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Last on B-mesons and CPV (for now)

  1. Jul 14, 2015 #1


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    Last one before my exam tomorrow....
    I was wondering. If we have B meson oscillations we can write the light/heavy eigenstates:
    [itex]|B_L> = p |B^0> + q |\bar{B}^0>[/itex]
    [itex]|B_H> = p |B^0> - q |\bar{B}^0> [/itex]
    with [itex]|p|^2 + |q|^2 =1[/itex]....
    How can I see that:
    [itex] \frac{q}{p}= -\dfrac{ \Delta m_B - (i/2) \Delta \Gamma_B}{2 [M_{12} - (i/2) \Gamma_{12}]}[/itex]
    Last edited: Jul 14, 2015
  2. jcsd
  3. Jul 14, 2015 #2


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    You can parameterize the mass matrix in real and imaginary parts as

    $$ \mathcal{M} = \begin{pmatrix} M_{11} - i\frac{\Gamma_{11}}{2} & M_{12} - i\frac{\Gamma_{12}}{2} \\ M_{12} + i\frac{\Gamma_{12}}{2} & M_{22} - i\frac{\Gamma_{2}}{2} \end{pmatrix}.$$

    Then find the eigenvectors to determine ##p,q##.
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