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src/integral/two_point/function_2p0m [ Modules ]

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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 ]

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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 ]

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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)