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src/integral/three_point/function_3p3m [ Modules ]

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NAME

  Module function_3p3m

USAGE

  use function_3p3m

DESCRIPTION

  This module is used to compute the three off-shell external leg three point function
  with no internal leg with/without Feynman parameters in n, n+2 dimensions

OUTPUT

  This module exports three functions:
  * f3p3m -- a function for the computation of the three mass three 
    point function with/without Feynman parameters in n, n+2 dimensions
  * f3p3m_c -- a function which computes the same thing as f3p3m, only 
    the format of the return values is different
  * i3_3mass -- a function for the computation of the scalar three mass three 
    point function in n dimensions

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_2p (src/integrals/two_point/generic_function_2p.f90)
  * multiply_div (src/module/multiply_div.f90)
  * s_matrix_type (src/module/s_matrix_type.f90)

src/integral/three_point/function_3p3m/f3p3m [ Functions ]

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NAME

  Function f3p3m

USAGE

  real_dim4 = f3p3m(dim,m1,m2,m3,par1,par2,par3)

DESCRIPTION

  This function computes the three off-shell external leg three point function in n 
  and n+2 dimension. It uses the formula of ref. 
  It switches to numerical evaluation if the Gram determinant is smaller than
  coupure_3p3m (in src/module/parametre.f90)

INPUTS

  * dim -- a character (length 3), to compute in n or n+2 dimensions, 
    the values are "ndi", "n+2"
  * m1 -- a real (type ki), the first mass squared
  * m2 -- a real (type ki), the second mass squared
  * m3 -- a real (type ki), the third mass squared
  * par1 -- an integer, the label of the third Feynman parameter
  * par2 -- an integer, the label of the second Feynman parameter
  * par3 -- an integer, the label of the first Feynman parameter
  Note that par1,par2 and par3 are supposed to be ordered, i.e.
  par1 <= par2 <= par3, note also that put zero for par1, par2 or par3
  if this Feynman parameter does not exist.
  Use the routine tri_int(t_in,t_out) to order the labels in the module 
  tri_croissant (src/module/tri.f90)

SIDE EFFECTS

  No side effect

RETURN VALUE

  An real (type ki) array of rank 1 and shape 4 corresponding to 
  the real/imaginary part of the coefficient of the 1/epsilon term
  and the real/imaginary part of the constant term. If par1 and/or par2
  are different from zero for dim="n+2", an error is returned.

EXAMPLE

 three mass three point function without Feynman parameters in n dimensions
 f3p3m("ndi",m1,m2,m3,0,0,0) 
 with one Feynman parameter at the numerator z_1 in n dimensions 
 f3p3m("ndi",m1,m2,m3,0,0,1) 
 with three Feynman parameters at the numerator z_2^2 z_3 in n dimensions 
 f3p3m("ndi",m1,m2,m3,2,2,3) 
 three mass three point function without Feynman parameters in n+2 dimensions 
 f3p3m("n+2",m1,m2,m3,0,0,0) 
 with one Feynman parameter at the numerator z_1 in n+2 dimensions 
 f3p3m("n+2",m1,m2,m3,0,0,1) 

src/integral/three_point/function_3p3m/f3p3m_c [ Functions ]

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NAME

  Function f3p3m_c

USAGE

  complex_dim3 = f3p3m_c(dim,m1,m2,m3,par1,par2,par3)

DESCRIPTION

  It computes the same thing that the function f3p3m, but the returned
  value is a complex (type ki) array of rank 1 and shape 2

INPUTS

  * dim -- a character (length 3), to compute in n or n+2 dimensions, 
    the values are "ndi", "n+2"
  * m1 -- a real (type ki), the first mass squared
  * m2 -- a real (type ki), the second mass squared
  * m3 -- a real (type ki), the third mass squared
  * par1 -- an integer, the label of the third Feynman parameter
  * par2 -- an integer, the label of the second Feynman parameter
  * par3 -- an integer, the label of the first Feynman parameter
  Note that par1,par2 and par3 are supposed to be ordered, i.e.
  par1 <= par2 <= par3, note also that put zero for par1, par2 or par3
  if this Feynman parameter does not exist.
  Use the routine tri_int(t_in,t_out) to order the labels in the module 
  tri_croissant (src/module/tri.f90)

SIDE EFFECTS

  No side effect

RETURN VALUE

  An complex (type ki) array of rank 1 and shape 2 corresponding to 
  the (real part,imaginary part) of the coefficient of the 1/epsilon term
  and the (real part,imaginary part) of the constant term. If par1 and/or par2
  are different from zero for dim="n+2", an error is returned.

EXAMPLE


src/integral/three_point/function_3p3m/i3_3mass [ Functions ]

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NAME

  Function i3_3mass

USAGE

  complex = i3_3mass(m1,m2,m3)

DESCRIPTION

  This function computes the scalar three off-shell external leg three point function
  in n dimension

INPUTS

  * m1 -- a real (type ki), the first mass squared
  * m2 -- a real (type ki), the second mass squared
  * m3 -- a real (type ki), the third mass squared

SIDE EFFECTS

  No side effect, it uses the value of rat_or_tot_par 
  (in src/module/parametre.f90)

RETURN VALUE

  It returns a complex (type ki)

EXAMPLE