src/integrals/four_point/generic_function_4p [ Modules ]
NAME
Module generic_function_4p
USAGE
use generic_function_4p
DESCRIPTION
This module contains the generic routines to compute the four point functions in n+2 and n+4 dimensions. It can compute the zero mass, one mass, two mass adjacent, two mass opposite, three mass and four mass four point functions with massless internal lines It can also calculate the IR divergent boxes with massive internal lines, but ONLY in the scalar case. For the latter, the (4-2*eps)-dim expressions are implemented
OUTPUT
It exports three public routines: * f4p -- a function to compute the four point function in n dimensions (used donly if internal masses are present) * f4p_np2 -- a function to compute the four point function in n+2 dimensions * f4p_np4 -- a function to compute the four point function in n+4 dimensions
USES
* precision (src/module/preci_double.f90) * matrice_s (src/kinematic/matrice_s.f90) ( only : dim_s, set_ref ) * array (src/module/array.f90) * tri_croissant (src/module/tri.f90) * constante (src/module/constante.f90) * function_4p1m (src/integrals/four_point/function_4p1m.f90) * function_4p2m_opp (src/integrals/four_point/function_4p2m_opp.f90) * function_4p2m_adj (src/integrals/four_point/function_4p2m_adj.f90) * function_4p3m (src/integrals/four_point/function_4p3m.f90) * function_4p4m (src/integrals/four_point/function_4p4m.f90) * cache (src/module/cache.f90) * sortie_erreur (src/module/sortie_erreur.f90) * generic_function_3p (src/integrals/generic_function_3p.f90) * parametre (src/module/parametre.f90), only : coupure_3p2m,coupure_3p3m,coupure_4p1m, coupure_4p2m_opp,coupure_4p2m_adj,coupure_4p3m,coupure_4p4m * equal (src/module/equal.f90)
src/integrals/four_point/generic_function_4p/f4p [ Functions ]
NAME
Function f4p
USAGE
real_dim4 = f4p(s_mat,b_pro,b_pin,parf1,parf2,parf3,parf4)
DESCRIPTION
This function computes the generic four point function in n dimensions only scalar case is implemented!!!
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators * b_pin -- an integer which represents the set of the pinched propagators * parf1 -- an integer (optional), the label of the one Feynman parameter * parf2 -- an integer (optional), the label of the second Feynman parameter * parf3 -- an integer (optional), the label of the third Feynman parameter * parf4 -- an integer (optional), the label of the forth Feynman parameter
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 6
EXAMPLE
src/integrals/four_point/generic_function_4p/f4p_np2 [ Functions ]
NAME
Function f4p_np2
USAGE
real_dim2 = f4p_np2(s_mat,b_pro,b_pin,parf1,parf2,parf3,parf4)
DESCRIPTION
This function computes recursively the generic four point function in n+2 dimensions, with or without Feynman parameters in the numerator using the formula of JHEP 10 (2005) 015.
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators * b_pin -- an integer which represents the set of the pinched propagators * parf1 -- an integer (optional), the label of the one Feynman parameter * parf2 -- an integer (optional), the label of the second Feynman parameter * parf3 -- an integer (optional), the label of the third Feynman parameter * parf4 -- an integer (optional), the label of the forth Feynman parameter
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 2
EXAMPLE
src/integrals/four_point/generic_function_4p/f4p_np2_numeric [ Functions ]
NAME
Function f4p_np2_numeric
USAGE
real_dim2 = f4p_np2_numeric(s_mat,b_pro,parf1,parf2,parf3,parf4)
DESCRIPTION
This function computes numerically the generic four point function in n+2 dimensions, with or without Feynman parameters in the numerator
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators * par1 -- an integer, the label of the one Feynman parameter * par2 -- an integer, the label of the second Feynman parameter * par3 -- an integer, the label of the third Feynman parameter * par4 -- an integer, the label of the forth Feynman parameter
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 2
EXAMPLE
src/integrals/four_point/generic_function_4p/f4p_np2_sca [ Functions ]
NAME
Function f4p_np2_sca
USAGE
real_dim2 = f4p_np2_sca(s_mat,b_pro)
DESCRIPTION
This function computes the generic four point function in n+2 dimensions, without Feynman parameters in the numerator
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 2
EXAMPLE
src/integrals/four_point/generic_function_4p/f4p_np4 [ Functions ]
NAME
Function f4p_np4
USAGE
real_dim4 = f4p_np4(s_mat,b_pro,b_pin,parf1,parf2,parf3,parf4)
DESCRIPTION
This function computes recursively the generic four point function in n+4 dimensions, with or without Feynman parameters in the numerator
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators * b_pin -- an integer which represents the set of the pinched propagators * parf1 -- an integer (optional), the label of the one Feynman parameter * parf2 -- an integer (optional), the label of the second Feynman parameter * parf3 -- an integer (optional), the label of the third Feynman parameter * parf4 -- an integer (optional), the label of the forth Feynman parameter
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 4.
EXAMPLE
src/integrals/four_point/generic_function_4p/f4p_np4_numeric [ Functions ]
NAME
Function f4p_np4_numeric
USAGE
real_dim4 = f4p_np4_numeric(s_mat,b_pro,parf1,parf2,parf3,parf4)
DESCRIPTION
This function computes numerically the generic four point function in n+4 dimensions, with or without Feynman parameters in the numerator
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators * parf1 -- an integer (optional), the label of the one Feynman parameter * parf2 -- an integer (optional), the label of the second Feynman parameter * parf3 -- an integer (optional), the label of the third Feynman parameter * parf4 -- an integer (optional), the label of the forth Feynman parameter
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 4.
EXAMPLE
src/integrals/four_point/generic_function_4p/f4p_sca [ Functions ]
NAME
Function f4p_sca
USAGE
real_dim6 = f4p_sca(s_mat,b_pro)
DESCRIPTION
This function computes the generic four point function in n dimensions, without Feynman parameters in the numerator
INPUTS
* s_mat -- a real (type ki) array of rank 2, the S matrix * b_pro -- an integer which represents the set of the four unpinched propagators
SIDE EFFECTS
No side effect
RETURN VALUE
It returns a real (type ki) array of rank 1 and shape 6
EXAMPLE