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src/integrals/four_point/function_4p4m [ Modules ]

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NAME

  Module function_4p4m

USAGE

  use function_4p4m

DESCRIPTION

  This module computes the six-dimensional and eight dimensional 
  three mass four point function with or without Feynman parameters
  in the numerator.

OUTPUT

  This module exports three functions f4p4m, f4p4m_c and f4
  all the other subroutines/functions of this module are private

USES

  * precision (src/module/precision_golem.f90)
  * numerical_evaluation (src/numerical/mod_numeric.f90)
  * dilogarithme (src/module/zdilog.f90)
  * logarithme (src/module/z_log.f90)
  * constante (src/module/constante.f90)
  * parametre (src/module/parametre.f90)
  * array (src/module/array.f90)
  * sortie_erreur (src/module/sortie_erreur.f90)
  * generic_function_3p (src/integrals/three_point/generic_function_3p.f90)
  * translate (src/module/translate.f90)

src/integrals/four_point/function_4p4m/f4 [ Functions ]

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NAME

  function f4

USAGE

  complex = f4(s,t,s1,s2,s3,s4)

DESCRIPTION

  This function is the "finite part" of the scalar four dimensional three  
  mass four point function.

INPUTS

  * s -- a real (type ki), (p1+p2)^2
  * t -- a real (type ki), (p2+p3)^2
  * s1 -- a real (type ki), p1^2
  * s2 -- a real (type ki), p2^2
  * s3 -- a real (type ki), p3^2
  * s4 -- a real (type ki), p4^2

SIDE EFFECTS

  No side effects
  Affected by the variable rat_or_tot_par (in src/module/parametre.f90)

RETURN VALUE

  this function returns a complex (type ki)

EXAMPLE


src/integrals/four_point/function_4p4m/f4p4m [ Functions ]

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NAME

  Function f4p4m

USAGE

  real_dim_4 = f4p4m(dim,s24,s13,s12,s23,s34,par1,par2,par3,par4)

DESCRIPTION

  This function computes the six dimensional/eight dimensional
  three mass four point function with or without Feynman parameters 
  in the numerator.

INPUTS

  * dim -- a character (dimension 3), dim="n+2" six dimensional 
           three mass four point function, dim="n+4" eight dimensional
           three mass four point function
  * s24 -- a real (type ki), the S matrix element 2,4
  * s13 -- a real (type ki), the S matrix element 1,3
  * s12 -- a real (type ki), the S matrix element 1,2
  * s23 -- a real (type ki), the S matrix element 2,3
  * s34 -- a real (type ki), the S matrix element 3,4
  * par1 -- an integer, the label of the fourth Feynman parameter, if none, put 0
  * par2 -- an integer, the label of the third Feynman parameter, if none, put 0
  * par3 -- an integer, the label of the second Feynman parameter, if none, put 0
  * par4 -- an integer, the label of the first Feynman parameter, if none, put 0

  Be careful that, in this function, the arguments par1, par2, par3 and par4
  are mandatory, otherwise use the generic four point function f4p_np2 (f4p_np4).

SIDE EFFECTS

  No side effects

RETURN VALUE

  this function returns an array of four reals (type ki) corresponding to the 
  real imaginary part of 1/epsilon coefficient, real, imaginary part of the 
  finite part (as epsilon --> 0)

EXAMPLE

  If the user wants to compute:
  * a six dimensional three mass four point function 
    with no Feynman parameters in the numerator:
    real_dim_4 = f4p4m("n+2",s24,s13,s12,s23,s34,0,0,0,0)
  * a eight dimensional three mass four point function 
    with no Feynman parameters in the numerator:
    real_dim_4 = f4p4m("n+4",s24,s13,s12,s23,s34,0,0,0,0)
  * a six dimensional three mass four point function 
    with the Feynman parameter z1 in the numerator:
    real_dim_4 = f4p4m("n+2",s24,s13,s12,s23,s34,0,0,0,1)
  * a six dimensional three mass four point function 
    with the Feynman parameters z1^2*z2 in the numerator:
    real_dim_4 = f4p4m("n+2",s24,s13,s12,s23,s34,0,2,1,1)

src/integrals/four_point/function_4p4m/f4p4m_c [ Functions ]

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NAME

  Function f4p4m_c

USAGE

  complex_dim_2 = f4p4m_c(dim,s24,s13,s14,s12,s23,s34,par1,par2,par3,par4)

DESCRIPTION

  This function computes the same thing that the function f4p4m

INPUTS

  * dim -- a character (dimension 3), dim="n+2" six dimensional 
           two adjacent mass four point function, dim="n+4" eight dimensional
           two adjacent mass four point function
  * s24 -- a real (type ki), the S matrix element 2,4
  * s13 -- a real (type ki), the S matrix element 1,3
  * s14 -- a real (type ki), the S matrix element 1,4
  * s12 -- a real (type ki), the S matrix element 1,2
  * s23 -- a real (type ki), the S matrix element 2,3
  * s34 -- a real (type ki), the S matrix element 3,4
  * par1 -- an integer, the label of the fourth Feynman parameter, if none, put 0
  * par2 -- an integer, the label of the third Feynman parameter, if none, put 0
  * par3 -- an integer, the label of the second Feynman parameter, if none, put 0
  * par4 -- an integer, the label of the first Feynman parameter, if none, put 0

SIDE EFFECTS

  No side effects

RETURN VALUE

  this function returns an array of two complexs (type ki) corresponding to the 
   1/epsilon coefficient and the finite part (as epsilon --> 0)

EXAMPLE

  see function f4p4m