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first import of structure, PYTHIA8 and DELPHES
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1<html>
2<head>
3<title>Parton Distributions</title>
4<link rel="stylesheet" type="text/css" href="pythia.css"/>
5<link rel="shortcut icon" href="pythia32.gif"/>
6</head>
7<body>
8
9<h2>Parton Distributions</h2>
10
11The parton distributions file contains the <code>PDF</code> class.
12<code>PDF</code> is the base class, from which specific <code>PDF</code> 
13classes are derived.
14
15<p/>
16The choice of which PDF to use is made by settings in the
17<code>Pythia</code> class, see <a href="PDFSelection.html" target="page">here</a>.
18These settings also allow to access all the proton PDF's available in the
19LHAPDF library [<a href="Bibliography.html" target="page">Wha05</a>]. Thus there is no need for a normal user
20to study the <code>PDF</code> class. The structure must only be understood
21when interfacing new PDF's, e.g. ones not yet found in LHAPDF.
22
23<h3>The PDF base class</h3>
24
25<code>PDF</code> defines the interface that all PDF classes should respect.
26The constructor requires the incoming beam species to be given:
27even if used for a proton PDF, one needs to know whether the beam
28is actually an antiproton. This is one of the reasons why <code>Pythia</code> 
29always defines two PDF objects in an event, one for each beam.
30
31<p/>
32Once a <code>PDF</code> object has been constructed, call it <code>pdf</code>,
33the main method is <code>pdf.xf( id, x, Q2)</code>, which returns
34<i>x*f_id(x, Q2)</i>, properly taking into account whether the beam
35is an antiparticle or not.
36
37<p/>
38Whenever the <code>xf</code> member is called with a new flavour, <i>x</i> 
39or <i>Q^2</i>, the <code>xfUpdate</code> member is called to do the actual
40updating. This routine may either update that particular flavour or all
41flavours at this <i>(x, Q^2)</i> point. (In the latter case the saved
42<code>id</code> value <code>idSav</code> should be set to 9.) The choice is
43to be made by the producer of a given set, based on what he/she deems most
44effective, given that sometimes only one flavour need be evaluated, and
45about equally often all flavours are needed at the same <i>x</i> and
46<i>Q^2</i>. Anyway, the latest value is always kept in memory. This is
47the other reason why <code>Pythia</code> has one separate <code>PDF</code> 
48object for each beam, so that values at different <i>x</i> can be kept
49in memory.
50
51<p/>
52Two further public methods are <code>xfVal( id, x, Q2)</code> and
53<code>xfSea( id, x, Q2)</code>. These are simple variants whereby
54the quark distributions can be subdivided into a valence and a sea part.
55If these are not directly accessible in the parametrization, onc can
56make the simplified choices <i>u_sea = ubar_sea, u_val = u_tot - u_sea</i>,
57and correspondingly for <i>d</i>. (Positivity will always be guaranteed
58at output.) The <code>xfUpdate</code> method should also take care of
59updating this information.
60
61<p/>
62A method <code>setExtrapolate(bool)</code> allows you to switch between
63freezing parametrizations  at the <i>x</i> and <i>Q^2</i> boundaries
64(<code>false</code>) or extrapolating them outside the boundaries
65(<code>true</code>). This method is only implemented for the LHAPDF class
66below. If you implement a new PDF you are free to use this method, but it
67would be smarter to hardcode the desired limiting behaviour.
68
69<h3>Derived classes</h3>
70
71There is only one pure virtual method, <code>xfUpdate</code>, that
72therefore must be implemented in any derived class. A reasonable
73number of such classes come with the program:
74
75<p/>
76For protons:
77<ul>
78<li><code>LHAPDFinterface</code> provides an interface to the
79LHAPDF library[<a href="Bibliography.html" target="page">Wha05</a>].</li>
80<li><code>GRV94L</code> gives the GRV 94 L parametrization
81[<a href="Bibliography.html" target="page">Glu95</a>].</li>
82<li><code>CTEQ5L</code> gives the CTEQ 5 L parametrization
83[<a href="Bibliography.html" target="page">Lai00</a>].</li>
84<li><code>MSTWpdf</code> gives the four distributions of the
85MRST/MSTW group that have been implemented.</li>
86<li><code>CTEQ6pdf</code> gives the six distributions of the
87CTEQ/CT group that have been implemented.</li>
88</ul>
89The current default is CTEQ 5L, which has been used in most studies
90to date.
91
92<p/>
93For charged pions:
94<ul>
95<li><code>GRVpiL</code> gives the GRV 1992 pi+ parametrization.</li>
96</ul>
97
98<p/>
99For Pomerons (used to describe diffraction):
100<ul>
101<li><code>PomFix</code> gives a simple but flexible
102<i>Q2</i>-independent parametrization.</li>
103<li><code>PomH1FitAB</code> gives the H1 2006 Fit A and Fit B
104parametrizations.</li>
105<li><code>PomH1Jets</code> gives the H1 2007 Jets parametrization.</li>
106</ul>
107
108<p/>
109For charged leptons (e, mu, tau):
110<ul>
111<li><code>Lepton</code> gives a QED parametrization [<a href="Bibliography.html" target="page">Kle89</a>].
112In QED there are not so many ambiguities, so here one set should be
113enough. On the other hand, there is the problem that the
114lepton-inside-lepton pdf is integrably divergent for <i>x -> 1</i>,
115which gives numerical problems. Like in PYTHIA 6, the pdf is therefore
116made to vanish for <i>x > 1 - 10^{-10}</i>, and scaled up in the range
117<i>1 - 10^{-7} &lt; x &lt; 1 - 10^{-10}</i> in such a way that the
118total area under the pdf is preserved.</li>
119<li><code>LeptonPoint</code> gives the trivial distribution of a
120pointlike (i.e. unresolved) charged lepton.</li>
121</ul>   
122
123<p/>
124For neutrinos:
125<ul>
126<li><code>NeutrinoPoint</code> is the only method, so there is no choice.
127Analogously to <code>LeptonPoint</code> it gives the distribution of a
128pointlike (i.e. unresolved) neutrino. A difference, however, is that
129neutrinos always are lefthanded, so there is no need to average over
130incoming spin states. Since the PYTHIA formalism assumes unpolarized
131beams, and thus implicitly includes a 1/2 for incoming fermions, the
132<code>NeutrinoPoint</code> PDF is normalized to 2 rather than 1
133to compensate for this.</li>
134</ul>   
135
136<p/>
137There is another method, <code>isSetup()</code>, that returns the
138base-class boolean variable <code>isSet</code>. This variable is
139initially <code>true</code>, but could be set <code>false</code> if the
140setup procedure of a PDF failed, e.g. if the user has chosen an unknown
141PDF set. 
142
143<p/> 
144The MRST/MSTW, CTEQ/CT and H1 PDF routines are based on the interpolation
145in <i>(x, Q)</i> grids. The grid files are stored in the
146<code>xmldoc</code> subdirectory, like settings and particle data.
147Only PDF sets that will be used are read in during the initialization
148stage.
149
150</body>
151</html>
152
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