#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
li = psd.LoopIntegralFromPropagators(
loop_momenta = ['k1','k2'],
external_momenta = ['p1','p2','p3','p4'],
propagators = ['k1**2-m1sq','(k1-p1)**2-m1sq','(k1-p1-p2)**2-m1sq','k2**2-m3sq','(k2-p3)**2-m3sq','(k1-k2-p1-p2-p3)**2-m2sq','(k1+k2)**2-m2sq'],
powerlist = [1,1,1,1,1,1,1],
replacement_rules = [
('p1*p1', 0),
('p2*p2', 0),
('p3*p3', 0),
('p4*p4', 0),
('p1*p2', 's/2'),
('p2*p3', 't/2'),
('p1*p3', '-s/2') ]
)
Mandelstam_symbols = ['s', 't']
mass_symbols = ['m1sq','m2sq','m3sq']
psd.loop_package(
#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
li = psd.LoopIntegralFromPropagators(
propagators = ['k1^2', '(k1+p1+p2)^2', '(k1-k2)^2', '(k1-k2+p1)^2-mZ^2', '(k2)^2', '(k2+p2)^2'],
loop_momenta = ['k1','k2'],
external_momenta = ['p1','p2','p3','p4'],
replacement_rules = [
('p1*p1', 0),
('p2*p2', 0),
('p3*p3', 's'),
('p1*p2', 's/2'),
('p2*p3', '-s/2'),
('p1*p3', '-s/2'),
('s', 'mZ^2'),
('mZ', 1)
]
)
Mandelstam_symbols = []
mass_symbols = []
psd.loop_package(
#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
li = psd.LoopIntegralFromPropagators(
loop_momenta = ['k1','k2','k3'],
external_momenta = ['p'],
propagators = ['(k1+p)**2-m1sq','(k1-k3)**2-m1sq','k2**2-m2sq','(k2-k3)**2-m3sq'],
powerlist = [1,1,1,1],
replacement_rules = [ ('p*p','s') ]
)
Mandelstam_symbols = ['s']
mass_symbols = ['m1sq','m2sq','m3sq']
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
#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
li = psd.LoopIntegralFromPropagators(loop_momenta=['k1', 'k2'],
external_momenta=['p1', 'p2', 'p3'],
propagators=[
'(k1+p1)**2', '(k2+p1+p2)**2',
'(k2-p3)**2', '(k1-k2+p3)**2',
'(k1-k2)**2-mm'
],
powerlist=[1, 1, 1, 1, 1],
replacement_rules=[('p1*p1', '0'),
('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
#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
li = psd.LoopIntegralFromPropagators(propagators=[
'k1**2-msq', '(k1+p1+p2)**2-msq', 'k2**2-msq', '(k2+p1+p2)**2-msq',
'(k1+p1)**2-msq', '(k1-k2)**2', '(k2-p3)**2-msq', '(k2+p1)**2',
'(k1-p3)**2'
],
powerlist=[1, 1, 0, 1, 1, 1, 1, 0, 0],
loop_momenta=['k1', 'k2'],
replacement_rules=[('p1*p1', 0),
('p2*p2', 0),
('p3*p3', 0),
('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],
#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
li = psd.LoopIntegralFromPropagators(
loop_momenta = ['k1','k2'],
external_momenta = ['p1','p2','p3','p4'],
Lorentz_indices = ['mu'],
propagators = ['k1**2','(k1+p2)**2','(k1-p1)**2','(k1-k2)**2','(k2+p2)**2','(k2-p1)**2','(k2+p2+p3)**2','(k1+p3)**2'],
powerlist = [1,1,1,1,1,1,1,0],
numerator = 'k1(mu)*k1(mu) + 2*k1(mu)*p3(mu) + p3(mu)*p3(mu)',
replacement_rules = [
('p1*p1', 0),
('p2*p2', 0),
('p3*p3', 0),
('p4*p4', 0),
('p1*p2', 's/2'),
('p2*p3', 't/2'),
('p1*p3', '-s/2-t/2')
]
)
Mandelstam_symbols = ['s', 't']
mass_symbols = []
#!/usr/bin/env python3
import pySecDec as psd
# example is 2-loop bubble with five propagators, two of them massive
if __name__ == "__main__":
# define Feynman Integral
li = psd.LoopIntegralFromPropagators(propagators=[
'k1**2-msq_', '(k1+k2)**2-msq_', '(k1+p1)**2', 'k2**2', '(k1+k2+p1)**2'
],
loop_momenta=['k1', 'k2'],
external_momenta=['p1'],
replacement_rules=[('p1*p1', 'psq'),
('msq_', 'msq')])
# find the regions and expand the integrals using expansion by regions
regions_generator_args = psd.loop_regions(
name='bubble2L_smallm',
loop_integral=li,
smallness_parameter='msq',
expansion_by_regions_order=1
) # this has to be 1 to catch the ultra-soft region
# generate code that will calculate the sum of all regions and all orders in
# the smallness parameter
psd.sum_package('bubble2L_smallm',
regions_generator_args,
regulators=['eps'],
requested_orders=[0],
#!/usr/bin/env python3
import pySecDec as psd
if __name__ == "__main__":
# example is case 8 of hep-ph/9704353, hep-ph/9605392
li = psd.LoopIntegralFromPropagators(propagators=[
'(k1+p1)**2', '(k1-p2)**2', '(k2+p1)**2', '(k2-p2)**2', 'k2**2',
'(k1-k2)**2-msq'
],
loop_momenta=['k1', 'k2'],
external_momenta=['p1', 'p2'],
replacement_rules=[('p1*p1', 0),
('p2*p2', 0),
('p1*p2', 's/2')])
Mandelstam_symbols = ['s']
mass_symbols = ['msq']
psd.loop_package(
name='triangle2L_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**(2+2*eps)''',
# the highest order of the final epsilon expansion
requested_orders=[0],