
   The CompHEP pdf file standard

                      Abstract
                      ~~~~~~~~

CompHEP pdf file standard is designed  to obtain unique software
realization  for  various  particle distribution functions.

In the   current moment  a lot of functions which describe parton 
distribution in hadrons are available and intensively used.
 They was created  by  various  teams  and are  realized by means of 
different software programs. In the same time almost all this programs
use  common algorithm. Namely, they  interpolate
data  stored   for some grid of function arguments in the file.

  In the process of development of CompHEP package we 
meet a challenge of providing the  user with a possibility  to operate with
large number of  distribution functions. 
After some experience of direct  embedding of ailing 
codes in our software,  we had  recognized that the best way should 
be a development  of one standard for pdf files and realization of
unique program that  will perform  the  interpolation taking into account 
some special features of partonic distribution functions.

 We especially were compelled  do it, because numerical calculations
in CompHEP are realized by means of C-software code, whereas 
traditionally pdf-functions are presenter by means of Fortran routines.

  This article contains description of our standard
and description of Fortran and C-routines designed by our group 
to provide work with such files.  Programs are distributed 
according to GNU General Public License (so-called copyleft).

    
   Comments to the existent pdf programs and  date files.
   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Generally  distribution function depends on two arguments, Feynman parameter
x and energy scale Q.
x is unitless and run in  [0,1] interval. Traditionally  Q is
presented in GeV unit.    Generally, distribution  functions are
obtained by fitting of experimental data.  It
leads to limits for small  values of x and for large values of Q  where
function  is valid.  Also there is limit about  1 GeV on
small Q values. Below  this limit the perturbative QCD theory,
which  is a basement of structure function
approach in particle physics,  does not valid.
 The authors of particle distribution functions pay attention of
user that they are not responsible for   extrapolation  of
functions outside these limits.

  Q parameter is changed on large interval, starting a value
about 1 GeV  up to a typical hight limit about 10^4 GeV.
QCD -motivated dependence on this parameter is a polynomial function
of log(Q). So a polynomial interpolation  for data on log(Q) grid
is used.

  x parameter  dependence has some features at the ends
of interval. Ordinary we expect x^(-1) behavior at small x
and (1-x)^n near x=1. Some authors ignore it and
use a  grid that contains enough  points
near x=0 and x=1 for good interpolation.  Other authors apply the 
interpolation procedure to   function  that previously  divided on these 
factors and restore factors  after  interpolation.  In the last case 
the size of data file may be reduced twice.

Ordinary  the polynomials of small power (one or two) are used
for interpolation. 

The correct usage of pdf  must be accompanied by the same   
formula  of  strong coupling constant alpha(Q) evaluation, 
that  was used in the process  of search of distribution  functions.
Although the alpha(s) dependence is presented by simple 
analytic formula, we   propose to include data for  this function
into the the pdf file as a table. It allows to realize some general approach 
to mutual evaluation of distribution function and alpha(Q).

           CompHEP structure of pdf data file.
           ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CompHEP pdf file contains several items of information,
Each item is started by a keyword. Numerical data following
a keyword must be separated by white-space characters, 
for example by   space, tab, or the new line symbol. 
The number of such symbols 
is not essential. The keyword and the following data must be separated by 
a white-space symbols too.
We start any  keyword  from the '#' symbol. 

The keywords are 

a) #x-grid       

After this word the file  has contain a sequence of numbers which 
specify the grid for the x variable.
 The number of points has exceed 2. Data must increase from point to point.
The data for the x-grid are finished by the first word in the file 
which can not be interpreted as a number. 

b) #q-grid  

Specifies the beginning of data for Q grid. The data must be positive  
to provide the further  transition to the logarithmic scale.
The  requirements formulated  for the x grid also  are valid here.
This item is optional. Generally we can consider distribution functions which
 do not  depend on the Q parameter. Artificial Q grid is not need in this case.

c) #x-min
   #x-max
   #q-min
   #q-max
These keywords are used to specify the minimum and maximum boundaries 
of  'x' and 'q' intervals,  where  results of interpolation should be correct.
An  appearance of one corresponding number after each of these keywords
is expected. These keywords are optional. If one of them is  absent then the 
first and the last points of 
the corresponding grid  are used to specify the boundaries. When  argument of 
particle  distribution function is out of the range the corresponding warning
is written into stderr device. 



d) #alpha 

This keywords starts a data for alpha(Q) for the Q  
grid points.  This item must contain just the same number of points as
Q parameter grid.  This item can not precede   the #q-grid one.  
The item is optional.

e)  #1-parton
    #2-parton
     ......

