* Revised Version 3/1/99 updated


	*** User Manual for the Nondiagonal Parton Evolution Package ***


			(c) Andreas Freund, 1998


Before I explain how to use the package, which is very easy by the way, 
let me tell you what you need and do not find here because I am not the author 
of that stuff.

First, one needs the CTEQ evolution package which can be downloaded from
http://www.phys.psu.edu/~cteq/. The download contains all the necessary 
information on how to use the package itself and the following files which
you need to run the package successfully:

				jccpac.f
				ckini.f
				moments.f
				qcdpac.f
				utlpac.f
				przpac.f
				pdfpac.f (to be replaced by pdfcpac3.f).

What you actually find is:

			makend4m.f

(Fortran file in which the initial pdf's, number of points in x and Q, as well
as the starting and end scale in Q. etc. are specified, handed down to the 
evolution and the final result of the evolution is saved in a data file.)

			pdfcpac3.f

(Fortran file which does the actual nondiagonal evolution.)

I have written an extension of the pdfpac.f file contained in the CTEQ-package
which allows one to do the evolution of nondiagonal parton distributions to
leading order called pdfcpac3.f. This replaces the pdfpac.f file 
in the original package. Everything else stays the same. Also you will find a 
file called makend4m.f which lets you start right off to do your own 
evolution. The file is documented and should be selfexplanatory.

How to get started: 1.) compile all the files including makend4m.f, 
			except ckini.f, via f77 -c filename.f.

		    2.) link the the files via f77 -o (name of executable file
			for example ndevol) makend4m.o ckini.f jccpac.o 
			pdfcpac3.o przpac.o qcdpac.o utlpac.o moments.o

When you start the executable file you will be prompted for 2 numbers. First 
for the number of points in x ( max. 525 ) and secondly for the number 
of points in Q between Qmin and Qmax.

To use the package for varying asymmetry parameter DEL, you have to change
DEL in pdfcpac3.f before you compile and then link the different files of the 
CTEQ-package. DEL is found in the parameter definitions of the subroutine
NINTEGR and can take on every positive value between 0 and 1. 
The file pdfcpac3.f is documented within the program.

				** Warning**

This evolution program is designed for the DGLAP case, i.e., xmin in the 
makepomdelnd1.f file ALWAYS has to be larger than or equal to DEL. The 
case xmin = DEL is a special case and sets x_2=0 , i.e., x = DEL throughout 
the whole evolution process. DEL = 0 gives you the normal parton evolution.

Also note that the nondiagonal code is only leading order, which means that
the parameter DKNL in the makepomdelnd1.f file, which controls whether LO or 
NLO evolution is used, ALWAYS has to be 1 (Until the NLO calculation for the
nondiagonal case has been done. If you set DKNL = 2 or -1 you will get the 
usual NLO diagonal evolution for unpolarized and LO diagonal evolution for the
polarized case BUT not the nondiagonal case. So beware!!! 


The code has been fully tested and is free of bugs (at least to the best of my
knowledge), however if you still come across something let me know right away
at freund@phys.psu.edu. 

Enjoy the program!

P.S.: A bug in the program was recently discovered and is now corrected! If
you have used the program to calculate the nondiagonal gluon distribution
your error was within 3% of the correct answer for x_1 of order DEL. However
the results for the quark evolution was wrong by a factor of 2 in the region
x_1 of order DEL. The results obtained now are correct and agree with other
nondiagonal evolution programs.