Data on meson parton distributions are scarce, so only very few sets have been constructed, and only for the . PYTHIA contains the Owens set 1 and 2 parton distributions [Owe84], which for a long time were essentially the only sets on the market, and the more recent dynamically generated GRV LO (updated version) [Glü92a]. The latter one is the default in PYTHIA. Further sets are found in PDFLIB and LHAPDF and can therefore be used by PYTHIA, just as described above for protons.

Like the proton was used as a template for simple hyperon sets, so also the pion is used to derive a crude ansatz for . The procedure is the same, except that now .

Sets of photon parton distributions have been obtained as for hadrons; an additional complication comes from the necessity to handle the matching of the vector meson dominance (VMD) and the perturbative pieces in a consistent manner. New sets have been produced where this division is explicit and therefore especially well suited for applications to event generation[Sch95]. The Schuler and Sjöstand set 1D is the default. Although the vector-meson philosophy is at the base, the details of the fits do not rely on pion data, but only on data. Here follows a brief summary of relevant details.

Real photons obey a set of inhomogeneous evolution equations, where the
inhomogeneous term is induced by
branchings.
The solution can be written as the sum of two terms,

(43) |

where each component and obeys a unit momentum sum rule.

In sets 1 the scale is picked at a low value, 0.6 GeV, where an identification of the nonperturbative component with a set of low-lying mesons appear natural, while sets 2 use a higher value, 2 GeV, where the validity of perturbation theory is better established. The data are not good enough to allow a precise determination of . Therefore we use a fixed value MeV, in agreement with conventional results for proton distributions. In the VMD component the and have been added coherently, so that at .

Unlike the , the has a direct component where the photon
acts as an unresolved probe. In the definition of this
adds a component , symbolically

(45) |

When jet production is studied for real incoming photons, the standard evolution approach is reasonable also for heavy flavours, i.e. predominantly the , but with a lower cut-off for . Moving to Deeply Inelastic Scattering, , there is an extra kinematical constraint: . It is here better to use the `Bethe-Heitler' cross section for . Therefore each distribution appears in two variants. For applications to real 's the parton distributions are calculated as the sum of a vector-meson part and an anomalous part including all five flavours. For applications to DIS, the sum runs over the same vector-meson part, an anomalous part and possibly a part for the three light flavours, and a Bethe-Heitler part for and .

In version 2 of the SaS distributions, which are the ones found here, the
extension from real to virtual photons was improved, and further options
made available [Sch96]. The resolved components of the photon
are dampened by phenomenologically motivated virtuality-dependent
dipole factors, while the direct ones are explicitly calculable.
Thus eq. () generalizes to

with the photon virtuality and the hard-process scale. In addition to the introduction of the dipole form factors, note that the lower input scale for the VMD states is here shifted from to some . This is based on a study of the evolution equation [Bor93] that shows that the evolution effectively starts `later' in for a virtual photon. Equation () is one possible answer. It depends on both and in a non-trivial way, however, so that results are only obtained by a time-consuming numerical integration rather than as a simple parametrization. Therefore several other alternatives are offered, that are in some sense equivalent, but can be given in simpler form.

In addition to the SaS sets, PYTHIA also contains the Drees-Grassie set
of parton distributions [Dre85] and, as for the proton, there is
an interface to PDFLIB and LHAPDF. These calls are
made with photon virtuality below the hard-process scale
. Further author-recommended constrains are implemented in the
interface to the GRS set [Glü99] which, along with SaS, is among
the few also to define parton distributions of virtual photons.
However, these sets do not allow a subdivision of the photon parton
distributions into one VMD part and one anomalous part. This
subdivision is necessary a sophisticated modelling of
and
events, see above and section .
As an alternative, for the VMD part alone, the
parton distribution can be found from the assumed equality

(47) |

The distribution can be further decomposed, by the flavour and the of the original branching . The flavour is distributed according to squared charge (plus flavour thresholds for heavy flavours) and the according to in the range . At the branching scale, the photon only consists of a pair, with distribution . A component , characterized by its and flavour, then is evolved homogeneously from to . For theoretical studies it is convenient to be able to access a specific component of this kind. Therefore also leading-order parameterizations of these decomposed distributions are available [Sch95].