## src/form_factor/form_factor_4p [ Modules ]

NAME

Module form_factor_4p

USAGE

use form_factor_4p

DESCRIPTION

This module contains the different form factors for four point amplitudes.

OUTPUT

It exports nine functions: * a40 -- a function to compute A^{4,0} * a41 -- a function to compute A^{4,1} * a42 -- a function to compute A^{4,2} * a43 -- a function to compute A^{4,3} * a44 -- a function to compute A^{4,4} * b42 -- a function to compute B^{4,2} * b43 -- a function to compute B^{4,3} * b44 -- a function to compute B^{4,4} * c44 -- a function to compute C^{4,4} Note that a4xx, b4xx and c4xx are generic functions which can be called either with a set of integers or with an integer whose bits represents the set

USES

* precision (src/module/precision_golem.f90) * generic_function_4p (src/integrals/four_point/generic_function_4p.f90) * generic_function_3p (src/integrals/three_point/generic_function_3p.f90) * matrice_s (src/kinematic/matrice_s.f90) * array (src/module/array.f90) * sortie_erreur (src/module/sortie_erreur.f90) * form_factor_type (src/module/form_factor_type.f90) * constante (src/module/constante.f90)

## src/form_factor/form_factor_4p/a40_b [ Functions ]

NAME

Function a40_b

USAGE

type(form_factor) = a40_b(b_pin)

DESCRIPTION

This function defines the form factor A^{4,0}.

INPUTS

* b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

The result returned is of the type form_factor It returns an array of three complex (type ki) corresponding to the real part, imaginary part of the coefficient in front 1/epsilon^2, the real part, imaginary part of the 1/epsilon term and the real part, imaginary part of the constant term.

EXAMPLE

## src/form_factor/form_factor_4p/a40_s [ Functions ]

NAME

Function a40_s

USAGE

type(form_factor) = a40_s(set)

DESCRIPTION

This function defines the form factor A^{4,0}.

INPUTS

* set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

The result returned is of the type form_factor It returns an array of three complex (type ki) corresponding to the real part, imaginary part of the coefficient in front 1/epsilon^2, the real part, imaginary part of the 1/epsilon term and the real part, imaginary part of the constant term.

EXAMPLE

## src/form_factor/form_factor_4p/a41_b [ Functions ]

NAME

Function a41_b

USAGE

type(form_factor) = a41_b(l1,b_pin)

DESCRIPTION

This function defines the form factor A^{4,1}(l_1).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

The result returned is of the type form_factor It returns an array of three complex (type ki) corresponding to the real part, imaginary part of the coefficient in front 1/epsilon^2, the real part, imaginary part of the 1/epsilon term and the real part, imaginary part of the constant term.

EXAMPLE

## src/form_factor/form_factor_4p/a41_s [ Functions ]

NAME

Function a41_s

USAGE

type(form_factor) = a41_s(l1,set)

DESCRIPTION

This function defines the form factor A^{4,1}(l_1).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/a42_b [ Functions ]

NAME

Function a42_b

USAGE

type(form_factor) = a42_b(l1,l2,b_pin)

DESCRIPTION

This function defines the form factor A^{4,2}(l1,l2).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/a42_s [ Functions ]

NAME

Function a42_s

USAGE

type(form_factor) = a42_s(l1,l2,set)

DESCRIPTION

This function defines the form factor A^{4,2}(l1,l2).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/a43_b [ Functions ]

NAME

Function a43_b

USAGE

type(form_factor) = a43_b(l1,l2,l3,b_pin)

DESCRIPTION

This function defines the form factor A^{4,3}(l1,l2,l3).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * l3 -- an integer corresponding to a label in the set of the three remaining propagators * b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/a43_s [ Functions ]

NAME

Function a43_s

USAGE

type(form_factor) = a43_s(l1,l2,l3,set)

DESCRIPTION

This function defines the form factor A^{4,3}(l1,l2,l3).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * l3 -- an integer corresponding to a label in the set of the three remaining propagators * set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/a44_b [ Functions ]

NAME

Function a44_b

USAGE

type(form_factor) = a44_b(l1,l2,l3,l4,b_pin)

DESCRIPTION

This function defines the form factor A^{4,4}(l1,l2,l3,l4).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * l3 -- an integer corresponding to a label in the set of the three remaining propagators * l4 -- an integer corresponding to a label in the set of the three remaining propagators * b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/a44_s [ Functions ]

NAME

Function a44_s

USAGE

type(form_factor) = a44_s(l1,l2,l3,l4,set)

DESCRIPTION

This function defines the form factor A^{4,4}(l1,l2,l3,l4).

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * l3 -- an integer corresponding to a label in the set of the three remaining propagators * l4 -- an integer corresponding to a label in the set of the three remaining propagators * set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/b42_b [ Functions ]

NAME

Function b42_b

USAGE

type(form_factor) = b42_b(b_pin)

DESCRIPTION

This function defines the form factor B^{4,2}.

INPUTS

* set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/b42_s [ Functions ]

NAME

Function b42_s

USAGE

type(form_factor) = b42_s(set)

DESCRIPTION

This function defines the form factor B^{4,2}.

INPUTS

* set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/b43_b [ Functions ]

NAME

Function b43_b

USAGE

type(form_factor) = b43_b(l1,b_pin)

DESCRIPTION

This function defines the form factor B^{4,3}.

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/b43_s [ Functions ]

NAME

Function b43_s

USAGE

type(form_factor) = b43_s(l1,set)

DESCRIPTION

This function defines the form factor B^{4,3}.

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/b44_b [ Functions ]

NAME

Function b44_b

USAGE

type(form_factor) = b44_b(l1,l2,b_pin)

DESCRIPTION

This function defines the form factor B^{4,4}.

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/b44_s [ Functions ]

NAME

Function b44_s

USAGE

type(form_factor) = b44_s(l1,l2,set)

DESCRIPTION

This function defines the form factor B^{4,4}.

INPUTS

* l1 -- an integer corresponding to a label in the set of the three remaining propagators * l2 -- an integer corresponding to a label in the set of the three remaining propagators * set -- an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable set_ref)

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/c44_b [ Functions ]

NAME

Function c44_b

USAGE

type(form_factor) = c44_b(b_pin)

DESCRIPTION

This function defines the form factor C^{4,4}.

INPUTS

* b_pin -- an integer whose bits represent an array of integers of rank 1 corresponding to the label of the propagators pinched (removed from the original set which is in the global variable b_ref)

SIDE EFFECTS

No side effect, it uses the value of the global variables b_ref and s_mat_p

RETURN VALUE

EXAMPLE

## src/form_factor/form_factor_4p/c44_s [ Functions ]

NAME

Function c44_s

USAGE

type(form_factor) = c44_s(set)

DESCRIPTION

This function defines the form factor C^{4,4}.

INPUTS

SIDE EFFECTS

No side effect

RETURN VALUE

EXAMPLE