Direct CP asymmetry
= Direct CP asymmetry
{title2=$A_{\rm CP}=(\Gamma-\bar\Gamma)/(\Gamma+\bar\Gamma)$}
A <direct CP asymmetry> compares <decay widths> for a process and its <CP symmetry> conjugate. Let two <decay amplitudes> contribute with real nonnegative magnitudes $a_1,a_2$, <absorptive phases> $\delta_i$ and <weak phases> $\phi_i$. Then $\mathcal A=a_1e^{i(\delta_1+\phi_1)}+a_2e^{i(\delta_2+\phi_2)}$ and $\overline{\mathcal A}=a_1e^{i(\delta_1-\phi_1)}+a_2e^{i(\delta_2-\phi_2)}$. Expanding the absolute squares gives
$$
|\mathcal A|^2-|\overline{\mathcal A}|^2=-4a_1a_2\sin(\delta_1-\delta_2)\sin(\phi_1-\phi_2).
$$
Thus two nonzero contributions and both kinds of relative phase are required in this example. Equal total <decay widths> under <CPT symmetry> constrain the sum over channels and do not forbid individual channel asymmetries.