`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.

`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 low-*x* boundary
(`false`

) or extrapolate them outside the boundary
(`true`

). This method works both for LHAPDF 5, LHAPDF6 and
modern internal PDFs. (For some older PDFs the behaviour implemented by
the original authors is maintained.) In either case the PDFs are frozen
at *Q_min* and *Q_max*. (And also at *x_max*, but
this is irrelevant when *x_max = 1*.)

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.

`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.`LHAGrid1`

can read and use files in the LHAPDF6 lhagrid1 format, assuming that the same x grid is used for all Q subgrids. Results are not exactly identical with LHAPDF6, owing to different interpolation.`nPDF, Isospin, EPS09`

three classes allowing to introduce nuclear modifications to a specified proton PDF. The first is base class for the other two, where`Isospin`

only provides the appropriate mix of protons and isospin-conjugate neutrons, while`EPS09`

also contains nuclear modification factors [Esk09].

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].`GammaPoint`

gives the trivial distribution of a pointlike (i.e. unresolved) photon.

For charged leptons (e, mu, tau) and the proton:

`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.`EPAexternal`

provides an external photon flux to study photoproduction with different fluxes. Still optimized for lepton beams, but also other fluxes can be studied.`Lepton2gamma`

gives the convolution between photon flux from leptons and photon PDFs.`ProtonPoint`

gives the equivalent photon spectrum of an unresolved proton.

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.