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src/integrals/four_point/generic_function_4p [ Modules ]

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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/precision_golem.f90)
  * matrice_s (src/kinematic/matrice_s.f90) ( only : dim_s, set_ref )
  * s_matrix_type (src/module/s_matrix_type.f90)
  * 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 ]

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NAME

  Function f4p

USAGE

  cmplx_dim3 = 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_p -- a derived type s_matrix_poly, 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 complex (type ki) array of rank 1 and shape 3

EXAMPLE


src/integrals/four_point/generic_function_4p/f4p_np2 [ Functions ]

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NAME

  Function f4p_np2

USAGE

  complex = 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_p -- a derived type (s_matrix_poly), giving 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 first 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 complex (type ki) number

 NOTE

 This function has been changed! It accepts only a s_matrix_poly-type as input 
 and returns a complex number instead of a real array!

src/integrals/four_point/generic_function_4p/f4p_np2_numeric [ Functions ]

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NAME

  Function f4p_np2_numeric

USAGE

  complex = f4p_np2_numeric(s_mat_p,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_p -- a derived type s_matrix_poly, 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 complex number!

NOTES

 This function has been changed! It only accepts a s_matrix_poly type object!
 It returns a complex number!

src/integrals/four_point/generic_function_4p/f4p_np2_sca [ Functions ]

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NAME

  Function f4p_np2_sca

USAGE

  complex = f4p_np2_sca(s_mat_p,b_pro,b_pin)

DESCRIPTION

  This function computes the generic four point function in n+2 dimensions, 
  without Feynman parameters in the numerator

INPUTS

  * s_mat_p -- a type s_matrix_poly object, 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 complex (type ki) number!

 NOTE

 This function now returns a complex number instaed of a real array!

src/integrals/four_point/generic_function_4p/f4p_np4 [ Functions ]

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NAME

  Function f4p_np4

USAGE

  complex_dim2 = f4p_np4(s_mat_p,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_p -- a type s_matrix_poly object, 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 complex (type ki) array of rank 1 and shape 2.

NOTES

 This function has been changed! It only accepts a s_matrix_poly type object as input.
 It returns a complex instead of a real array!

src/integrals/four_point/generic_function_4p/f4p_np4_numeric [ Functions ]

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NAME

  Function f4p_np4_numeric

USAGE

  complex_dim2 = f4p_np4_numeric(s_mat_p,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_p -- a derived type s_matrix_poly, 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 complex (type ki) array of rank 1 and shape 2.

NOTES

 This function has been changed! It only accepts a s_matrix_poly type object!
 It returns a complex array!

src/integrals/four_point/generic_function_4p/f4p_sca [ Functions ]

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NAME

  Function f4p_sca

USAGE

  real_dim6 = f4p_sca(s_mat_p,b_pro)

DESCRIPTION

  This function computes the generic four point function in n  dimensions, 
  without Feynman parameters in the numerator

INPUTS

  * s_mat_p -- a s_matrix_poly type, 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