give it.

3. Jan 11, 2012

### Avodyne

And the matrix as you give it is unitary.

4. Jan 12, 2012