def evaluate_kernel(self, xs, kTs, parent):
# Retrieve the collinear variable x
x = xs[0]
kT = kTs[0]
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None, ((parent, (kT, )), ), ],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None},
(1, 0): {'finite': None}, }
})
# The factor 'x' that should be part of the initial_state_crossing_factor cancels
# against the extra prefactor 1/x in the collinear factorization formula
# (see Eq. (8) of NNLO compatible NLO scheme publication arXiv:0903.1218v2)
initial_state_crossing_factor = 1.
# Correct for the ratio of color-averaging factor between the real ME
# initial state flavor (quark) and the one of the reduced Born ME (gluon)
initial_state_crossing_factor *= (self.NC**2-1)/float(self.NC)
z = 1./x
norm = initial_state_crossing_factor * self.TR
# We re-use here the Altarelli-Parisi Kernel of the P_q\bar{q} final state kernel
evaluation['values'][(0, 0)]['finite'] = norm
evaluation['values'][(1, 0)]['finite'] = 4. * norm * z*(1.-z) / kT.square()
return evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables and compute basic quantities
z1, z2, z3 = zs
s12 = sij(1, 2, zs, kTs)
s13 = sij(1, 3, zs, kTs)
s23 = sij(2, 3, zs, kTs)
s123 = s12 + s13 + s23
t123 = tijk(1, 2, 3, zs, kTs, s_ij=s12, s_ik=s13, s_jk=s23)
# Assemble kernel
sqrbrk = -(t123**2) / (s12 * s123)
sqrbrk += (4 * z3 + (z1 - z2)**2) / (z1 + z2)
sqrbrk += z1 + z2 - s12 / s123
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'values': {
(0, 0): {
'finite': None
}
}
})
evaluation['values'][(
0, 0)]['finite'] = self.CF * self.TR * s123 / (2 * s12) * sqrbrk
return evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables and compute basic quantities
z1, z2, z3 = zs
k1, k2, k3 = kTs
s12 = sij(1, 2, zs, kTs)
s13 = sij(1, 3, zs, kTs)
s23 = sij(2, 3, zs, kTs)
s123 = s12 + s13 + s23
# Assemble kernel
kernel = self.evaluate_unsymmetrized_kernel((z1, z2, z3),
(s12, s13, s23, s123), kTs)
kernel += self.evaluate_unsymmetrized_kernel(
(z2, z1, z3), (s12, s23, s13, s123), (k2, k1, k3))
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'values': {
(0, 0): {
'finite': None
}
}
})
evaluation['values'][(0, 0)]['finite'] = kernel
return evaluation
def evaluate_kernel(self, xs, kTs, parent):
# Retrieve the collinear variable x
x = xs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None}}
})
# The factor 'x' that should be part of the initial_state_crossing_factor cancels
# against the extra prefactor 1/x in the collinear factorization formula
# (see Eq. (8) of NNLO compatible NLO scheme publication arXiv:0903.1218v2)
initial_state_crossing_factor = 1.
# Correct for the ratio of color-averaging factor between the real ME
# initial state flavor (quark) and the one of the reduced Born ME (quark)
initial_state_crossing_factor *= 1.
z = 1./x
# We re-use here the Altarelli-Parisi Kernel of the P_qg final state kernel, including
# its soft subtraction
# We must subtract the soft-collinear (CxS *not* SxC) from this contribution:
# P_qg = self.CF * ( (1.+z**2)/(1.-z) )
# CxS(P_qg) = self.CF * ( 2 / (x - 1) ) = self.CF * ( 2 z / (1 - z) )
# P_qg-CxS(P_qg) = self.CF * (1 + z**2 - 2*z) / (1 - z) = self.CF * ( 1 - z)
norm = initial_state_crossing_factor * self.CF
evaluation['values'][(0, 0)]['finite'] = norm * (1 - z)
return evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables
z = zs[0]
kT = kTs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None, ((parent,( kT, )), ), ],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None},
(1, 0): {'finite': None}, }
})
# The line below implements the g_{\mu\nu} part of the splitting kernel.
# Notice that the extra longitudinal terms included in the spin-correlation 'None'
# from the relation:
# \sum_\lambda \epsilon_\lambda^\mu \epsilon_\lambda^{\star\nu}
# = g^{\mu\nu} + longitudinal terms
# are irrelevant because Ward identities evaluate them to zero anyway.
# We must subtract the soft-collinear (CxS *not* SxC) from this contribution:
# P_gg = 2.*self.CA * ( (1.-z) / z + z / (1.- z) )
# CxS(P_gg) = 2.*self.CA * ( (1.-z) / z + z / (1.- z) )
# SxC(P_gg) = 2.*self.CA * ( 1 / z + 1 / (1.- z) )
# P_gg-CxS(P_gg) = 0
# P_gg-SxC(P_gg) = -4.*self.CA
evaluation['values'][(0, 0)]['finite'] = -4.*self.CA
evaluation['values'][(1, 0)]['finite'] = -2.*self.CA * 2.*z*(1.-z) / kT.square()
return evaluation
def kernel(self, zs, kTs, parent, reduced_kinematics):
# Retrieve the collinear variables
z = zs[0]
kT = kTs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [
None,
((parent, (kT, )), ),
],
'color_correlations': [None],
'reduced_kinematics': [reduced_kinematics],
'values': {
(0, 0, 0): {
'finite': None
},
(1, 0, 0): {
'finite': None
},
}
})
# Compute the kernel
# The line below implements the g_{\mu\nu} part of the splitting kernel.
# Notice that the extra longitudinal terms included in the spin-correlation 'None'
# from the relation:
# \sum_\lambda \epsilon_\lambda^\mu \epsilon_\lambda^{\star\nu}
# = g^{\mu\nu} + longitudinal terms
# are irrelevant because Ward identities evaluate them to zero anyway.
evaluation['values'][(0, 0, 0)]['finite'] = \
0.
evaluation['values'][(1, 0, 0)]['finite'] = \
-2. * self.CA * 2. * z * (1. - z) / kT.square()
return evaluation
def evaluate_kernel(self, xs, kTs, parent):
# Retrieve the collinear variable x
x = xs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None}}
})
# The factor 'x' that should be part of the initial_state_crossing_factor cancels
# against the extra prefactor 1/x in the collinear factorization formula
# (see Eq. (8) of NNLO compatible NLO scheme publication arXiv:0903.1218v2)
initial_state_crossing_factor = 1.
# Correct for the ratio of color-averaging factor between the real ME
# initial state flavor (gluon) and the one of the reduced Born ME (quark)
initial_state_crossing_factor *= (self.NC/float(self.NC**2-1))
z = 1./x
norm = initial_state_crossing_factor * self.CF
# We re-use here the Altarelli-Parisi Kernel of the P_gq final state kernel
evaluation['values'][(0, 0)]['finite'] = norm * ( (1.+(1.-z)**2)/z )
return evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables
z = zs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None}}
})
evaluation['values'][(0, 0)]['finite'] = self.CF * (1.+(1.-z)**2)/z
return evaluation
def soft_kernel(self, evaluation, colored_partons, all_steps_info, global_variables):
"""Evaluate a collinear type of splitting kernel, which *does* need to know about the reduced process
Should be specialised by the daughter class if not dummy
"""
new_evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [ None, ],
'color_correlations': [ ],
'reduced_kinematics': evaluation['reduced_kinematics'],
'values': { }
})
overall_lower_PS_point = all_steps_info[-1]['lower_PS_point']
soft_leg_number = all_steps_info[-1]['bundles_info'][0]['final_state_children'][0]
pr = all_steps_info[-1]['higher_PS_point'][soft_leg_number]
colored_parton_numbers = sorted(colored_partons.keys())
for i, a in enumerate(colored_parton_numbers):
for b in colored_parton_numbers[i:]:
# Write the eikonal for that pair
if a!=b:
mult_factor = 1.
else:
mult_factor = 1./2.
