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, )