Parton Distributions

The parton distributions file contains the PDF class. PDF is the base class, from which specific PDF classes are derived.

The choice of which PDF to use is made by settings in the Pythia class, see here. These settings also allow to access all the proton PDF's available in the LHAPDF library [Wha05]. Thus there is no need for a normal user to study the PDF class. The structure must only be understood when interfacing new PDF's, e.g. ones not yet found in LHAPDF.

The PDF base class

PDF defines the interface that all PDF classes should respect. The constructor requires the incoming beam species to be given: even if used for a proton PDF, one needs to know whether the beam is actually an antiproton. This is one of the reasons why Pythia always defines two PDF objects in an event, one for each beam.

Once a PDF object has been constructed, call it pdf, the main method is pdf.xf( id, x, Q2), which returns x*f_id(x, Q2), properly taking into account whether the beam is an antiparticle or not.

Whenever the xf member is called with a new flavour, x or Q^2, the xfUpdate member is called to do the actual updating. This routine may either update that particular flavour or all flavours at this (x, Q^2) point. (In the latter case the saved id value idSav should be set to 9.) The choice is to be made by the producer of a given set, based on what he/she deems most effective, given that sometimes only one flavour need be evaluated, and about equally often all flavours are needed at the same x and Q^2. Anyway, the latest value is always kept in memory. This is the other reason why Pythia has one separate PDF object for each beam, so that values at different x can be kept in memory.

Two further public methods are xfVal( id, x, Q2) and xfSea( id, x, Q2). These are simple variants whereby the quark distributions can be subdivided into a valence and a sea part. If these are not directly accessible in the parametrization, onc can make the simplified choices u_sea = ubar_sea, u_val = u_tot - u_sea, and correspondingly for d. (Positivity will always be guaranteed at output.) The xfUpdate method should also take care of updating this information.

A method setExtrapolate(bool) allows you to switch between freezing parametrizations at the x and Q^2 boundaries (false) or extrapolating them outside the boundaries (true). This method is only implemented for the LHAPDF class below. If you implement a new PDF you are free to use this method, but it would be smarter to hardcode the desired limiting behaviour.

Derived classes

There is only one pure virtual method, xfUpdate, that therefore must be implemented in any derived class. Currently the list of such classes is tiny:

For protons:

GRV94L gives the GRV 94 L parametrization [Glu95].
CTEQ5L gives the CTEQ 5 L parametrization [Lai00].
LHAPDFinterface provides an interface to the LHAPDF library[Wha05].

The default is CTEQ 5L, which is the most recent of the two hardcoded sets.

For charged leptons (e, mu, tau):

Lepton gives a QED parametrization [Kle89]. In QED there are not so many ambiguities, so here one set should be enough. On the other hand, there is the problem that the lepton-inside-lepton pdf is integrably divergent for x -> 1, which gives numerical problems. Like in PYTHIA 6, the pdf is therefore made to vanish for x > 1 - 10^{-10}, and scaled up in the range 1 - 10^{-7} < x < 1 - 10^{-10} in such a way that the total area under the pdf is preserved.

There is another method, isSetup(), that returns the base-class boolean variable isSet. This variable is initially true, but could be set false if the setup procedure of a PDF failed, e.g. if the user has chosen an unknown PDF set.