Keywords  of this type  mark the beginning of data for  distributions.
They can not precede #x-grid and #q-grid items because the power 
of data for  such item   must be in the strong correspondence with 
the powers of x-grid and q-grid. In the beginning one  have to write all  
data corresponding  to
the smallest Q value. After that data for the second point of Q grid 
must be presented. By other words,  parton distribution  data must be 
present by a two  dimension array of 
x-grid and q-grid indexes where the x-grid index runs the first.

Such  item can optionally be finished by word 'powers' after that
one or two numbers (say r0 and r1) are follow. 
It means that after interpolation of the data  the result must be 
multiplied on factor x^r0 *(1-x)^r1 to get the real parton distribution.
If only one number is presented it will corresponds to the r0.

f) #distribution 

After this word the title name of distribution and the list 
of parton is expected.  The title name has been surrounded by the "
symbols. The name  may contain space symbols inside.

 Partons whose distributions are  identical (say b and b-bar quarks
in the proton)  may be  combined into a  group.
Partons of one group should be closed into   brackets ( ) and 
separated by the comma. 

For example:

#distribution "CTEQ99Z (proton)" (b,b-bar) (c,c-bar) (s,s-bar) d u g u-bar d-bar         

 The position of the group  or parton name  in the list
corresponds to the  ordinal number of  data (see above) . So, the parton of
the first  group ( b and b-bar in the example)  are described by 
the  #1-parton item data. 

 One file can contain several '#distribution' keywords. In practice case 
we need  two of them to describe in one file both  particle
and anti-particle distributions. In the case of alias distribution CTEQ99Z
it should be 

#distribution "CTEQ99Z (anti-proton)" (b,b-bar) (c,c-bar) (s,s-bar)
                                        d-bar u-bar g u d         


g)#mass 

  This is an  optional  keyword allows to introduce mass of 
the composite  particle.
It is expected that corresponding numerical value
follows  this keyword. Default value for mass parameter is 1 GeV.

h)#lExtrapolation 
  The presence of this keyword means that linear interpolation has been
used  



         C-programs 
        ~~~~~~~~~~~
Here we describe software programs written in C 
which provide the user with a possibility to work 
with data files of above format.

The first function that we would like to present is  

void  makePdfList(char * file, char * parton, pdfList ** list);

This function opens the file 'file' and look for the 
#distribution  keywords. If such a word is detected and 
the name  'parton' presented in the lits of its constituents,
then the corresponding records is added to the  list 
of available distributions. The record in  this list is 
organized in the following way.
 

typedef struct pdfList
{ struct pdfList * next;  
  char *  name;      /*  the title name of distribution        */     
  char * file;       /* name of file where it is stored        */
  int   position;    /* ordering number of parton in the list of functions*/
} pdfList; 

The second function   

int    getPdfData(char * file, int n_parton, pdfStr * data );
                     /* read 'file' and  fill items of  'data' */




typedef struct pdfStr
{ double mass;       /* mass of composite particle             */
  int  nq;           /* number of points in Q-scale grid       */ 
  int  nx;           /* number of points in X-scale grid       */
  double * x_grid;   /* data for the X-grid                    */
  double * q_grid;   /* log() data for the Q-grid              */
  double * alpha;    /* data for QCD-alpha(Q) corresponding to */ 
                     /* the Q-grid points*/ 
  double * strfun;   /* data for interpolation of distibution corresponding */
                     /* to  (Q-grid)*(X-grid) points;          */ 
                     /* index of (X-grid) is rinning first     */
  double pow0;       /* factor x^pow *(1-x)^pow1  must be      */   
  double pow1;       /* applied after interpolation            */ 
} pdfStr;  

extern void   delPdfList(pdfList * list);


extern void   delPdfList(pdfList * list);
                     /* free  memory allocated for 'list' */
                     
extern int    getPdfData(char * file, int n_parton, pdfStr * data );
                     /* read 'file' and  fill items of  'data' */ 

extern void   freePdfData( pdfStr * data);
                    /* free  memory allocated for data items   */
                    /* and assigne NULL to  them.              */

extern double interFunc(double x, double q, pdfStr * W); 
                     /* interpolates data for given x and q    */ 
                     /* according to information stored in W.  */
                     /* result should be multiplied by the     */  
                     /* power factors later on                 */
extern double interAlpha(double q, pdfStr * W );
                     /* interpolates data for QCD-alpha(Q)     */

#endif

