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<chapter name="Parton Distributions">
<h2>Parton Distributions</h2>
The parton distributions file contains the <code>PDF</code> class.
<code>PDF</code> is the base class, from which specific <code>PDF</code>
classes are derived.
<p/>
The choice of which PDF to use is made by settings in the
<code>Pythia</code> class, see <aloc href="PDFSelection">here</aloc>.
These settings also allow to access all the proton PDF's available in the
LHAPDF library <ref>Wha05</ref>. Thus there is no need for a normal user
to study the <code>PDF</code> class. The structure must only be understood
when interfacing new PDF's, e.g. ones not yet found in LHAPDF.
<h3>The PDF base class</h3>
<code>PDF</code> 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 <code>Pythia</code>
always defines two PDF objects in an event, one for each beam.
<p/>
Once a <code>PDF</code> object has been constructed, call it <code>pdf</code>,
the main method is <code>pdf.xf( id, x, Q2)</code>, which returns
<ei>x*f_id(x, Q2)</ei>, properly taking into account whether the beam
is an antiparticle or not.
<p/>
Whenever the <code>xf</code> member is called with a new flavour, <ei>x</ei>
or <ei>Q^2</ei>, the <code>xfUpdate</code> member is called to do the actual
updating. This routine may either update that particular flavour or all
flavours at this <ei>(x, Q^2)</ei> point. (In the latter case the saved
<code>id</code> value <code>idSav</code> 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 <ei>x</ei> and
<ei>Q^2</ei>. Anyway, the latest value is always kept in memory. This is
the other reason why <code>Pythia</code> has one separate <code>PDF</code>
object for each beam, so that values at different <ei>x</ei> can be kept
in memory.
<p/>
Two further public methods are <code>xfVal( id, x, Q2)</code> and
<code>xfSea( id, x, Q2)</code>. 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 <ei>u_sea = ubar_sea, u_val = u_tot - u_sea</ei>,
and correspondingly for <ei>d</ei>. (Positivity will always be guaranteed
at output.) The <code>xfUpdate</code> method should also take care of
updating this information.
<p/>
A method <code>setExtrapolate(bool)</code> allows you to switch between
freezing parametrizations at the <ei>x</ei> and <ei>Q^2</ei> boundaries
(<code>false</code>) or extrapolating them outside the boundaries
(<code>true</code>). 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.
<h3>Derived classes</h3>
There is only one pure virtual method, <code>xfUpdate</code>, that
therefore must be implemented in any derived class. A reasonable
number of such classes come with the program:
<p/>
For protons:
<ul>
<li><code>LHAPDFinterface</code> provides an interface to the
LHAPDF library<ref>Wha05</ref>.</li>
<li><code>GRV94L</code> gives the GRV 94 L parametrization
<ref>Glu95</ref>.</li>
<li><code>CTEQ5L</code> gives the CTEQ 5 L parametrization
<ref>Lai00</ref>.</li>
<li><code>MSTWpdf</code> gives the four distributions of the
MRST/MSTW group that have been implemented.</li>
<li><code>CTEQ6pdf</code> gives the six distributions of the
CTEQ/CT group that have been implemented.</li>
</ul>
The current default is CTEQ 5L, which has been used in most studies
to date.
<p/>
For charged pions:
<ul>
<li><code>GRVpiL</code> gives the GRV 1992 pi+ parametrization.</li>
</ul>
<p/>
For Pomerons (used to describe diffraction):
<ul>
<li><code>PomFix</code> gives a simple but flexible
<ei>Q2</ei>-independent parametrization.</li>
<li><code>PomH1FitAB</code> gives the H1 2006 Fit A and Fit B
parametrizations.</li>
<li><code>PomH1Jets</code> gives the H1 2007 Jets parametrization.</li>
</ul>
<p/>
For charged leptons (e, mu, tau):
<ul>
<li><code>Lepton</code> gives a QED parametrization <ref>Kle89</ref>.
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 <ei>x -> 1</ei>,
which gives numerical problems. Like in PYTHIA 6, the pdf is therefore
made to vanish for <ei>x > 1 - 10^{-10}</ei>, and scaled up in the range
<ei>1 - 10^{-7} < x < 1 - 10^{-10}</ei> in such a way that the
total area under the pdf is preserved.</li>
<li><code>LeptonPoint</code> gives the trivial distribution of a
pointlike (i.e. unresolved) charged lepton.</li>
</ul>
<p/>
For neutrinos:
<ul>
<li><code>NeutrinoPoint</code> is the only method, so there is no choice.
Analogously to <code>LeptonPoint</code> 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
<code>NeutrinoPoint</code> PDF is normalized to 2 rather than 1
to compensate for this.</li>
</ul>
<p/>
There is another method, <code>isSetup()</code>, that returns the
base-class boolean variable <code>isSet</code>. This variable is
initially <code>true</code>, but could be set <code>false</code> if the
setup procedure of a PDF failed, e.g. if the user has chosen an unknown
PDF set.
<p/>
The MRST/MSTW, CTEQ/CT and H1 PDF routines are based on the interpolation
in <ei>(x, Q)</ei> grids. The grid files are stored in the
<code>xmldoc</code> subdirectory, like settings and particle data.
Only PDF sets that will be used are read in during the initialization
stage.
</chapter>
<!-- Copyright (C) 2012 Torbjorn Sjostrand -->
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