Parton Distributions

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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,Buc15]. 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, one 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 LHAPDF5 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.

With insideBounds(double x, double Q2) you can probe whether an (x, Q^2) pair falls inside the fit region or not. The alphaS(double Q2) method returns the alpha_s of the PDF at the given Q^2 scale, while mQuarkPDF(int id) returns the quark masses used to set flavour thresholds. Currently these three methods are only implemented for LHAPDF6.

Derived classes

There is only one pure virtual method, xfUpdate, that therefore must be implemented in any derived class. A reasonable number of such classes come with the program:

For protons:

LHAPDF provides a plugin interface class to the LHAPDF library[Wha05,Buc15]. It loads either the LHAPDF5 or LHAPDF6 class.
GRV94L gives the GRV 94 L parametrization [Glu95].
CTEQ5L gives the CTEQ 5 L parametrization [Lai00].
MSTWpdf gives the four distributions of the MRST/MSTW group that have been implemented.
CTEQ6pdf gives the six distributions of the CTEQ/CT group that have been implemented.
NNPDF gives four distributions from the NNPDF 2.3 QCD+QED sets that have been implemented.

The current default is NNPDF 2.3.

For charged pions:

GRVpiL gives the GRV 1992 pi+ parametrization.

For Pomerons (used to describe diffraction):

PomFix gives a simple but flexible Q2-independent parametrization.
PomH1FitAB gives the H1 2006 Fit A and Fit B parametrizations.
PomH1Jets gives the H1 2007 Jets parametrization.

For photons:

CJKL gives the CJKL parametrization [Cor03].

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.
LeptonPoint gives the trivial distribution of a pointlike (i.e. unresolved) charged lepton.
Lepton2gamma gives the convolution between photon flux from leptons and photon PDFs.

For neutrinos:

NeutrinoPoint is the only method, so there is no choice. Analogously to LeptonPoint it gives the distribution of a pointlike (i.e. unresolved) neutrino. A difference, however, is that neutrinos always are lefthanded, so there is no need to average over incoming spin states. Since the PYTHIA formalism assumes unpolarized beams, and thus implicitly includes a 1/2 for incoming fermions, the NeutrinoPoint PDF is normalized to 2 rather than 1 to compensate for this.

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.

The MRST/MSTW, CTEQ/CT, NNPDF and H1 PDF routines are based on the interpolation in (x, Q) grids. The grid files are stored in the xmldoc subdirectory, like settings and particle data. Only PDF sets that will be used are read in during the initialization stage. Just as input streams can be used to initialize the settings and particle data, so can the individual PDFs be constructed. See the header files for explicit constructor descriptions.