Last on B-mesons and CPV (for now)

[ChrisVer]

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

 

[fzero]

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 $p,q$.