Baryons

For protons, many sets exist on the market. These are obtained by fits to experimental data, constrained so that the $Q^2$ dependence is in accordance with the standard QCD evolution equations. The current default in PYTHIA is CTEQ 5L [Lai00], a leading-order fit. Several other sets are found in PYTHIA. The complete list is:

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EHLQ sets 1 and 2 [Eic84];

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DO sets 1 and 2 [Duk82];

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the GRV 92L (updated version) fit [Glü92];

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the CTEQ 3L, CTEQ 3M and CTEQ 3D fits [Lai95];

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the GRV 94L, GRV 94M and GRV 94D fits [Glü95]; and

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the CTEQ 5L and CTEQ 5M1 fits [Lai00].

Of these, EHLQ, DO, GRV 92L, CTEQ 3L, GRV94L and CTEQ5L are leading-order parton distributions, while CTEQ 3D and GRV94D are in the next-to-leading-order DIS scheme and the rest in the next-to-leading order $\overline{\mathrm{MS}}$ scheme. The EHLQ and DO sets are by now rather old, and are kept mainly for backwards compatibility. Since only Born-level matrix elements are included in the program, there is no particular reason to use higher-order parton distributions -- the resulting combination is anyway only good to leading-order accuracy. (Some higher-order corrections are effectively included by the parton-shower treatment, but there is no exact match.)

There is a steady flow of new parton-distribution sets on the market. To keep track of all of them is a major work on its own. Therefore PYTHIA contains an interface to an external library of parton distribution functions, PDFLIB [Plo93]. This is an encyclopedic collection of almost all proton, pion and photon parton distributions proposed from the late 70's to the late 90's. Three dummy routines come with the PYTHIA package, so as to avoid problems with unresolved external references if PDFLIB is not linked. One should also note that PYTHIA does not check the results, but assumes that sensible answers will be returned, also outside the nominal $(x, Q^2)$ range of a set. Only the sets that come with PYTHIA have been suitably modified to provide reasonable answers outside their nominal domain of validity.

PDFLIB has been frozen in recent years. Instead a new project has taken over the same rôle, LHAPDF, the Les Houches Accord PDF interface [Gie02], containing all new sets of the last five years or so. While LHAPDF has a native input/output format different from the PDFLIB one, the LHAGLUE subpackage allows LHAPDF to be called in exactly the same way as PDFLIB is. Therefore the PYTHIA external-PFD-interface works for PDFLIB and LHAPDF alike.

From the proton parton distributions, those of the neutron are obtained by isospin conjugation, i.e. $f_{\u }^{\mathrm{n}} = f_{\d }^{\mathrm{p}}$ and $f_{\d }^{\mathrm{n}} = f_{\u }^{\mathrm{p}}$.

The program does allow for incoming beams of a number of hyperons: $\Lambda^0$, $\Sigma^{-,0,+}$, $\Xi^{-,0}$ and $\Omega^-$. Here one has essentially no experimental information. One could imagine to construct models in which valence $\mathrm{s}$ quarks are found at larger average $x$ values than valence $\u$ and $\d$ ones, because of the larger $\mathrm{s}$-quark mass. However, hyperon beams is a little-used part of the program, included only for a few specific studies. Therefore a simple approach has been taken, in which an average valence quark distribution is constructed as $f_{\mathrm{val}} = (f_{\u ,\mathrm{val}}^{\mathrm{p}} + f_{\d ,\mathrm{val}}^{\mathrm{p}})/3$, according to which each valence quark in a hyperon is assumed to be distributed. Sea-quark and gluon distributions are taken as in the proton. Any proton parton distribution set may be used with this procedure.