pi = overall_lower_PS_point[a]
pk = overall_lower_PS_point[b]
composite_weight = EpsilonExpansion({'finite': 0.})
for (sc, cc, rk), coll_weight in evaluation['values'].items():
if evaluation['spin_correlations'][sc] is None:
# We *subtract* here the contribution because the non-spin-correlated contributin is -g^{\mu\nu}
composite_weight -= SoftKernels.eikonal_g(self, pi, pk, pr, spin_corr_vector=None)*EpsilonExpansion(coll_weight)
else:
# Normally the collinear current should have built spin-correlations with the leg number corresponding
# to the soft one in the context of this soft current
assert len(evaluation['spin_correlations'][sc])==1
parent_number, spin_corr_vecs = evaluation['spin_correlations'][sc][0]
assert soft_leg_number==parent_number
assert len(spin_corr_vecs)==1
spin_corr_vec = spin_corr_vecs[0]
composite_weight += SoftKernels.eikonal_g(self, pi, pk, pr, spin_corr_vector=spin_corr_vec)*EpsilonExpansion(coll_weight)
new_evaluation['color_correlations'].append( ((a, b), ) )
new_evaluation['values'][(0,len(new_evaluation['color_correlations'])-1,0)] = composite_weight*mult_factor
return new_evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables
z = zs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None}}
})
# We must subtract the soft-collinear (CxS *not* SxC) from this contribution:
# P_gq = self.CF * ((1.-z)**2 + 1.)/z
# CxS(P_gq) = self.CF * 2.*(1.-z) / z
# SxC(P_gq) = self.CF * 2. / z
# P_gq-CxS(P_gq) = self.CF * z
# P_gq-SxC(P_gq) = self.CF * ((1.-z)**2 - 1.)/z
evaluation['values'][(0, 0)]['finite'] = self.CF * z
return evaluation
def evaluate_kernel(self, xs, kTs, parent):
# Retrieve the collinear variable x
x = xs[0]
kT = kTs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None, ((parent,( kT, )), ), ],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None},
(1, 0): {'finite': None}, }
})
# The factor 'x' that should be part of the initial_state_crossing_factor cancels
# against the extra prefactor 1/x in the collinear factorization formula
# (see Eq. (8) of NNLO compatible NLO scheme publication arXiv:0903.1218v2)
initial_state_crossing_factor = 1.
# Correct for the ratio of color-averaging factor between the real ME
# initial state flavor (gluon) and the one of the reduced Born ME (gluon)
initial_state_crossing_factor *= 1.
z = 1./x
# The line below implements the g_{\mu\nu} part of the splitting kernel.
# Notice that the extra longitudinal terms included in the spin-correlation 'None'
# from the relation:
# \sum_\lambda \epsilon_\lambda^\mu \epsilon_\lambda^{\star\nu}
# = g^{\mu\nu} + longitudinal terms
# are irrelevant because Ward identities evaluate them to zero anyway.
# We re-use here the Altarelli-Parisi Kernel of the P_qg final state kernel, including
# its soft subtraction
# We must subtract the soft-collinear (CxS *not* SxC) from this contribution:
# P_gg = 2.*self.CA * ( (z/(1.-z)) + ((1.-z)/z) )
# CxS(P_gg) = 2.*self.CA * ( (z/(1.-z)) )
# P_gg-CxS(P_gg) = 2.*self.CA * ((1.-z)/z)
norm = initial_state_crossing_factor * 2. * self.CA
evaluation['values'][(0, 0)]['finite'] = norm * ((1.-z)/z)
evaluation['values'][(1, 0)]['finite'] = -norm * 2.*z*(1.-z) / kT.square()
return evaluation
def kernel(self, zs, kTs, parent, reduced_kinematics):
# Retrieve the collinear variables
z = zs[0]
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'reduced_kinematics': [reduced_kinematics],
'values': {
(0, 0, 0): {
'finite': None
}
}
})
# Compute the kernel using
# f9d0839fc58905d67367e3e67efabee05ee390f9:madgraph/iolibs/template_files/OLD_subtraction/cataniseymour/NLO/local_currents.py:146
evaluation['values'][(0, 0, 0)]['finite'] = \
self.CF*z
return evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables and compute basic quantities
z1, z2, z3 = zs
s12 = sij(1, 2, zs, kTs)
s13 = sij(1, 3, zs, kTs)
s23 = sij(2, 3, zs, kTs)
misc.sprint(s12, s13, s23)
s123 = s12 + s13 + s23
# Assemble kernel
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'values': {}
})
ker = 0
# ker += 2*C123(z1, z2, z3, s12, s13, s23, s123)
evaluation['values'][(0, 0)] = {
'finite': 0.5 * self.CF * self.TR * ker
}
return evaluation
def evaluate_kernel(self, xs, kTs, parent):
# Retrieve the collinear variable x
x = xs[0]
kT = kTs[0]
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [None, ((parent, (kT, )), ), ],
'color_correlations' : [None],
'values' : {(0, 0): {'finite': None},
(1, 0): {'finite': None}, }
})
# The factor 'x' that should be part of the initial_state_crossing_factor cancels
# against the extra prefactor 1/x in the collinear factorization formula
# (see Eq. (8) of NNLO compatible NLO scheme publication arXiv:0903.1218v2)
initial_state_crossing_factor = -1.
# Correct for the ratio of color-averaging factor between the real ME
# initial state flavor (quark) and the one of the reduced Born ME (gluon)
initial_state_crossing_factor *= ((self.NC**2-1)/float(self.NC))
z = 1./x
# We re-use here the Altarelli-Parisi Kernel of the P_q\bar{q} final state kernel
# The line below implements the g_{\mu\nu} part of the splitting kernel.
# Notice that the extra longitudinal terms included in the spin-correlation 'None'
# from the relation:
# \sum_\lambda \epsilon_\lambda^\mu \epsilon_\lambda^{\star\nu}
# = g^{\mu\nu} + longitudinal terms
# are irrelevant because Ward identities evaluate them to zero anyway.
norm = initial_state_crossing_factor * self.TR
evaluation['values'][(0, 0)]['finite'] = norm
evaluation['values'][(1, 0)]['finite'] = norm * 4. * z*(1.-z) / kT.square()
return evaluation
def evaluate_subtraction_current(self,
current,
higher_PS_point=None,
momenta_dict=None,
reduced_process=None,
hel_config=None,
Q=None,
**opts):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the higher phase-space point.")
if momenta_dict is None:
raise CurrentImplementationError(self.name() +
" requires a momenta dictionary.")
if reduced_process is None:
raise CurrentImplementationError(self.name() +
" requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() +
" requires specification of the total incoming momentum Q.")
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Retrieve leg numbers
children = tuple(self.leg_numbers_map[i]
for i in sorted(self.leg_numbers_map.keys()))
parent = momenta_dict.inv[frozenset(children)]
# Perform mapping
self.mapping_singular_structure.legs = self.get_recoilers(
reduced_process, excluded=(parent, ))
lower_PS_point, mapping_vars = self.mapping.map_to_lower_multiplicity(
higher_PS_point,
self.mapping_singular_structure,
momenta_dict,
compute_jacobian=self.divide_by_jacobian)
# Retrieve kinematics
# The Q variable of the mapping cannot be relied upon
#Q = mapping_vars['Q']
if self.has_initial_state:
pC = higher_PS_point[children[0]] - sum(higher_PS_point[child]
for child in children[1:])
else:
pC = sum(higher_PS_point[child] for child in children)
qC = lower_PS_point[parent]
jacobian = mapping_vars.get('jacobian', 1)
reduced_kinematics = (None, lower_PS_point)
# Include the counterterm only in a part of the phase space
if self.has_initial_state:
pA = higher_PS_point[children[0]]
pR = sum(higher_PS_point[child] for child in children[1:])
# Initial state collinear cut
if self.is_cut(Q=Q, pA=pA, pR=pR):
return utils.SubtractionCurrentResult.zero(
current=current,
hel_config=hel_config,
reduced_kinematics=('IS_CUT', lower_PS_point))
else:
# Final state collinear cut
if self.is_cut(Q=Q, pC=pC):
return utils.SubtractionCurrentResult.zero(
current=current,
hel_config=hel_config,
reduced_kinematics=('IS_CUT', lower_PS_point))
# Evaluate kernel
# First construct variables necessary for its evaluation
# pass the mapping variables to the variables function, except for Q which is provided externally
mapping_vars.pop('Q', None)
kernel_arguments = self.variables(higher_PS_point,
qC,
children,
Q=Q,
**mapping_vars)
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [
None,
],
'color_correlations': [
None,
],
'reduced_kinematics': [reduced_kinematics],
'values': {}
})
evaluation = self.kernel(evaluation, parent, *kernel_arguments)
# Add the normalization factors
pC2 = pC.square()
norm = (8. * math.pi * alpha_s / pC2)**(len(children) - 1)
norm *= self.factor(Q=Q, pC=pC, qC=qC)
norm /= jacobian
for k in evaluation['values']:
evaluation['values'][k]['finite'] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(
self, current,
higher_PS_point=None, momenta_dict=None, reduced_process=None,
hel_config=None, Q=None, **opts ):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before mapping." )
if momenta_dict is None:
raise CurrentImplementationError(
self.name() + " requires a momentum routing dictionary." )
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment." )
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q." )
"""Important note about the IF CS:
- in this scheme we want to use "tilded" momenta for the dipole legs in eikonals. This is explicitly implemented in the soft local current
- this implies that the correct form for the local C(ir)S(r) taken as the collinear limit of the eikonals is
1/ (p_r + p_i_tilde)^2 (1-z_r)/z_r where z_r = p_r.Q/(p_r+p_i_tilde).Q
- Specializing to the case where the collinear partner of the soft particle is an initial state particle (i = a ), we have
p_a_tilde = xi p_a and 2p_a.Q = Q^2 so that the soft-collinear takes the form
1/(p_r+xi p_a)^2 * xi/y_rQ where y_rQ is the usual Hungarian variable
this simplifies to
1/(p_r+p_a)^2 * 1/y_rQ which is exactly the soft collinear as computed *without* tilded variables (i.e. exactly eq.5.29 of 0903.1218)
As a result we use exactly the same way of evaluating the counterterms as in honest-to-god colorful.
