gauge.

### Implementation of the Born resonance histories in the [[****]{}]{}

The internal implementation of the Born flavour structure can be inherited from the present Born level structure in the , starting with the extension of ref. [[@Campbell:2014kua]]{} for the inclusion of narrow width resonances. In this implementation, the full flavour structure of a Born term is represented by two arrays, and , where the index labels the particular Born full flavour structure $f_b$. The index labels the external leg and the internal resonances, with 1 and 2 representing the incoming legs, and the (integer) value of the array represents the corresponding flavour code (that coincides with the PDG code, except for gluons, that are labeled 0). The integer array represents the resonance pointers, so that the whole resonance structure can be reconstructed. For example, for the case of the full flavour structure corresponding to the process $g g \rightarrow (t \rightarrow (W^+ \rightarrow
e^+ \nu_e) b) ( \bar{t} \rightarrow (W^- \rightarrow {\mu}^-
\bar{\nu}_{{\mu}})  \bar{b} )$, we have

.

We see that the resonance pointer list contains zero for particles generated at the production stage (in `POWHEG` we represent the fictitious production stage resonance as having index 0), while for 