src/integral/three_point/function_3p3m [ Modules ]
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 ]
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 ]
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 ]
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