"""
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
children = tuple(self.leg_numbers_map[i]
for i in sorted(self.leg_numbers_map.keys()))
parent = momenta_dict.inv[frozenset(children)]
# Perform mapping
this_mapping_singular_structure = self.mapping_singular_structure.get_copy()
this_mapping_singular_structure.legs = self.get_recoilers(reduced_process, excluded=(parent, ))
lower_PS_point, mapping_vars = self.mapping.map_to_lower_multiplicity(
higher_PS_point, this_mapping_singular_structure, momenta_dict,
compute_jacobian=self.divide_by_jacobian )
reduced_kinematics = (None, lower_PS_point)
jacobian = mapping_vars.get('jacobian', 1.)
# Include the counterterm only in a part of the phase space
# children are the the set of particles that are going unresolved.
# Here we have C and S going collinear with S soft.
# The parent is the mapped C with a soft mapping, usually refered to as Ctilde.
# S is just removed in a soft mapping.
# Here S is a single particle but we obtain it as a list soft_children\
# to illustrate how multiple softs would be obtained
pCtilde = lower_PS_point[parent]
soft_children = [ self.leg_numbers_map[soft_leg_number] for soft_leg_number in self.leg_numbers_map if soft_leg_number>9 ]
pS = sum(higher_PS_point[child] for child in soft_children)
collinear_final_children = [ self.leg_numbers_map[soft_leg_number] for soft_leg_number in self.leg_numbers_map if
0 < soft_leg_number <= 9 ]
if len(collinear_final_children)>0:
pCfinal = sum(higher_PS_point[child] for child in collinear_final_children)
else:
pCfinal = vectors.LorentzVector()
pCinitial = higher_PS_point[self.leg_numbers_map[0]]
pCmother = pCinitial - pCfinal - pS
if self.is_cut(Q=Q, pC=pCmother, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current, hel_config=hel_config, reduced_kinematics=('IS_CUT', lower_PS_point))
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'reduced_kinematics': [reduced_kinematics],
'values': { }
})
# Evaluate kernel
kernel_arguments = self.variables(higher_PS_point, pCtilde, children, Q=Q)
# kernel_arguments = self.variables(higher_PS_point, pCinitial, children, Q=Q)
# There is no need for the ratio of color-averaging factor between the real ME
# initial state flavor and the one of the reduced Born ME as they are either both
# gluons or both quarks
evaluation = self.kernel(evaluation, parent, *kernel_arguments)
# Add the normalization factors
norm = (8. * math.pi * alpha_s)**(len(soft_children)+len(collinear_final_children)) / ((2.*pCtilde.dot(pS))*pS.square())
norm *= self.factor(Q=Q, pC=pCmother, pS=pS)
if self.divide_by_jacobian:
norm /= jacobian
for k in evaluation['values']:
evaluation['values'][k]['finite'] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(
evaluation,
hel_config=hel_config,
squared_orders=tuple(sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(
self, current,
higher_PS_point=None, momenta_dict=None, reduced_process=None,
hel_config=None, Q=None, **opts):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before and after mapping.")
if momenta_dict is None:
raise CurrentImplementationError(
self.name() + " requires a momentum routing dictionary.")
if reduced_process is None:
raise CurrentImplementationError(
self.name() + " requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q.")
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Now find all colored leg numbers in the reduced process
all_colored_parton_numbers = []
for leg in reduced_process.get('legs'):
if self.model.get_particle(leg.get('id')).get('color') == 1:
continue
all_colored_parton_numbers.append(leg.get('number'))
soft_momenta = [ higher_PS_point[self.leg_numbers_map[soft_leg_number]] for soft_leg_number in
self.leg_numbers_map if soft_leg_number>9 ]
pS = sum(soft_momenta)
# Perform mapping
this_mapping_singular_structure = self.mapping_singular_structure.get_copy()
this_mapping_singular_structure.legs = self.get_recoilers(reduced_process)
lower_PS_point, mapping_vars = self.mapping.map_to_lower_multiplicity(
higher_PS_point, this_mapping_singular_structure, momenta_dict,
compute_jacobian=self.divide_by_jacobian)
reduced_kinematics = (None, lower_PS_point)
jacobian = mapping_vars.get('jacobian', 1.)
# Include the counterterm only in a part of the phase space
if self.is_cut(Q=Q, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current, hel_config=hel_config, reduced_kinematics=('IS_CUT', lower_PS_point))
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [],
'reduced_kinematics': [reduced_kinematics, ],
'values': {}
})
# Normalization factors
norm = (8. * math.pi * alpha_s)**(len(soft_momenta))*(1./pS.square()**2)
norm *= self.factor(Q=Q, pS=pS)
if self.divide_by_jacobian:
norm /= jacobian
colored_partons_momenta = vectors.LorentzVectorDict()
for colored_parton_number in all_colored_parton_numbers:
# We want to used the reduced kinematics for our soft current
colored_partons_momenta[colored_parton_number] = lower_PS_point[colored_parton_number]
# Alternatively, the expression below would have given us the resolved one
#colored_partons_momenta[colored_parton_number] = sum(higher_PS_point[child] for child in momenta_dict[colored_parton_number])
color_correlation_index = 0
for color_correlator, weight in self.soft_kernel(
self, colored_partons_momenta, soft_momenta, all_colored_parton_numbers):
evaluation['color_correlations'].append(color_correlator)
complete_weight = weight*norm
evaluation['values'][(0, color_correlation_index, 0)] = {'finite': complete_weight[0]}
color_correlation_index += 1
result = utils.SubtractionCurrentResult()
result.add_result(
evaluation,
hel_config=hel_config,
squared_orders=tuple(sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(
self, current,
higher_PS_point=None, momenta_dict=None, reduced_process=None,
hel_config=None, **opts ):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the higher phase-space point." )
if momenta_dict is None:
raise CurrentImplementationError(
self.name() + " requires a momenta dictionary." )
if reduced_process is None:
raise CurrentImplementationError(
self.name() + " requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment." )
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Retrieve leg numbers
soft_leg_number = self.leg_numbers_map[0]
# Perform mapping
self.mapping_singular_structure.legs = self.get_recoilers(reduced_process)
lower_PS_point, mapping_vars = soft_mapping.map_to_lower_multiplicity(
higher_PS_point, self.mapping_singular_structure, momenta_dict,
compute_jacobian=self.divide_by_jacobian )
# Retrieve kinematics
Q = mapping_vars['Q']
pS = higher_PS_point[soft_leg_number]
jacobian = mapping_vars.get('jacobian', 1)
# Include the counterterm only in a part of the phase space
if self.is_cut(Q=Q, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current, hel_config=hel_config,
reduced_kinematics=(None, lower_PS_point))
# Normalization factors
norm = -4 * math.pi * alpha_s
norm *= self.factor(Q=Q, pS=pS)
norm /= jacobian
# Find all colored leg numbers in the reduced process
all_colored_parton_numbers = []
for leg in reduced_process.get('legs'):
if self.model.get_particle(leg.get('id')).get('color') == 1:
continue
all_colored_parton_numbers.append(leg.get('number'))
# Initialize the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [],
'reduced_kinematics': [(None, lower_PS_point)],
'values': {}
})
# Loop over colored parton number pairs (a, b)
# and add the corresponding contributions to this current
color_correlation_index = 0
for i, a in enumerate(all_colored_parton_numbers):
# Use the symmetry of the color correlation and soft current (a,b) <-> (b,a)
for b in all_colored_parton_numbers[i:]:
# Write the eikonal for that pair
if a != b:
mult_factor = 2.
