src/integral/two_point/function_2p0m [ Modules ]
NAME
Module function_2p0m
USAGE
use function_2p0m
DESCRIPTION
This module is used to compute the two-point function with zero momentum and two equal masses: I_2(0,m^2,m^2) and the two-point function with zero momentum and two different masses: I_2(0,m1^2,m2^2) with/without Feynman parameters in n dimensions
OUTPUT
This module exports the functions:
* f2p0m_1mi -- a function for the computation of the
two-point integrals
with zero momentum and two equal masses: I2({j})(0,m^2,m^2)
with/without Feynman parameters, in n dimensions
* f2p0m_m1m2 -- a function for the computation of the
two-point integrals
with zero momentum and two different masses: I2({j})(0,m1^2,m2^2)
with/without Feynman parameters, in n dimensions
scalar functions:
i20m1: computes the scalar two point function
with zero momentum and one propagator having nonzero mass:
I_2^n(0,0,m^2)
i20mm: computes the scalar two point function
with zero momentum and two massive propagators
with equal masses: I_2^n(0,m^2,m^2)
i20m1m2: computes the scalar two point function
with zero momentum and two massive propagators
with different masses: I_2^n(0,m1^2,m2^2)
USES
* precision (src/module/precision_golem.f90) * logarithme (src/module/z_log.f90) * sortie_erreur (src/module/sortie_erreur.f90) * constante (src/module/constante.f90)
src/integral/two_point/function_2p0m/f2p0m_1mi [ Functions ]
NAME
Function f2p0m_1mi
USAGE
real_dim4 = f2p0m_1mi(msq_r,par1,par2) complex_dim2 = f2p0m_1mi(msq_c,par1,par2)
DESCRIPTION
This function computes the two point function in n dimensions
with zero momentum and two massive propagators with m1=m2
with up to two Feynman parameters in the numerator.
It retuns an array of (4 reals / 2 complex) corresponding to the
real/imaginary part of the coefficient of the 1/epsilon term
and the real/imaginary part of the constant term.
corresponds to eqs.(A.9),(A.10) in hep-ph/0504267
note overall minus sign has to be corrected in first line of (A.10)
note also that for rank one A_j^{2,1}=MINUS I_2(j,...)
INPUTS
* m1_sq -- real/complex (type ki), the value of the mass * par1 -- an integer, the label of one Feynman parameter * par2 -- an integer, the label of the second Feynman parameter Note that par1,par2 are ordered internally, i.e. par1 <= par2, note also to use zero for par1, par2 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/complex (type ki) array of rank 1 and shape 4/2 corresponding to the real/imaginary part of the coefficient of the coefficient of the 1/epsilon term and the real/imaginary part of the constant term.
EXAMPLE
light-like-momentum two point function without Feynman parameters f2p0m_1mi(msq,0,0) with one Feynman parameter in the numerator z_1 f2p0m_1mi(msq,0,1) with two Feynman parameters in the numerator z_2**2 f2p0m_1mi(msq,2,2) with two Feynman parameters in the numerator z1*z_2 f2p0m_1mi(msq,1,2)
src/integral/two_point/function_2p0m/f2p0m_m1m2 [ Functions ]
NAME
Function f2p0m_m1m2
USAGE
real_dim6 = f2p0m_m1m2(m1sq_r,m2sq_r,par1,par2) complex_dim3 = f2p0m_m1m2(m1sq_c,m2sq_c,par1,par2)
DESCRIPTION
This function computes the two point function in n dimensions
with zero momentum and two massive propagators with m1 not= m2
with up to two Feynman parameters in the numerator.
It retuns an array of (6 reals / 3 complex) corresponding to the real/imaginary
part of the coefficient of the 1/epsilon**2 term, real/imaginary part of the
coefficient of the 1/epsilon term and the real/imaginary part of the
constant term.
corresponds to eqs.(A.8) in hep-ph/0504267
note that for rank one A_j^{2,1}=MINUS I_2(j,...)
INPUTS
* m1_sq,m2_sq -- real/complex (type ki), the values of the masses * par1 -- an integer, the label of one Feynman parameter * par2 -- an integer, the label of the second Feynman parameter Note that par1,par2 are ordered internally, i.e. par1 <= par2, note also to use zero for par1, par2 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/complex (type ki) array of rank 1 and shape 6/3 corresponding to the real/imaginary part of the coefficient of the 1/epsilon**2 term, real/imaginary part of the coefficient of the 1/epsilon term and the real/imaginary part of the constant term.
EXAMPLE
light-like-momentum two point function without Feynman parameters f2p0m_m1m2(m1sq,m2sq,0,0) with one Feynman parameter in the numerator z_1 f2p0m_m1m2(m1sq,m2sq,0,1) with two Feynman parameters in the numerator z_2**2 f2p0m_m1m2(m1sq,m2sq,2,2) with two Feynman parameters in the numerator z1*z_2 f2p0m_m1m2(m1sq,m2sq,1,2)