term corresponding to several different resonance histories of the final state. Each resonance history corresponds to a [[**[tree graph]{}**]{}]{}, where the [[**[leaves]{}**]{}]{} of the tree are the final state particle, and the [[**[intermediate nodes]{}**]{}]{} are the resonances. In our case, we include in the tree also the two initial state particles, before the root node.

![image](tree)

The root of the tree does not correspond necessarily to any real resonance. For uniformity of treatment, we will however associate to the root a fictitious resonance, and we will refer to it as the “production resonance”.

For each given initial and final flavour configurations, we have several possible resonance histories. We will denote with $F_b$ the initial and final flavour structure of the Born process, irrespective of the internal nodes of the resonance history. We will instead denote with $f_b$ the flavour structure including the resonances decay cascade. We will also refer to it as the [[**[resonance history]{}**]{}]{}. Summarizing, we will refer to $F_b$ as the [[**[bare flavour structure]{}**]{}]{} of the process, and to $f_b$ as the [[**[full]{}**]{}]{} [[**flavour**]{}]{} [[**structure**]{}]{}, or simply as the [[**flavour structure**]{}]{}.

The Born contributions will be labeled as $B_{F_b}$. Thus, $B_{F_b}$ is the square of the amplitude for 