else:
mult_factor = 1.
pa = higher_PS_point[a]
pb = higher_PS_point[b]
eikonal = self.eikonal(pa, pb, pS)
evaluation['color_correlations'].append( ((a, b), ) )
evaluation['values'][(0, color_correlation_index, 0)] = {
'finite': norm * mult_factor * eikonal }
color_correlation_index += 1
result = utils.SubtractionCurrentResult()
result.add_result(
evaluation,
hel_config=hel_config,
squared_orders=tuple(sorted(current.get('squared_orders').items())) )
return result
def evaluate_subtraction_current(self,
current,
higher_PS_point=None,
lower_PS_point=None,
leg_numbers_map=None,
reduced_process=None,
hel_config=None,
Q=None,
**opts):
if higher_PS_point is None or lower_PS_point is None:
raise CurrentImplementationError(
self.name() +
" needs the phase-space points before and after mapping.")
if leg_numbers_map is None:
raise CurrentImplementationError(
self.name() +
" requires a leg numbers map, i.e. a momentum dictionary.")
if reduced_process is None:
raise CurrentImplementationError(self.name() +
" requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q.")
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Now find all colored leg numbers in the reduced process
all_colored_parton_numbers = []
for leg in reduced_process.get('legs'):
if self.model.get_particle(leg.get('id')).get('color') == 1:
continue
all_colored_parton_numbers.append(leg.get('number'))
# Identify the soft leg numbers and momenta
soft_leg_number_A = current.get('singular_structure').legs[0].n
soft_leg_number_B = current.get('singular_structure').legs[1].n
pA = higher_PS_point[soft_leg_number_A]
pB = higher_PS_point[soft_leg_number_B]
pS = pA + pB
# Include the counterterm only in a part of the phase space
if self.is_cut(Q=Q, pS=pS):
return utils.SubtractionCurrentResult.zero(current=current,
hel_config=hel_config)
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [],
'values': {}
})
# Normalization factors
couplings_factors = 4. * math.pi * alpha_s
norm = couplings_factors**2 * self.factor(Q=Q, pS=pS)
# Keep track of the color correlators added
color_correlators_added = {}
color_correlation_max_index = 0
# Now loop over the colored parton numbers to implement the squared double-soft
# current flow. Note that significant improvement can be obtained by taking advantage
# of the symmetries, as well as writing fully expanded hard-coded expressions with
# all dot-products cached.
# For efficiency, we choose here to define coefficients of each single product of
# correlators. So, typically in the abelian piece, the color correlator reads:
# ( '{}' denotes an anti-commutator below and '.' denotes a dot-product )
# { T_i . T_j, T_k . T_l }
# And we will register *two* entries:
# evaluation['color_correlations'].append(
# (
# ( ( (i,-1,i), (k,-2,k) ), ( (j,-1,j), (l,-2,l) ) ),
# )
# )
# And:
# evaluation['color_correlations'].append(
# (
# ( ( (i,-2,i), (k,-1,k) ), ( (j,-2,j), (l,-1,l) ) ),
# )
# )
# As opposed to directly defining their sum:
# evaluation['color_correlations'].append(
# (
# ( ( (i,-1,i), (k,-2,k) ), ( (j,-1,j), (l,-2,l) ) ),
# ( ( (i,-2,i), (k,-1,k) ), ( (j,-2,j), (l,-1,l) ) )
# )
# )
for i in all_colored_parton_numbers:
for j in all_colored_parton_numbers:
# Compute the non-abelian eikonal
pi = sum(higher_PS_point[child]
for child in leg_numbers_map[i])
pj = sum(higher_PS_point[child]
for child in leg_numbers_map[j])
# pi = lower_PS_point[i]
# pj = lower_PS_point[j]
non_abelian_eikonal = self.non_abelian_eikonal(pi, pj, pA, pB)
non_abelian_kernel = -self.CA * norm * non_abelian_eikonal
# Implement the non-abelian piece
non_abelian_correlator = ((((i, -1, i), ), ((j, -1, j), )), )
if non_abelian_correlator in color_correlators_added:
color_correlation_index = color_correlators_added[
non_abelian_correlator]
evaluation['values'][(0, color_correlation_index
)]['finite'] += non_abelian_kernel
else:
evaluation['color_correlations'].append(
non_abelian_correlator)
color_correlation_index = color_correlation_max_index
color_correlators_added[
non_abelian_correlator] = color_correlation_max_index
color_correlation_max_index += 1
evaluation['values'][(0, color_correlation_index)] = {
'finite': non_abelian_kernel
}
for k in all_colored_parton_numbers:
for l in all_colored_parton_numbers:
# Compute the abelian eikonal
pk = sum(higher_PS_point[child]
for child in leg_numbers_map[k])
pl = sum(higher_PS_point[child]
for child in leg_numbers_map[l])
# pk = lower_PS_point[k]
# pl = lower_PS_point[l]
eik_ij = self.eikonal(pi, pj, pA)
eik_kl = self.eikonal(pk, pl, pB)
abelian_kernel = 0.5 * norm * eik_ij * eik_kl
# Implement the abelian piece
abelian_correlator_A = (
self.create_CataniGrazzini_correlator((i, j),
(k, l)), )
abelian_correlator_B = (
self.create_CataniGrazzini_correlator((k, l),
(i, j)), )
for correlator in [
abelian_correlator_A, abelian_correlator_B
]:
if correlator in color_correlators_added:
color_correlation_index = color_correlators_added[
correlator]
#misc.sprint('Adding %f ((%d,%d,%d)->%f, (%d,%d,%d)->%f) to CC: %d, %s'%\
# (abelian_kernel,
# i,j,soft_leg_number_A,self.eikonal(PS_point, i, j, soft_leg_number_A),
# k,l,soft_leg_number_B,self.eikonal(PS_point, k, l, soft_leg_number_B),
# color_correlation_index, str(correlator)
# ))
evaluation['values'][(
0, color_correlation_index
)]['finite'] += abelian_kernel
else:
evaluation['color_correlations'].append(
correlator)
color_correlation_index = color_correlation_max_index
color_correlators_added[
correlator] = color_correlation_max_index
color_correlation_max_index += 1
evaluation['values'][(
0, color_correlation_index)] = {
'finite': abelian_kernel
}
#misc.sprint('Adding %f ((%d,%d,%d)->%f, (%d,%d,%d)->%f) to CC: %d, %s'%\
# (abelian_kernel,
# i,j,soft_leg_number_A,self.eikonal(PS_point, i, j, soft_leg_number_A),
# k,l,soft_leg_number_B,self.eikonal(PS_point, k, l, soft_leg_number_B),
# color_correlation_index, str(correlator)
# ))
result = utils.SubtractionCurrentResult()
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
#misc.sprint('==BELOW LIST CC==')
#for i, cc in enumerate(evaluation['color_correlations']):
# misc.sprint('Color correlator: %d : %s = %f'%(i, cc, evaluation['values'][(0,i)]['finite']))
#misc.sprint('==ABOVE LIST CC==')
