Parton distribution program

This a brief explanation of the FORTRAN program that computes the parton distribution.

Main part of the program

The main part of the program just serves to get the data from the user, pass this data to the function parton, and output the results.

Function PARTON

This is the heart of the program. Function parton accepts three parameters: the parton number (i.e. the parton for which one wishes to have the distribution), the momentum fraction at which the distribution is required, and the scale.

The data is read in from the file specified by the user into the three dimensional matrix H(-2:6,NAMAX,NBMAX). The first index of H refers to the parton number, with the following meaning:

-2:dbar, -1:ubar, 0:gluon, 1:u, 2:d, 3:s, 4:c, 5:b, 6:t, with sbar=s, cbar=c, bbar=b, tbar=t

For each parton, there is a two dimensional lattice of values of the parton distribution. One of the axes is a function of the momentum fraction X (LX=LOG(X/(1-X))), the other is a function of the scale MU (LMU=LOG(MU)). The first axis is also labelled by the integer A running from 1 to NA, and the second by the integer B running from 1 to NB. (A,B) are the coordinates of a point on the lattice. So, for example, H(-1,3,7) refers to the value of the ubar distribution for a given value of the momentum fraction X represented by A=3 and a given value of the scale MU represented by B=7.

Once the data from the file has been read into the matrix H, the first derivatives and the mixed second derivative of the parton distribution,

We are now ready to perform the interpolation (or extrapolation should the need arise).

After the interpolation is completed, the function PARTON returns the interpolated value to the main program.

In general, the accuracy of the interpolation is very good. But see the caveats.

Davison E. Soper and Parvez Anandam
Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA
soper@bovine.uoregon.edu
anandam@darkwing.uoregon.edu