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[Licence| Download | New Version Template] addb_v1_0.gz(25 Kbytes)
Manuscript Title: Numerical solution of Q**2 evolution equations in a brute-force method.
Authors: M. Miyama, S. Kumano
Program title: BF1
Catalogue identifier: ADDB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 94(1996)185
Programming language: Fortran.
Computer: AlphaServer 2100 4/200.
Operating system: OpenVMS V6.1.
Keywords: Particle physics, Elementary, Qcd, Structure function, Parton distribution, Q**2 evolution, Numerical solution.
Classification: 11.5.

Nature of problem:
This program solves Altarelli-Parisi Equations or modified evolution equations (Mueller-Qiu) with or without next-to-leading-order alphas effects for a spin-independent structure function or quark distribution. Both flavor-nonsinglet and singlet cases are provided, so that the distributions, xq , xq , xq+ = xq + xqbar (i=quark flavor), xg, xF , NS S i - i i NS xF , and xF+ in the nucleon and in nuclei can be evolved. S i

Solution method:
We divide the variable x (and Q**2) into very small steps, and integration and differentiation are defined by
 
df(x)    [f(x   )-f(x )]                                                
              m+1     m                                                  
 ----  =  ---------------  and                                           
  dx      Delta x                                                        
                 m                                                       

 Integral(dxf(x)) = Zigma (m=1, Nx) Delta x f(x ).     
                                           m   m   
Then, the integro-differerential equations are simply solved step by step, and this method is so called brute-force method. If the step numbers are increased, accurate results should be obtained.

Restrictions:
This program is used for calculating Q**2 evolution of a spin- independent flavor-nonsinglet-quark, singlet-quark, qi+, and gluon distributions (and corresponding structure functions) in the leading order or in the next-to-leading-order of alphas. Q**2 evolution equations are the Altarelli-Parisi equations and the modified ones (Mueller-Qiu). The double precision aithmetic is used. The renormalization scheme is the modified minimal subtraction scheme (MSbar). A user provides the initial structure function or quark distribution as a subroutine or as a data file. Examples are explained in sections 4.2 and 4.3. Then, the user inputs twenty-one parameters in section 4.1.

Running time:
Approximately five minutes on AlphaSever 2100 4/200 in the nonsinglet case, sixty minutes in the singlet-quark evolution, and eighty minutes in the singlet evolution with recombination effects.