return result
def evaluate_kernel(self, zs, kTs, parent):
#misc.sprint("HELLO")
# Retrieve the collinear variables and compute basic quantities
z1, z2, z3 = zs
k1, k2, k3 = kTs
s12 = sij(1, 2, zs, kTs)
s13 = sij(1, 3, zs, kTs)
s23 = sij(2, 3, zs, kTs)
s123 = s12 + s13 + s23
CA = self.CA
k12 = k1 + k2
k23 = k2 + k3
k13 = k1 + k3
u12 = k1 / z1 - k2 / z2
u23 = k2 / z2 - k3 / z3
u31 = k1 / z1 - k3 / z3
# Assemble kernel
kernel_gmunu = self.evaluate_permuted_gmunu(z1, z2, z3, s12, s13, s23)
kernel_u12mu_u12nu = (8 * CA**2 * s123 * z1**2 *
z2**2) / (s12**2 * (1 - z3) * z3)
kernel_u23mu_u23nu = (8 * CA**2 * s123 * z2**2 *
z3**2) / (s23**2 * (1 - z1) * z1)
kernel_u13mu_u13nu = (8 * CA**2 * s123 * z1**2 *
z3**2) / (s13**2 * (1 - z2) * z2)
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [
None,
((parent, (k1, )), ),
((parent, (k2, )), ),
((parent, (k3, )), ),
((parent, (u12, )), ),
((parent, (u23, )), ),
((parent, (u31, )), ),
],
'color_correlations': [None],
'values': {
(0, 0): {
'finite': -kernel_gmunu
}, # for the minus sign: Madgraph multiplies this by -g_mu_nu
(1, 0): {
'finite': self.evaluatecoefk1k1(z1, z2, z3, s12, s13, s23)
},
(2, 0): {
'finite': self.evaluatecoefk2k2(z1, z2, z3, s12, s13, s23)
},
(3, 0): {
'finite': self.evaluatecoefk3k3(z1, z2, z3, s12, s13, s23)
},
(4, 0): {
'finite': kernel_u12mu_u12nu
},
(5, 0): {
'finite': kernel_u23mu_u23nu
},
(6, 0): {
'finite': kernel_u13mu_u13nu
},
}
})
return evaluation
def evaluate_kernel(self, zs, kTs, parent):
# Retrieve the collinear variables and compute basic quantities
z1, z2, z3 = zs
k1, k2, k3 = kTs
s12 = sij(1, 2, zs, kTs)
s13 = sij(1, 3, zs, kTs)
s23 = sij(2, 3, zs, kTs)
s123 = s12 + s13 + s23
CF = self.CF
CA = self.CA
TR = self.TR
t231 = tijk(2, 3, 1, zs, kTs, s_ij=s23, s_ik=s12, s_jk=s13)
t321 = tijk(3, 2, 1, zs, kTs, s_ij=s23, s_ik=s13, s_jk=s12)
k23 = k2 + k3
u23 = k2 / z2 - k3 / z3
# Assemble kernel
kernel_gmunu = (CF * TR * (2 - s23**2 / (s12 * s13) - s123**2 /
(s12 * s13)) + CA * TR *
(0.5 + s123**2 / (s12 * s13) + t231**2 /
(4. * s23**2) + t321**2 / (4. * s23**2) + s123 /
(s23 * (1 - z1)) - s123 / (2. * s12 *
(1 - z1) * z1) - s123 /
(2. * s13 * (1 - z1) * z1) - s123 / (s23 *
(1 - z1) * z1) -
(2 * s123 * z1) / (s23 * (1 - z1)) + (s123**2 * z2) /
(s12 * s23 * (1 - z1)) + (s123 * z2) /
(2. * s13 * (1 - z1) * z1) - (s123**2 * z2) /
(2. * s12 * s23 * (1 - z1) * z1) + (s123**2 * z3) /
(s13 * s23 * (1 - z1)) + (s123 * z3) /
(2. * s12 * (1 - z1) * z1) - (s123**2 * z3) /
(2. * s13 * s23 * (1 - z1) * z1)))
kernel_k1mu_k1nu = ((2 * CA * TR * s123) / (s12 * s13) -
(4 * CF * TR * s123) / (s12 * s13))
kernel_k2mu_k2nu = ((-4 * CF * TR * s123) / (s12 * s13) + CA * TR *
(((4 * s123) / (s12 * s13) +
(s123 *
((-16 * z3**2) / ((1 - z1) * z1) - 4 *
(1 + (2 * (-z1 + z2) * z3) /
((1 - z1) * z1)))) / (s13 * s23)) / 4. +
((4 * s123) / (s12 * s13) +
(s123 * (8 - 4 * (1 + (2 * z2 * (-z1 + z3)) /
((1 - z1) * z1)))) /
(s12 * s23)) / 4.))
kernel_k3mu_k3nu = ((-4 * CF * TR * s123) / (s12 * s13) + CA * TR *
(((4 * s123) / (s12 * s13) +
(s123 * (8 - 4 * (1 + (2 * (-z1 + z2) * z3) /
((1 - z1) * z1)))) /
(s13 * s23)) / 4. +
((4 * s123) / (s12 * s13) +
(s123 *
((-16 * z2**2) / ((1 - z1) * z1) - 4 *
(1 + (2 * z2 * (-z1 + z3)) /
((1 - z1) * z1)))) / (s12 * s23)) / 4.))
kernel_k23mu_k23nu = ((4 * CF * TR * s123) / (s12 * s13) + CA * TR *
(((-4 * s123) / (s12 * s13) +
(4 * s123 *
(1 + (2 * (-z1 + z2) * z3) /
((1 - z1) * z1))) / (s13 * s23)) / 4. +
((-4 * s123) / (s12 * s13) +
(4 * s123 *
(1 + (2 * z2 * (-z1 + z3)) /
((1 - z1) * z1))) / (s12 * s23)) / 4.))
kernel_u23mu_u23nu = ((-8 * CA * TR * s123 * z2**2 * z3**2) /
(s23**2 * (1 - z1) * z1))
# Instantiate the structure of the result
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [
None,
((parent, (k1, )), ),
((parent, (k2, )), ),
((parent, (k3, )), ),
((parent, (k23, )), ),
((parent, (u23, )), ),
],
'color_correlations': [None],
'values': {
(0, 0): {
'finite': -kernel_gmunu
}, # for the minus sign: Madgraph multiplies this by -g_mu_nu
(1, 0): {
'finite': kernel_k1mu_k1nu
},
(2, 0): {
'finite': kernel_k2mu_k2nu
},
(3, 0): {
'finite': kernel_k3mu_k3nu
},
(4, 0): {
'finite': kernel_k23mu_k23nu
},
(5, 0): {
'finite': kernel_u23mu_u23nu
},
}
})
return evaluation
def evaluate_subtraction_current(self,
current,
higher_PS_point=None,
momenta_dict=None,
reduced_process=None,
hel_config=None,
Q=None,
**opts):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before mapping.")
if momenta_dict is None:
raise CurrentImplementationError(
self.name() + " requires a momentum routing dictionary.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q.")
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Perform mapping
this_mapping_singular_structure = self.mapping_singular_structure.get_copy(
)
this_mapping_singular_structure.legs = self.get_recoilers(
reduced_process)
lower_PS_point, mapping_vars = self.mapping.map_to_lower_multiplicity(
higher_PS_point,
this_mapping_singular_structure,
momenta_dict,
compute_jacobian=self.divide_by_jacobian)
reduced_kinematics = (None, lower_PS_point)
# Include the counterterm only in a part of the phase space
children = tuple(self.leg_numbers_map[i]
for i in sorted(self.leg_numbers_map.keys()))
pC_child = higher_PS_point[children[0]]
pS = higher_PS_point[children[1]]
parent = momenta_dict.inv[frozenset(children)]
if self.is_cut(Q=Q, pC=pC_child, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current,
hel_config=hel_config,
reduced_kinematics=('IS_CUT', lower_PS_point))
pC_mother = pC_child - pS
pC_tilde = lower_PS_point[parent]
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'reduced_kinematics': [reduced_kinematics],
'values': {
(0, 0, 0): {
'finite': None
}
}
})
# Evaluate kernel
xs, kTs = self.variables(higher_PS_point, pC_tilde, children, Q=Q)
x = xs[0]
# See Eq. (4.17) of NNLO compatible NLO scheme publication arXiv:0903.1218v2
# There is no need for the ratio of color-averaging factor between the real ME
# initial state flavor and the one of the reduced Born ME as they are either both
# gluons or both quarks
evaluation['values'][(0, 0,
0)]['finite'] = self.color_charge * (2. /
(1. - x))
