def CqqFF_Finite_Gabor_EEJJ(a0, y12in):
'''Final-final collinear integrated counterterm for qq for m=2'''
if abs(y12in - 1.) < 1e-6:
y12 = 1 - 1e-6
else:
y12 = y12in
#misc.sprint("In CqqFF")
#misc.sprint("y12 = " + str(y12))
return (
-10 / 9 - (8 * a0) / (3 * (a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) + (4 * a0 * y12) /
((a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) - (4 * a0 * y12**2) / (3 * (a0 * (-2 + y12) - y12) *
(-2 + y12)**2 * (-1 + y12)) +
(2 * MPL.G([0], a0)) / 3 + (2 * MPL.G([0], y12)) / 3 +
(2 * y12 * MPL.G([y12 / (a0 * (-2 + y12))], 1)) / (3 *
(-2 + y12)**2) -
(16 * a0 * MPL.G([y12 / (a0 * (-1 + y12))], 1)) /
(3 * (a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) - (8 * y12 * MPL.G([y12 / (a0 * (-1 + y12))], 1)) /
(3 * (a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) + (8 * a0 * y12 * MPL.G([y12 / (a0 *
(-1 + y12))], 1)) /
((a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) + (8 * y12**2 * MPL.G([y12 / (a0 * (-1 + y12))], 1)) /
(3 * (a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) - (4 * a0 * y12**2 * MPL.G([y12 / (a0 *
(-1 + y12))], 1)) /
((a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) - (2 * y12**3 * MPL.G([y12 / (a0 * (-1 + y12))], 1)) /
(3 * (a0 * (-2 + y12) - y12) * (-2 + y12)**2 *
(-1 + y12)) + (2 * a0 * y12**3 * MPL.G([y12 / (a0 *
(-1 + y12))], 1)) /
(3 * (a0 * (-2 + y12) - y12) * (-2 + y12)**2 * (-1 + y12)))
def SoftFF_Finite_Gabor_EEJJ(y0,Yin):
'''Final-final soft+soft-colinear integrated counterterm for qg for m=2'''
if abs(Yin-1.) < 1e-6:
Y = 1-1e-6
else:
Y = Yin
return (-math.pi**2/6 + 2*(y0 + MPL.G([0], Y)*(y0 - MPL.G([0], y0))) - MPL.G([0, 0], Y) + MPL.G([1, 0], Y))
def SoftFF_Finite_Gabor_DIVJAC_NOD0(y0,Yin):
'''Final-final soft+soft-colinear integrated counterterm canonically normalized for the soft rescaling mapping'''
if abs(Yin-1.) < 1e-6:
Y = 1-1e-6
else:
Y = Yin
return (-math.pi**2/6 + 2*(y0 + MPL.G([0], Y)*(y0 - MPL.G([0], y0))) - MPL.G([0, 0], Y) + MPL.G([1, 0], Y))
def CqqFF_Finite_Gabor_DIVJAC_NOD0(a0,y12in):
'''Final-final collinear integrated counterterm for qq canonically normalized for the rescaling mapping'''
if abs(y12in-1.) < 1e-6:
y12 = 1-1e-6
else:
y12 = y12in
return ((10*(-2 + y12)*y12 - 2*a0*(20 - 17*y12 + 5*y12**2))/(9*(a0*(-2 + y12) - y12)*(-2 + y12)) +
(4*(-1 + y12)*MPL.G([0], 2))/(3*(-2 + y12)**2) + (4*(3 - 3*y12 + y12**2)*MPL.G([0], a0))/(3*(-2 + y12)**2) -
(4*(-1 + y12)*MPL.G([0], y12))/(3*(-2 + y12)**2) + (2*MPL.G([a0/(-1 + a0)], y12))/3 +
(4*(-1 + y12)*MPL.G([(2*a0)/(-1 + a0)], y12))/(3*(-2 + y12)**2))
def test_weight_0_values(self, list_of_arguments = None):
if list_of_arguments is None:
args = [1., 2., 3, 4, 0.1]
else:
args = list_of_arguments
results = [mpl.G([], x) for x in args]
for result in results:
self.assertAlmostEquals(result, 1.)
