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.