# Add the normalization factors
# Note: normalising with (pC_tilde+pS).square() will *not* work!
norm = 8. * math.pi * alpha_s / (pC_child + pS).square()
norm *= self.factor(Q=Q, pC=pC_mother, pS=pS)
for k in evaluation['values']:
evaluation['values'][k]['finite'] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(
self, current,
higher_PS_point=None, lower_PS_point=None,
leg_numbers_map=None, reduced_process=None, hel_config=None,
Q=None, **opts ):
if higher_PS_point is None or lower_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before and after mapping." )
if leg_numbers_map is None:
raise CurrentImplementationError(
self.name() + " requires a leg numbers map, i.e. a momentum dictionary." )
if reduced_process is None:
raise CurrentImplementationError(
self.name() + " requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment." )
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q." )
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Now find all colored leg numbers in the reduced process
all_colored_parton_numbers = []
for leg in reduced_process.get('legs'):
if self.model.get_particle(leg.get('id')).get('color')==1:
continue
all_colored_parton_numbers.append(leg.get('number'))
soft_leg_number = current.get('singular_structure').legs[0].n
pS = higher_PS_point[soft_leg_number]
# Include the counterterm only in a part of the phase space
if self.is_cut(Q=Q, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current, hel_config=hel_config)
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations' : [ None ],
'color_correlations' : [],
'values' : {}
})
# Normalization factors
norm = -4. * math.pi * alpha_s
norm *= self.factor(Q=Q, pS=pS)
color_correlation_index = 0
# Now loop over the colored parton number pairs (a,b)
# and add the corresponding contributions to this current
for i, a in enumerate(all_colored_parton_numbers):
# Use the symmetry of the color correlation and soft current (a,b) <-> (b,a)
for b in all_colored_parton_numbers[i:]:
# Write the eikonal for that pair
if a!=b:
mult_factor = 2.
else:
mult_factor = 1.
pa = sum(higher_PS_point[child] for child in leg_numbers_map[a])
pb = sum(higher_PS_point[child] for child in leg_numbers_map[b])
# pa = lower_PS_point[a]
# pb = lower_PS_point[b]
eikonal = self.eikonal(pa, pb, pS)
evaluation['color_correlations'].append( ((a, b), ) )
evaluation['values'][(0, color_correlation_index)] = {
'finite': norm * mult_factor * eikonal }
color_correlation_index += 1
result = utils.SubtractionCurrentResult()
result.add_result(
evaluation,
hel_config=hel_config,
squared_orders=tuple(sorted(current.get('squared_orders').items())) )
return result
def evaluate_subtraction_current(self,
current,
higher_PS_point=None,
momenta_dict=None,
reduced_process=None,
hel_config=None,
Q=None,
**opts):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before mapping.")
if momenta_dict is None:
raise CurrentImplementationError(
self.name() + " requires a momentum routing dictionary.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q.")
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
children = tuple(self.leg_numbers_map[i]
for i in sorted(self.leg_numbers_map.keys()))
parent = momenta_dict.inv[frozenset(children)]
# Perform mapping
this_mapping_singular_structure = self.mapping_singular_structure.get_copy(
)
this_mapping_singular_structure.legs = self.get_recoilers(
reduced_process, excluded=(parent, ))
lower_PS_point, mapping_vars = self.mapping.map_to_lower_multiplicity(
higher_PS_point,
this_mapping_singular_structure,
momenta_dict,
compute_jacobian=self.divide_by_jacobian)
reduced_kinematics = (None, lower_PS_point)
# Include the counterterm only in a part of the phase space
# children are the the set of particles that are going unresolved.
# Here we have C and S going collinear with S soft.
# The parent is the mapped C with a soft mapping, usually refered to as Ctilde.
# S is just removed in a soft mapping.
# Here S is a single particle but we obtain it as a list soft_children\
# to illustrate how multiple softs would be obtained
pCtilde = lower_PS_point[parent]
soft_children = [
self.leg_numbers_map[1],
]
pS = sum(higher_PS_point[child] for child in soft_children)
if self.is_cut(Q=Q, pC=pCtilde, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current,
hel_config=hel_config,
reduced_kinematics=('IS_CUT', lower_PS_point))
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'reduced_kinematics': [
reduced_kinematics,
],
'values': {
(0, 0, 0): {
'finite': None
}
}
})
# Evaluate kernel
zs = self.variables([pS, pCtilde], Q)
z = zs[0]
evaluation['values'][(
0, 0, 0)]['finite'] = self.color_charge * 2. * (1. - z) / z
# Add the normalization factors
s12 = (pCtilde + pS).square()
norm = 8. * math.pi * alpha_s / s12
norm *= self.factor(Q=Q, pC=pCtilde, pS=pS)
for k in evaluation['values']:
evaluation['values'][k]['finite'] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(self,
current,
higher_PS_point=None,
momenta_dict=None,
reduced_process=None,
hel_config=None,
Q=None,
**opts):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() +
" needs the phase-space points before and after mapping.")
if momenta_dict is None:
raise CurrentImplementationError(
self.name() + " requires a momentum routing dictionary.")
if reduced_process is None:
raise CurrentImplementationError(self.name() +
" requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q.")
"""Important note about the IF CS:
- in this scheme we want to use "tilded" momenta for the dipole legs in eikonals. This is explicitly implemented in the soft local current
- this implies that the correct form for the local C(ir)S(r) taken as the collinear limit of the eikonals is
1/ (p_r + p_i_tilde)^2 (1-z_r)/z_r where z_r = p_r.Q/(p_r+p_i_tilde).Q
- Specializing to the case where the collinear partner of the soft particle is an initial state particle (i = a ), we have
p_a_tilde = xi p_a and 2p_a.Q = Q^2 so that the soft-collinear takes the form
1/(p_r+xi p_a)^2 * xi/y_rQ where y_rQ is the usual Hungarian variable
this simplifies to
1/(p_r+p_a)^2 * 1/y_rQ which is exactly the soft collinear as computed *without* tilded variables (i.e. exactly eq.5.29 of 0903.1218)
As a result we use exactly the same way of evaluating the counterterms as in honest-to-god colorful.
"""
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Now find all colored leg numbers in the reduced process
all_colored_parton_numbers = []
for leg in reduced_process.get('legs'):
if self.model.get_particle(leg.get('id')).get('color') == 1:
continue
all_colored_parton_numbers.append(leg.get('number'))
soft_leg_number = self.leg_numbers_map[0]
pS = higher_PS_point[soft_leg_number]
# Perform mapping
this_mapping_singular_structure = self.mapping_singular_structure.get_copy(
)
this_mapping_singular_structure.legs = self.get_recoilers(
reduced_process)
lower_PS_point, mapping_vars = self.mapping.map_to_lower_multiplicity(
higher_PS_point,
this_mapping_singular_structure,
momenta_dict,
compute_jacobian=self.divide_by_jacobian)
reduced_kinematics = (None, lower_PS_point)
# Include the counterterm only in a part of the phase space
if self.is_cut(Q=Q, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current,
hel_config=hel_config,
reduced_kinematics=('IS_CUT', lower_PS_point))
# Retrieve kinematics
pS = higher_PS_point[soft_leg_number]
jacobian = mapping_vars.get('jacobian', 1.)
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [],
'reduced_kinematics': [
reduced_kinematics,
],
'values': {}
})
# Normalization factors
norm = -4. * math.pi * alpha_s
norm *= self.factor(Q=Q, pS=pS)
if self.divide_by_jacobian:
norm /= jacobian
color_correlation_index = 0
# Now loop over the colored parton number pairs (a,b)
# and add the corresponding contributions to this current
for i, a in enumerate(all_colored_parton_numbers):
# Use the symmetry of the color correlation and soft current (a,b) <-> (b,a)
for b in all_colored_parton_numbers[i:]:
# Write the eikonal for that pair
if a != b:
mult_factor = 2.
else:
mult_factor = 1.
