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A matrix element of an interaction operator between hadron states. It contains strong interaction dynamics beyond the explicit CKM matrix factors of a weak interaction decay; its magnitude and strong phase need not be identical for two different channels.

Put $r=B/A$. Equal two-body phase space gives ${\Gamma }_{S,L}\propto |A{|}^2|1\pm r{|}^2/2$, so the decay-rate asymmetry is exactlyThe stated magnitude assumption fixes $|r|={\tan }^2{\theta }_C$. Retaining the relative strong phase $\delta$ in the convention of b therefore givesA magnitude assumption alone does not determine $\mathcal{R}$. For example, $r=i{\tan }^2{\theta }_C$ has the stipulated magnitude but gives $\mathcal{R}=0$, whereas a real positive $r$ gives a positive asymmetry. With the additional aligned-amplitude assumption $\delta =0$, conventionally used for this idealised extraction, the intended leading result is $\boxed{\mathcal{R}\simeq 2{\tan }^2{\theta }_C}$. The sign of $r$ here refers to the complete amplitude after choosing the kaon phase convention, not to a bare CKM matrix product. A flavour-symmetry relation can supply further information, but is stronger than the printed magnitude assumption.

A phase in a hadronic matrix element generated by strong interaction dynamics, including rescattering of final states. It does not change sign under conjugation of the weak coupling constant. Interference measurements depend on relative strong phases, rather than their common overall value.