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Kobayashi Maskawa Matrix Error ?

  1. Jan 11, 2012 #1
    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. jcsd
  3. Jan 11, 2012 #2


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    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.
  4. Jan 11, 2012 #3


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    And the matrix as you give it is unitary.
  5. Jan 12, 2012 #4
    Thanks very much for your answer.
    In fact, the matrix that I give is unitary as you said.
    But this is not EXACTLY the matrix as in the paper of Kobayashi and Maskawa ;
    The V_3,3 term have been corrected. In the paper they write a sin(θ3) term in place of a cos(θ3) term.

    Thank you ! :smile:
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