#pa = sum(higher_PS_point[child] for child in momenta_dict[a])
#pb = sum(higher_PS_point[child] for child in momenta_dict[b])
pa = lower_PS_point[a]
pb = lower_PS_point[b]
eikonal = self.eikonal(pa, pb, pS)
evaluation['color_correlations'].append(((a, b), ))
evaluation['values'][(0, color_correlation_index, 0)] = {
'finite': norm * mult_factor * eikonal
}
color_correlation_index += 1
result = utils.SubtractionCurrentResult()
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(
self, current,
higher_PS_point=None, lower_PS_point=None,
leg_numbers_map=None, reduced_process=None, hel_config=None,
Q=None, **opts ):
if higher_PS_point is None or lower_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before and after mapping." )
if leg_numbers_map is None:
raise CurrentImplementationError(
self.name() + " requires a leg numbers map, i.e. a momentum dictionary." )
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment." )
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q." )
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Include the counterterm only in a part of the phase space
children = self.get_sorted_children(current, self.model)
pC = sum(higher_PS_point[child] for child in children)
soft_children = []
for substructure in current.get('singular_structure').substructures:
soft_children += [leg.n for leg in substructure.get_all_legs()]
pS = sum(higher_PS_point[child] for child in soft_children)
parent = leg_numbers_map.inv[frozenset(children)]
if self.is_cut(Q=Q, pC=pC, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current, hel_config=hel_config)
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'values': {(0, 0): {'finite': None}}
})
# Evaluate kernel
zs, kTs = self.variables(higher_PS_point, lower_PS_point[parent], children, Q=Q)
z = zs[0]
evaluation['values'][(0, 0)]['finite'] = self.color_charge * 2.*(1.-z) / z
# Add the normalization factors
s12 = pC.square()
norm = 8. * math.pi * alpha_s / s12
norm *= self.factor(Q=Q, pC=pC, pS=pS)
for k in evaluation['values']:
evaluation['values'][k]['finite'] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(
evaluation,
hel_config=hel_config,
squared_orders=tuple(sorted(current.get('squared_orders').items())))
return result
def evaluate_integrated_current(self,
current,
PS_point,
reduced_process=None,
leg_numbers_map=None,
hel_config=None,
compute_poles=False,
**opts):
""" Now evalaute the current and return the corresponding instance of
SubtractionCurrentResult. See documentation of the mother function for more details."""
if not hel_config is None:
raise CurrentImplementationError(
"Subtraction current implementation " +
"%s does not support helicity assignment." %
self.__class__.__name__)
if leg_numbers_map is None:
raise CurrentImplementationError(
"Subtraction current implementation " +
"%s requires the leg_number_map." % self.__class__.__name__)
if reduced_process is None:
raise CurrentImplementationError(
"Subtraction current implementation " +
"%s requires the reduced_process." % self.__class__.__name__)
result = utils.SubtractionCurrentResult()
ss = current.get('singular_structure').substructures[0]
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Retrieve kinematic variables from the specified PS point
children_numbers = tuple(leg.n for leg in ss.legs)
parent_number = leg_numbers_map.inv[frozenset(children_numbers)]
p12 = PS_point[parent_number]
Q = sum([
PS_point[l.get('number')]
for l in reduced_process.get_initial_legs()
])
Q_square = Q.square()
y12 = 2. * Q.dot(p12) / Q_square
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'values': {
(0, 0): {}
}
})
#Virtuality cut in the integration
alpha_0 = currents.SomogyiChoices.alpha_0
finite_part = HE.CggFF_Finite_Gabor_DIVJAC_NOD0(alpha_0, y12)
value = EpsilonExpansion({
0: finite_part,
-1: (11. / 3. - 4. * math.log(y12)),
-2: 2.
})
logMuQ = math.log(mu_r**2 / Q_square)
prefactor = EpsilonExpansion({0: 1., 1: logMuQ, 2: 0.5 * logMuQ**2})
prefactor *= self.SEpsilon
# Now add the normalization factors
value *= prefactor * (alpha_s / (2. * math.pi)) * self.CA
# Truncate expansion so as to keep only relevant terms
value.truncate(min_power=-2, max_power=0)
# Now register the value in the evaluation
evaluation['values'][(0, 0)] = value.to_human_readable_dict()
# And add it to the results
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(
self, current,
higher_PS_point=None, lower_PS_point=None,
leg_numbers_map=None, reduced_process=None, hel_config=None,
Q=None, **opts ):
if higher_PS_point is None or lower_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the phase-space points before and after mapping." )
if leg_numbers_map is None:
raise CurrentImplementationError(
self.name() + " requires a leg numbers map, i.e. a momentum dictionary." )
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment." )
if Q is None:
raise CurrentImplementationError(
self.name() + " requires the total mapping momentum Q." )
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Include the counterterm only in a part of the phase space
children = self.get_sorted_children(current, self.model)
pC = higher_PS_point[children[0]]
pS = higher_PS_point[children[1]]
pC = pC + pS
parent = leg_numbers_map.inv[frozenset(children)]
if self.is_cut(Q=Q, pC=pC, pS=pS):
return utils.SubtractionCurrentResult.zero(
current=current, hel_config=hel_config)
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [None],
'values': {(0, 0): {'finite': None}}
})
# Evaluate kernel
xs, kTs = self.variables(higher_PS_point, lower_PS_point[parent], children, Q=Q)
x = xs[0]
# See Eq. (4.17) of NNLO compatible NLO scheme publication arXiv:0903.1218v2
# There is no need for the ratio of color-averaging factor between the real ME
# initial state flavor and the one of the reduced Born ME as they are either both
# gluons or both quarks
evaluation['values'][(0, 0)]['finite'] = self.color_charge * ( 2. / (1. - x) )
# Add the normalization factors
s12 = pC.square()
norm = 8. * math.pi * alpha_s / s12
norm *= self.factor(Q=Q, pC=pC, pS=pS)
for k in evaluation['values']:
evaluation['values'][k]['finite'] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(
evaluation,
hel_config=hel_config,
squared_orders=tuple(sorted(current.get('squared_orders').items())))
return result
def evaluate_integrated_current(self,
current,
PS_point,
reduced_process=None,
leg_numbers_map=None,
hel_config=None,
compute_poles=False,
**opts):
""" Evaluates this current and return the corresponding instance of
SubtractionCurrentResult. See documentation of the mother function for more details."""
if not hel_config is None:
raise CurrentImplementationError(
"Subtraction current implementation " +
"%s does not support helicity assignment." %
self.__class__.__name__)
if leg_numbers_map is None:
raise CurrentImplementationError(
"Subtraction current implementation " +
"%s requires the leg_number_map." % self.__class__.__name__)
if reduced_process is None:
raise CurrentImplementationError(
"Subtraction current implementation " +
"%s requires a reduced_process." % self.__class__.__name__)
result = utils.SubtractionCurrentResult()
ss = current.get('singular_structure').substructures[0]
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Retrieve kinematic variables from the specified PS point
soft_leg_number = ss.legs[0].n
# Use the momenta map, in case it has been remapped.
# Although for the soft current it's typically not the case
soft_leg_number = leg_numbers_map.inv[frozenset([
soft_leg_number,
])]
Q = sum([
PS_point[l.get('number')]
for l in reduced_process.get_initial_legs()
])
Q_square = Q.square()
# Now find all colored leg numbers in the reduced process
all_colored_parton_numbers = []
for leg in reduced_process.get('legs'):
if self.model.get_particle(leg.get('id')).get('color') == 1:
continue
all_colored_parton_numbers.append(leg.get('number'))
# Now instantiate what the result will be
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [None],
'color_correlations': [],
'values': {}
})
logMuQ = math.log(mu_r**2 / Q_square)
prefactor = EpsilonExpansion({0: 1., 1: logMuQ, 2: 0.5 * logMuQ**2})
prefactor *= self.SEpsilon
# Now add the normalization factors
prefactor *= (alpha_s / (2. * math.pi))
prefactor.truncate(min_power=-2, max_power=2)
#Virtuality cut in the integration
y_0 = 0.5
color_correlation_index = 0
# Now loop over the colored parton number pairs (a,b)
# and add the corresponding contributions to this current
for i, a in enumerate(all_colored_parton_numbers):
# Use the symmetry of the color correlation and soft current (a,b) <-> (b,a)
for b in all_colored_parton_numbers[i + 1:]:
evaluation['color_correlations'].append(((a, b), ))
# We multiply by a factor 2. because we symmetrized the sum below
value = prefactor * 2.
pa = PS_point[a]
pb = PS_point[b]
Y = (pa.dot(pb) * Q_square) / (2. * Q.dot(pa) * Q.dot(pb))
finite_part = HE.SoftFF_Finite_Gabor_DIVJAC_NOD0(y_0, Y)
value *= EpsilonExpansion({
0: finite_part,
-1: math.log(Y),
-2: 0.
