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## src/integrals/four_point/function_4p1m [ Modules ]

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NAME

  Module function_4p1m


USAGE

  use function_4p1m


DESCRIPTION

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


OUTPUT

  This module exports three functions f4p1m,f4p1m_c and f1
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_4p1m/f1 [ Functions ]

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NAME

  function f1


USAGE

  complex = f1(a,b,c)


DESCRIPTION

  This function is the "finite part" of the scalar four dimensional one/zero mass
four point function. The expression has been taken in
Nucl. Phys. {\bf B615} (2001) , 385


INPUTS

  * a -- a real (type ki), (p1+p2)^2
* b -- a real (type ki), (p2+p3)^2
* c -- 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_4p1m/f4p1m [ Functions ]

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NAME

  Function f4p1m


USAGE

  real_dim_4 = f4p1m(dim,s24,s13,s34,par1,par2,par3,par4)


DESCRIPTION

  This function computes the six dimensional/eight dimensional
one mass four point function with or without Feynman parameters
in the numerator, Note that it also computes the zero mass four
point function


INPUTS

  * dim -- a character (dimension 3), dim="n+2" six dimensional
one mass four point function, dim="n+4" eight dimensional
one 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
* 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 one mass four point function
with no Feynman parameters in the numerator:
real_dim_4 = f4p1m("n+2",s24,s13,s34,0,0,0,0)
* a eight dimensional one mass four point function
with no Feynman parameters in the numerator:
real_dim_4 = f4p1m("n+4",s24,s13,s34,0,0,0,0)
* a six dimensional zero mass four point function
with no Feynman parameters in the numerator:
real_dim_4 = f4p1m("n+2",s24,s13,0._ki,0,0,0,0)
* a six dimensional one mass four point function
with the Feynman parameter z1 in the numerator:
real_dim_4 = f4p1m("n+2",s24,s13,s34,0,0,0,1)
* a six dimensional one mass four point function
with the Feynman parameters z1^2*z2 in the numerator:
real_dim_4 = f4p1m("n+2",s24,s13,s34,0,2,1,1)


## src/integrals/four_point/function_4p1m/f4p1m_c [ Functions ]

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NAME

  Function f4p1m_c


USAGE

  complex_dim_2 = f4p1m_c(dim,s24,s13,s34,par1,par2,par3,par4)


DESCRIPTION

  This function computes the same thing that the fucntion f4p1m


INPUTS

  * dim -- a character (dimension 3), dim="n+2" six dimensional
one mass four point function, dim="n+4" eight dimensional
one 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
* 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 f4p1m