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