= Effective Hamiltonian for neutral-meson mixing
{title2=$H_{\rm eff}=M-i\Gamma/2$}
A decaying particle-antiparticle pair is described by a two-dimensional <effective Hamiltonian for neutral-meson mixing> with dispersive matrix $M$ and decay matrix $\Gamma$, both <Hermitian matrices>. The <effective Hamiltonian for neutral-meson mixing> itself is generally not a <Hermitian matrix>. <CPT> symmetry equates its diagonal entries, by separately equating diagonal <masses> and <decay widths>. For $H_{\rm eff}=\begin{pmatrix}a&b\\c&a\end{pmatrix}$ the <eigenvalues> are $a\pm\sqrt{bc}$ and generic <eigenvectors> are $(\sqrt b,\pm\sqrt c)^T$, with correlated square-root branches. Complex <eigenvalues> give <masses> and <decay widths> through $\mu=m-i\Gamma/2$.
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