def CqgFF_Finite_Gabor_EEJJ(a0,y12in):
'''Final-final collinear integrated counterterm for qg for m=2'''
if abs(y12in-1.) < 1e-6:
y12 = 1-1e-6
else:
y12 = y12in
#misc.sprint("In CqgFF")
#misc.sprint("y12 = " + str(y12))
#misc.sprint("a0 = " + str(a0))
return (5 - math.pi**2/3 + 3/(2*(-1 + y12)) - (3*y12)/(2*(-1 + y12)) - (3*MPL.G([0], a0))/2 - (3*MPL.G([0], y12))/2 +
MPL.G([0], a0)*MPL.G([0], y12) + MPL.G([0], a0)*MPL.G([-a0], y12) - MPL.G([0], y12)*MPL.G([-y12], a0) +
(3*(a0 + y12 - a0*y12)*MPL.G([y12/(-1 + y12)], a0))/(2*a0*(-1 + y12)**2) -
((3*y12 - 4*a0*MPL.G([0], y12) + 4*a0*y12*MPL.G([0], y12))*MPL.G([y12/(-1 + y12)], a0))/(2*a0*(-1 + y12)**2) +
MPL.G([0, 0], a0) + MPL.G([0, 0], y12) - 2*MPL.G([0, -y12], a0) - (2*MPL.G([0, y12/(-1 + y12)], a0))/(-1 + y12) +
(2*y12*MPL.G([0, y12/(-1 + y12)], a0))/(-1 + y12) + MPL.G([-a0, 0], y12) - MPL.G([-y12, 0], a0) +
(2*MPL.G([y12/(-1 + y12), 0], a0))/(-1 + y12) - (2*MPL.G([y12/(-1 + y12), y12/(-1 + y12)], a0))/(-1 + y12))
def CggFF_Finite_Gabor_EEJJ(a0,y12in):
'''Final-final collinear integrated counterterm for gg for m=2'''
if abs(y12in-1.) < 1e-6:
y12 = 1-1e-6
else:
y12 = y12in
#misc.sprint("In CggFF")
#misc.sprint("y12 = " + str(y12))
return (100/9 - (2*math.pi**2)/3 + (40 - 42*y12 + 13*y12**2)/(3*(-2 + y12)**2*(-1 + y12)) -
(y12*(4 - 84*a0 - 46*y12 + 126*a0*y12 + 42*y12**2 - 64*a0*y12**2 - 11*y12**3 + 11*a0*y12**3))/
(3*(-2 + y12)**2*(-1 + y12)*(-2*a0 - y12 + a0*y12)) - (11*MPL.G([0], a0))/3 - (11*MPL.G([0], y12))/3 +
2*MPL.G([0], a0)*MPL.G([0], y12) + 2*MPL.G([0], a0)*MPL.G([-a0], y12) - 2*MPL.G([0], y12)*MPL.G([-y12], a0) -
(2*y12*(2 + y12)*MPL.G([y12/(-2 + y12)], a0))/(3*a0*(-2 + y12)**3) +
(2*y12*(2 - a0*(-2 + y12) + y12)*MPL.G([y12/(-2 + y12)], a0))/(3*a0*(-2 + y12)**3) -
(11*y12*MPL.G([y12/(-1 + y12)], a0))/(3*a0*(-1 + y12)**2) + (11*(a0 + y12 - a0*y12)*MPL.G([y12/(-1 + y12)], a0))/
(3*a0*(-1 + y12)**2) - (4*MPL.G([0], y12)*MPL.G([y12/(-1 + y12)], a0))/(-1 + y12) + 2*MPL.G([0, 0], a0) +
2*MPL.G([0, 0], y12) - 4*MPL.G([0, -y12], a0) - (4*MPL.G([0, y12/(-1 + y12)], a0))/(-1 + y12) +
(4*y12*MPL.G([0, y12/(-1 + y12)], a0))/(-1 + y12) + 2*MPL.G([-a0, 0], y12) - 2*MPL.G([-y12, 0], a0) +
(4*MPL.G([y12/(-1 + y12), 0], a0))/(-1 + y12) - (4*MPL.G([y12/(-1 + y12), y12/(-1 + y12)], a0))/(-1 + y12))
def SoftIF_Finite_Gabor_DIVJAC_NOD0(y0, Y):
'''Mapping independent initial-final soft+soft-colinear integrated counterterm'''
