Flavour Selection

In either string or independent fragmentation, an iterative approach is used to describe the fragmentation process. Given an initial quark $\mathrm{q}= \mathrm{q}_0$, it is assumed that a new $\mathrm{q}_1 \overline{\mathrm{q}}_1$ pair may be created, such that a meson $\mathrm{q}_0 \overline{\mathrm{q}}_1$ is formed, and a $\mathrm{q}_1$ is left behind. This $\mathrm{q}_1$ may at a later stage pair off with a $\overline{\mathrm{q}}_2$, and so on. What need be given is thus the relative probabilities to produce the various possible $\mathrm{q}_i \overline{\mathrm{q}}_i$ pairs, $\u\overline{\mathrm{u}}$, $\d\overline{\mathrm{d}}$, $\mathrm{s}\overline{\mathrm{s}}$, etc., and the relative probabilities that a given $\mathrm{q}_{i-1}\overline{\mathrm{q}}_i$ quark pair combination forms a specific meson, e.g. for $\u\overline{\mathrm{d}}$ either $\pi^+$, $\rho^+$ or some higher state.

In PYTHIA, it is assumed that the two aspects can be factorized, i.e. that it is possible first to select a $\mathrm{q}_i \overline{\mathrm{q}}_i$ pair, without any reference to allowed physical meson states, and that, once the $\mathrm{q}_{i-1}\overline{\mathrm{q}}_i$ flavour combination is given, it can be assigned to a given meson state with total probability unity. Corrections to this factorized ansatz will come in the baryon sector.