MRST 2006 NNLO PDFs
-------------------

The enclosed Fortran and C++ code provides public access to the parton
distribution functions (PDFs) published in:

  A. D. Martin, W. J. Stirling, R. S. Thorne and G. Watt,
  "Update of Parton Distributions at NNLO",
  arXiv:0706.0459 [hep-ph].

Please reference this paper if you use the PDFs for a publication.

Unpack the tarball with "tar zxvf mrst2006nnlo.tar.gz" to give the
following files:

  README    : This documentation file.
  pdf.f     : Fortran code to access grids.
  pdf.h     : C++ class header file.
  pdf.C     : C++ class implementation file.
  example.f : Fortran example code.
  example.C : C++ example code.
  Makefile  : Compilation using Make utility.

Grids containing the PDFs are stored in files named

  Grids/mrst2006nnlo.ii.dat

where ii = 00 labels the central fit and ii = 01 to ii = 30 label the
eigenvector sets.  The grids are provided for

  10^-6 <= x <= 1 and 1 GeV^2 <= Q^2 <= 10^9 GeV^2

An extrapolation is returned with a warning message (by default, but
see below) if the PDFs are requested for smaller x or larger Q^2.  This
new extrapolation (thanks to J.Andersen) fixes a problem with the
previous MRST Fortran code where meaningless results were returned
(but with a warning message) if the PDFs were requested outside of the
grids.  The program terminates (by default, but see below) if an attempt
is made to access the PDFs with x <= 0 or x > 1 or Q^2 < 1 GeV^2.  The
antistrange distribution "sbar" is now distinct from the strange
distribution "str".  This is to allow for a strange asymmetry in
future PDF releases, although str = sbar is assumed for the MRST 2006
NNLO sets provided here.  As usual, it is always the momentum density
that is returned, that is, x times the number density.  Note that the
PDFs are discontinuous at NNLO at the heavy quark thresholds mc^2 and mb^2.
To account for this, Q^2 grid points are chosen at mc^2-eps, mc^2,
mb^2-eps, mb^2 (with eps = 10^-6 GeV^2).  If the PDFs are requested for
mc^2-eps < Q^2 < mc^2 the value at mc^2-eps is used, and similarly if
mb^2-eps < Q^2 < mb^2 the value at mb^2-eps is used.

For the MRST 2006 NNLO fit, mc = 1.43 GeV, mb = 4.3 GeV and
Lambda_{QCD}^{nf=4} = 0.2808 GeV => alpha_S(M_Z) = 0.1191.


Example programs
----------------

To compile the Fortran and C++ example programs:

  g77 example.f pdf.f -o example
  g++ example.C pdf.C -o example_cpp

Or alternatively just type "make".  Then run the programs with:

  ./example
  ./example_cpp

The Fortran and C++ example programs should give identical output.
Verify this with:

  diff xg_vs_x.dat xg_vs_x_cpp.dat
  diff xg_vs_q2.dat xg_vs_q2_cpp.dat


Fortran code
------------

There are three user interfaces for the Fortran code.

  call GetAllPDFs(prefix,i,x,q,upv,dnv,usea,dsea,str,sbar,chm,bot,glu)
  call GetAllPDFsAlt(prefix,i,x,q,xpdf)
  xf = GetOnePDF(prefix,i,x,q,f)

See source code of example.f for usage.  The prefix specifies the
location of the grid files and i labels the eigenvector sets where
i=0 is the central fit.  xpdf(-6:6) is an array containing all PDFs
with the index given by the PDG convention.  The numbering scheme
for the flavour "f" is the same as that used internally in previous
MRST routines, i.e.
1=upv 2=dnv 3=glu 4=usea 5=chm 6=str 7=bot 8=dsea 9=sbar.

Setting warn=.false. at the start of the GetOnePDF subroutine will
suppress the warning issued when extrapolating to small x or large Q^2.
Setting fatal=.false. at the start of the GetOnePDF subroutine will
mean that zero is returned if the PDFs are called with x <= 0 or
x > 1 or Q^2 <= 1 GeV^2 instead of terminating the program (the default
behaviour).


C++ code
--------

To use the C++ code, first declare an object of class c_pdf, passing
the desired grid file as an argument:

  c_pdf pdf("filename.dat");

To interpolate all flavours, do

  pdf.update(x,q);

and then access the individual flavours with 

  upv = pdf.cont.upv;
  dnv = pdf.cont.dnv;
  etc.

Or to interpolate just a single flavour, do

  xf = pdf.parton(f,x,q);

where the numbering scheme for the flavour "f" is
1=upv 2=dnv 3=glu 4=usea 5=chm 6=str 7=bot 8=dsea 9=sbar.
Alternatively the enumerated constants defined in pdf.h can be used.
See source code of example.C for usage.

The "warn" and "fatal" options described above for the Fortran version
can be set using the constructor

  c_pdf pdf("filename.dat",warn,fatal);

The default settings are warn=true and fatal=true.  Change either of these
at your peril.


Comments to watt(at)hep.ucl.ac.uk
Last updated: 4th June 2007