Form for the Parton Table

Lattice:

For x, the points lie between a minimum and a maximum x, evenly distributed in LX

LX = DLOG(X/(1.0D0 - X))
so
X = DEXP(LX)/(1.0D0+DEXP(LX))

For mu, the points lie between a minimum and a maximum mu, evenly distributed in LMU

LMU = DLOG(MU)
so
MU = DEXP(LMU)

Values:

DLOG( pdf + 1.0D-16 )

where pdf is the value of the parton distribution function at this point. The tiny value 1.0D-16 is added so that the table can handle zero values for the parton distributions. (We assume that the parton distribution functions are never negative.)

Here is the standard form:

!  CTEQ3M parton distributions generated by DES 14 August 1995                 
!  The comment area follows.
!  Each comment line starts with an exclamation point as initial character.
!  The first line after the comment line has to be PARTON DATA.
PARTON DATA
   VERSION =       110496  
    LAMBDA =     0.1580000000    
NFL_LAMBDA =          5
      XMIN =     0.1000000000E-04
      XMAX =     0.9500000000    
 N_XPOINTS =         32
     MUMIN =      1.600000000    
     MUMAX =      1000.000000    
N_MUPOINTS =         32
  11.901      11.896      14.505      11.899      11.902      11.204     -36.841     -36.841     -36.841    
  12.050      12.048      14.772      12.050      12.052      11.488      10.176     -36.841     -36.841    
  12.189      12.188      15.003      12.190      12.191      11.728      10.887     -36.841     -36.841    
  12.319      12.318      15.207      12.320      12.320      11.936      11.313     -36.841     -36.841    
    .
    .
    .

1. Header line
   • always starts with the `!' character.
   • written by person who made the table.
   • may be read by user program and inserted in user program output.
2. Comment lines
   • always start with the `!' character;
   • may contain relevant information on the source of the data, references, and so on;
   • are normally not used by the user program;
   • may be useful to a person who looks at the parton table.
3. Line consisting of the string `PARTON DATA' alone.
   • This line serves to delimit the variable length comment section from the fixed format data section to follow.
4. Version number of the table format.
   • An integer. (Really, it's a date.)
   • Inserted by program that writes the table.
   • Checked by program that reads the table, to be sure that the table is in the format expected.
5. Value of lambda (MS-bar) used.
   • This is for use in the user program
   • Since user programs are normally in the five flavor range, we recommend the five flavor value.
6. Number of flavors in the definition of lambda.
7. Minimum value of x for table.
8. Maximum value of x for table.
9. Number of points in the x range.
10. Minimum value of the scale mu for table.
11. Maximum value of the scale mu for table.
12. Number of points in the mu range.
13. The data.

Each row corresponds to a different (x,mu) lattice point. The columns corresponds to different partons:

dbar  ubar  gluon   u    d    s    c    b    t

The lattice points are written in the order

(x1,mu1), (x1,mu2), (x1,mu3), ...
(x2,mu1), (x2,mu2), (x2,mu3), ...
(x3,mu1), (x3,mu2), (x3,mu3), ...
   ...  ,  ...    ,   ...   , ...

      DO 30 N=1,NX
      DO 30 M=1,NMU
      WRITE(99,50)F(-2,N,M),F(-1,N,M),F(0,N,M),F(1,N,M),
     >            F(2,N,M),F(3,N,M),F(4,N,M),F(5,N,M),F(6,N,M)
 50   FORMAT(9G12.5)
C
 30   CONTINUE

Code to write a table

dbar  ubar  gluon   u    d    s    c    b    t
 -2    -1     0     1    2    3    4    5    6

      NFL = 6