})
# Truncate expansion so as to keep only relevant terms
value.truncate(min_power=-2, max_power=0)
evaluation['values'][(
0,
color_correlation_index)] = value.to_human_readable_dict()
color_correlation_index += 1
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result
def evaluate_subtraction_current(self,
current,
higher_PS_point=None,
momenta_dict=None,
reduced_process=None,
hel_config=None,
Q=None,
**opts):
if higher_PS_point is None:
raise CurrentImplementationError(
self.name() + " needs the higher phase-space point.")
if momenta_dict is None:
raise CurrentImplementationError(self.name() +
" requires a momenta dictionary.")
if reduced_process is None:
raise CurrentImplementationError(self.name() +
" requires a reduced_process.")
if not hel_config is None:
raise CurrentImplementationError(
self.name() + " does not support helicity assignment.")
if Q is None:
raise CurrentImplementationError(
self.name() +
" requires specification of the total incoming momentum Q.")
# Retrieve alpha_s and mu_r
model_param_dict = self.model.get('parameter_dict')
alpha_s = model_param_dict['aS']
mu_r = model_param_dict['MU_R']
# Retrieve leg numbers
overall_children = [
] # the legs becoming unresolved in the resolved process (momenta in the real-emission ME)
overall_parents = [
] # the parent legs in the top-level reduced process (momenta in the mapped ME of this CT)
# We take one defining structure (self.structure[0]). Its top-level substructures are the independent bundles
# eg (C(1,2),C(4,5),S(6)).
# Using structure[0] as the defining structure is fine for the purpose below since they should
# all use the same leg numbers
for bundle in self.structure[0].substructures:
overall_children.append(
tuple(self.leg_numbers_map[l.n]
for l in bundle.get_all_legs()))
if self.has_parent(bundle, len(overall_children[-1])):
overall_parents.append(
self.get_parent(frozenset(overall_children[-1]),
momenta_dict))
else:
overall_parents.append(None)
all_steps = [
{
'higher_PS_point': higher_PS_point
},
]
overall_jacobian = 1.
for i_step, mapping_information in enumerate(self.mapping_rules):
# Now obtain recoilers
reduced_recoilers = mapping_information['reduced_recoilers'](
reduced_process, excluded=tuple(overall_parents))
additional_recoilers = sub.SubtractionLegSet(
SubtractionLeg(self.map_leg_number(l.n, overall_parents),
l.pdg, l.state)
for l in mapping_information['additional_recoilers'])
all_recoilers = sub.SubtractionLegSet(
list(reduced_recoilers) + list(additional_recoilers))
# Now recursively apply leg numbers mappings
mapping_singular_structure = mapping_information[
'singular_structure'].get_copy()
self.map_leg_numbers_in_singular_structure(
mapping_singular_structure, overall_parents)
# Now assign the recoilers (whose leg numbers have already been mapped)
mapping_singular_structure.legs = all_recoilers
# Build the momenta_dict by also substituting leg numbers
this_momenta_dict = bidict({
self.map_leg_number(k, overall_parents):
frozenset([self.map_leg_number(n, overall_parents) for n in v])
for k, v in mapping_information['momenta_dict'].items()
})
lower_PS_point, mapping_vars = mapping_information[
'mapping'].map_to_lower_multiplicity(
all_steps[-1]['higher_PS_point'],
mapping_singular_structure,
this_momenta_dict,
compute_jacobian=self.divide_by_jacobian)
if mappings.RelabellingMapping.needs_relabelling(
this_momenta_dict):
lower_PS_point = mappings.RelabellingMapping.map_to_lower_multiplicity(
lower_PS_point, None, this_momenta_dict)
all_steps[-1]['lower_PS_point'] = lower_PS_point
# Q is provided externally
mapping_vars.pop('Q', None)
all_steps[-1]['mapping_vars'] = mapping_vars
overall_jacobian *= mapping_vars.get('jacobian', 1.)
bundles_info = []
for bundle in mapping_singular_structure.substructures:
bundles_info.append({})
all_legs = bundle.get_all_legs()
# This sorting is important so that the variables generated can be related to the legs specified
# in the mapping singular structures of the mapping rules
all_initial_legs = sorted(
[l for l in all_legs if l.state == l.INITIAL],
key=lambda l: l.n)
all_final_legs = sorted(
[l for l in all_legs if l.state == l.FINAL],
key=lambda l: l.n)
bundles_info[-1]['initial_state_children'] = tuple(
l.n for l in all_initial_legs)
bundles_info[-1]['final_state_children'] = tuple(
l.n for l in all_final_legs)
if self.has_parent(bundle, len(all_legs)):
bundles_info[-1]['parent'] = self.get_parent(
frozenset(l.n for l in all_legs), this_momenta_dict)
else:
bundles_info[-1]['parent'] = None
# Retrieve kinematics
bundles_info[-1]['cut_inputs'] = {}
if bundle.name() == 'C':
if len(all_initial_legs) > 0:
bundles_info[-1]['cut_inputs']['pA'] = -sum(
all_steps[-1]['higher_PS_point'][l.n]
for l in all_initial_legs)
bundles_info[-1]['cut_inputs']['pC'] = sum(
all_steps[-1]['higher_PS_point'][l.n]
for l in all_final_legs)
elif bundle.name() == 'S':
bundles_info[-1]['cut_inputs']['pS'] = sum(
all_steps[-1]['higher_PS_point'][l.n]
for l in all_final_legs)
all_steps[-1]['bundles_info'] = bundles_info
# Get all variables for this level
if mapping_information['variables'] is not None:
all_steps[-1]['variables'] = mapping_information['variables'](
all_steps[-1]['higher_PS_point'],
all_steps[-1]['lower_PS_point'],
bundles_info,
Q=Q,
**mapping_vars)
else:
all_steps[-1]['variables'] = {}
# Add the next higher PS point for the next level if necessary
if i_step < (len(self.mapping_rules) - 1):
all_steps.append({'higher_PS_point': lower_PS_point})
overall_lower_PS_point = all_steps[-1]['lower_PS_point']
reduced_kinematics = (None, overall_lower_PS_point)
global_variables = {
'overall_children': overall_children,
'overall_parents': overall_parents,
'leg_numbers_map': self.leg_numbers_map,
'Q': Q,
}
# Build global variables if necessary
if self.variables is not None:
global_variables.update(self.variables(all_steps,
global_variables))
# Apply cuts: include the counterterm only in a part of the phase-space
for i_step, step_info in enumerate(all_steps):
cut_inputs = dict(step_info)
if self.mapping_rules[i_step]['is_cut'](cut_inputs,
global_variables):
return utils.SubtractionCurrentResult.zero(
current=current,
hel_config=hel_config,
reduced_kinematics=('IS_CUT', overall_lower_PS_point))
# for i_step, step_info in enumerate(all_steps):
# misc.sprint("Higher PS point at step #%d: %s"%(i_step, str(step_info['higher_PS_point'])))
# misc.sprint("Lower PS point at step #%d: %s"%(i_step, str(step_info['lower_PS_point'])))
# Evaluate kernel
evaluation = utils.SubtractionCurrentEvaluation({
'spin_correlations': [
None,
],
'color_correlations': [
None,
],
'reduced_kinematics': [
reduced_kinematics,
],
'values': {}
})
# Apply collinear kernel (can be dummy)
evaluation = self.kernel(evaluation, all_steps, global_variables)
# Apply soft kernel (can be dummy), which also knows about the reduced process
evaluation = self.call_soft_kernel(evaluation, reduced_process,
all_steps, global_variables)
# Add the normalization factors
# WARNING! In this implementation the propagator denominators must be included in the kernel evaluation.
norm = (8. * math.pi * alpha_s)**(self.squared_orders['QCD'] / 2)
norm /= overall_jacobian
for k in evaluation['values']:
for term in evaluation['values'][k]:
evaluation['values'][k][term] *= norm
# Construct and return result
result = utils.SubtractionCurrentResult()
result.add_result(evaluation,
hel_config=hel_config,
squared_orders=tuple(
sorted(current.get('squared_orders').items())))
return result