return (-4 * (-1 + math.sqrt(1 - y0)) * (1 + MPL.G([0], Y)) - 4 * (1 + MPL.G([0], Y)) * (
MPL.G([0], 2) - MPL.G([0], 1 + math.sqrt(1 - y0))) -
(MPL.G([0], Y) * (MPL.G([0], Y) + 4 * MPL.G([0], y0))) / 2 + MPL.G([0, 1], 1 - Y))
def CqgFF_Finite_Gabor_DIVJAC_NOD0(a0,y12in):
'''Final-final collinear integrated counterterm for qg canonically normalized for the rescaling mapping'''
if abs(y12in-1.) < 1e-6:
y12 = 1-1e-6
else:
y12 = y12in
return ((7 - math.pi**2)/2 + 3*MPL.G([0], y12)**2 + MPL.G([0], a0)*(-3 + (4 - 8/y12)*MPL.G([1], y12)) +
MPL.G([0], y12)*(-MPL.G([-a0], y12) - 2*MPL.G([a0/(-1 + a0)], y12)) - (3*MPL.G([a0/(-1 + a0)], y12))/2 -
2*MPL.G([0, 0], y12) + MPL.G([0, -a0], y12) + 2*MPL.G([0, a0/(-1 + a0)], y12) + (-4 + 8/y12)*MPL.G([1, 0], y12) +
(4 - 8/y12)*MPL.G([1, a0/(-1 + a0)], y12) + MPL.G([-a0, 0], y12) + 2*MPL.G([a0/(-1 + a0), 0], y12) -
2*MPL.G([a0/(-1 + a0), a0/(-1 + a0)], y12))
def CggFF_Finite_Gabor_DIVJAC_NOD0(a0,y12in):
'''Final-final collinear integrated counterterm for gg canonically normalized for the rescaling mapping'''
if abs(y12in-1.) < 1e-6:
y12 = 1-1e-6
else:
y12 = y12in
return (((-67 + 9*math.pi**2)*(-2 + y12)*y12 + a0*(268 - 9*math.pi**2*(-2 + y12)**2 - 262*y12 + 67*y12**2))/
(9*(a0*(-2 + y12) - y12)*(-2 + y12)) - (4*(-1 + y12)*MPL.G([0], 2))/(3*(-2 + y12)**2) + 6*MPL.G([0], y12)**2 +
MPL.G([0], a0)*((-2*(42 - 42*y12 + 11*y12**2))/(3*(-2 + y12)**2) + (8*(-2 + y12)*MPL.G([1], y12))/y12) +
MPL.G([0], y12)*((4*(-1 + y12))/(3*(-2 + y12)**2) - 2*MPL.G([-a0], y12) - 4*MPL.G([a0/(-1 + a0)], y12)) -
(11*MPL.G([a0/(-1 + a0)], y12))/3 - (4*(-1 + y12)*MPL.G([(2*a0)/(-1 + a0)], y12))/(3*(-2 + y12)**2) -
4*MPL.G([0, 0], y12) + 2*MPL.G([0, -a0], y12) + 4*MPL.G([0, a0/(-1 + a0)], y12) + (-8 + 16/y12)*MPL.G([1, 0], y12) +
(8*(-2 + y12)*MPL.G([1, a0/(-1 + a0)], y12))/y12 + 2*MPL.G([-a0, 0], y12) + 4*MPL.G([a0/(-1 + a0), 0], y12) -
4*MPL.G([a0/(-1 + a0), a0/(-1 + a0)], y12))
def integrated_bs_endpoint_finite(dipole_invariant):
"""Finite part of the endpoint contribution of the collinear-subtracted eikonal integrated over the SoftVsInitial mapping unresolved PS (BS)"""
return -math.log(16.) * math.log(dipole_invariant) - math.log(
dipole_invariant)**2 + 2. * (MPL.G([1, 0], dipole_invariant) -
math.pi**2 / 6.)
def check_MPL(self, entries, x, target_value, places=7):
a = mpl.G(entries, x)
b = target_value
check = abs(a-b)/(abs(a)+abs(b))
return self.assertAlmostEquals(check,0.,places=places)
