psd.loop_package(
name = 'banana_3mass',
loop_integral = li,
real_parameters = Mandelstam_symbols + mass_symbols,
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders = [0],
# the optimization level to use in FORM (can be 0, 1, 2, 3)
form_optimization_level = 4,
# the WorkSpace parameter for FORM
form_work_space = '200M',
# the method to be used for the sector decomposition
# valid values are ``iterative`` or ``geometric`` or ``geometric_ku``
decomposition_method = 'geometric',
# if you choose ``geometric[_ku]`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
# whether or not to produce code to perform the contour deformation
# contour deformation is not required if we only want to compute euclidean points (all Mandelstam invariants negative)
contour_deformation = True,
# list of qmc integral transforms for which to build code
pylink_qmc_transforms = ['korobov2x2']
)
psd.loop_package(
name = 'hyperelliptic',
loop_integral = li,
real_parameters = Mandelstam_symbols + mass_symbols,
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders = [0],
# the optimization level to use in FORM (can be 0, 1, 2, 3)
form_optimization_level = 4,
# the method to be used for the sector decomposition
# valid values are ``iterative`` or ``geometric`` or ``geometric_ku``
decomposition_method = 'geometric',
# if you choose ``geometric[_ku]`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
# whether or not to produce code to perform the contour deformation
# contour deformation is not required if we only want to compute euclidean points (all Mandelstam invariants negative)
contour_deformation = True,
# no symmetries --> no need to run the full symmetry finder
use_Pak = False,
)
Mandelstam_symbols = ['s12', 's23']
mass_symbols = ['mt2', 'mH2', 'mZ2']
psd.loop_package(
name='hz2L_nonplanar',
loop_integral=li,
real_parameters=Mandelstam_symbols + mass_symbols,
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders=[0],
# the optimization level to use in FORM (can be 0, 1, 2, 3)
form_optimization_level=4,
# the WorkSpace parameter for FORM
form_work_space='200M',
# the method to be used for the sector decomposition
# valid values are ``iterative`` or ``geometric`` or ``geometric_ku``
decomposition_method='geometric',
# if you choose ``geometric[_ku]`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
# there are no symmetries
use_dreadnaut=False,
use_Pak=False,
)
psd.loop_package(
name = 'triangle2L_split',
additional_prefactor = '-exp(2*EulerGamma*eps)',
loop_integral = li,
real_parameters = Mandelstam_symbols + mass_symbols,
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders = [0],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level = 2,
# the WorkSpace parameter for FORM
form_work_space = '1G',
# the method to be used for the sector decomposition
# valid values are ``iterative`` or ``geometric`` or ``geometric_ku``
decomposition_method = 'iterative',
# if you choose ``geometric[_ku]`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
# whether or not to produce code to perform the contour deformation
# contour deformation is not required if we only want to compute euclidean points (all Mandelstam invariants negative)
contour_deformation = True,
# there are singularities at one due to ``s = mZ^2``
split = True,
)
('p2*p2', '0'),
('p3*p3', '0'),
('p1*p2', 's/2'),
('p1*p3', 't/2'),
('p2*p3',
'(mm-s-t)/2')])
Mandelstam_symbols = ['s', 't']
mass_symbols = ['mm']
psd.loop_package(
name='Nbox2L_split_c',
loop_integral=li,
real_parameters=Mandelstam_symbols + mass_symbols,
additional_prefactor='1',
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders=[0],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level=4,
# the method to be used for the sector decomposition
# valid values are ``iterative`` and ``geometric``
decomposition_method='iterative',
contour_deformation=True,
# there are singularities at one due to ``p4*p4 = mm``
#split = True # not needed for (quasi-)finite integrals
pylink_qmc_transforms=['korobov3'])
('p1*p2', 's/2'),
('p2*p3',
'pp4/2-s/2-t/2'),
('p1*p3', 't/2')])
Mandelstam_symbols = ['s', 't', 'pp4']
mass_symbols = ['msq']
psd.loop_package(
name='elliptic2L_euclidean',
loop_integral=li,
real_parameters=Mandelstam_symbols + mass_symbols,
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders=[0],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level=2,
# the WorkSpace parameter for FORM
form_work_space='100M',
# the method to be used for the sector decomposition
# valid values are ``iterative`` and ``geometric``
decomposition_method='iterative',
# if you choose ``geometric`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
contour_deformation=False)
psd.loop_package(
name = 'triangle3L',
loop_integral = li,
real_parameters = Mandelstam_symbols + mass_symbols,
#additional_prefactor = 'gamma( (4-2*eps)/2-1 )**3',
additional_prefactor = '(-eps*gamma(-eps))**3', # work around slow gamma expansion in sympy 1.0
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders = [4],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level = 2,
# the WorkSpace parameter for FORM
form_work_space = '100M',
# the method to be used for the sector decomposition
# valid values are ``iterative`` or ``geometric`` or ``geometric_ku``
decomposition_method = 'iterative',
# if you choose ``geometric[_ku]`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
contour_deformation = False
)
psd.loop_package(
name = 'formfactor4L',
loop_integral = li,
# normalization as defined in equation (2.4) of arXiv:1510.06758
additional_prefactor = sp.gamma(li.dimensionality/2 - 1) ** li.L,
real_parameters = Mandelstam_symbols + mass_symbols,
# the highest order of the final epsilon expansion --> change this value to whatever you think is appropriate
requested_orders = [1],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level = 4,
# the WorkSpace parameter for FORM
form_work_space = '1G',
# the method to be used for the sector decomposition
# valid values are ``iterative`` and ``geometric``
decomposition_method = 'geometric',
# if you choose ``geometric`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
contour_deformation = False,
# there are no symmetries
use_dreadnaut = False,
use_Pak = False,
)
psd.loop_package(
name='bubble2L_full',
loop_integral=li,
real_parameters=Mandelstam_symbols + mass_symbols,
#additional_prefactor = '''gamma(1-2*eps)/(gamma(1+eps)*gamma(1+eps)*gamma(1-eps)*gamma(1-eps))*msq**(1+2*eps)''',
# in hep-ph/9605392 the i^2 from i*Pi^(D/2) per loop is pulled out
additional_prefactor='-1',
# the highest order of the final epsilon expansion
requested_orders=[0],
# the optimization level to use in FORM (can be 0, 1, 2, 3, 4)
form_optimization_level=2,
# the WorkSpace parameter for FORM
form_work_space='1G',
# the method to be used for the sector decomposition
# valid values are ``iterative`` and ``geometric``
decomposition_method='geometric',
# if you choose ``geometric`` and 'normaliz' is not in your
# $PATH, you can set the path to the 'normaliz' command-line
# executable here
#normaliz_executable='/path/to/normaliz',
# whether or not to produce code to perform the contour deformation
contour_deformation=True,
)