| 1 | ################################################################################
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| 2 | #
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| 3 | # Copyright (c) 2010 The MadGraph Development team and Contributors
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| 4 | #
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| 5 | # This file is a part of the MadGraph 5 project, an application which
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| 6 | # automatically generates Feynman diagrams and matrix elements for arbitrary
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| 7 | # high-energy processes in the Standard Model and beyond.
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| 8 | #
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| 9 | # It is subject to the MadGraph license which should accompany this
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| 10 | # distribution.
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| 11 | #
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| 12 | # For more information, please visit: http://madgraph.phys.ucl.ac.be
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| 13 | #
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| 14 | ################################################################################
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| 15 | ## Diagram of Class
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| 16 | ##
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| 17 | ## Variable <--- HelasLib.ScalarVariable
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| 18 | ## |
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| 19 | ## +- LorentzObject <--- Gamma
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| 20 | ## |
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| 21 | ## +- Sigma
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| 22 | ## |
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| 23 | ## +- P
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| 24 | ##
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| 25 | ## list <--- AddVariable
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| 26 | ## |
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| 27 | ## +- MultVariable <--- MultLorentz
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| 28 | ##
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| 29 | ## list <--- LorentzObjectRepresentation <-- ConstantObject
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| 30 | ##
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| 31 | ################################################################################
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| 32 |
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| 33 | import madgraph.interface.helasamp_lib as HelasLib
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| 34 |
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| 35 | #===============================================================================
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| 36 | # P (Impulsion)
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| 37 | #===============================================================================
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| 38 | class P(HelasLib.LorentzObject):
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| 39 | """ Helas Object for an Impulsion """
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| 40 |
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| 41 | def __init__(self, lorentz1, particle, prefactor=1, constant=0):
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| 42 |
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| 43 | self.particle = particle
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| 44 | HelasLib.LorentzObject.__init__(self, [lorentz1], [], ['P%s'%particle], \
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| 45 | prefactor=prefactor,constant=constant)
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| 46 |
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| 47 |
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| 48 | def create_representation(self):
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| 49 | self.sub0 = HelasLib.ScalarVariable('P%s_0' % self.particle, self.tag)
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| 50 | self.sub1 = HelasLib.ScalarVariable('P%s_1' % self.particle, self.tag)
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| 51 | self.sub2 = HelasLib.ScalarVariable('P%s_2' % self.particle, self.tag)
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| 52 | self.sub3 = HelasLib.ScalarVariable('P%s_3' % self.particle, self.tag)
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| 53 |
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| 54 | self.representation= HelasLib.LorentzObjectRepresentation(
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| 55 | [self.sub0, self.sub1, self.sub2, self.sub3],
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| 56 | self.lorentz_ind,[],self.tag)
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| 57 |
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| 58 | #===============================================================================
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| 59 | # Mass
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| 60 | #===============================================================================
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| 61 | class Mass(HelasLib.LorentzObject):
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| 62 | """ Helas Object for a Mass"""
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| 63 |
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| 64 | def __init__(self, particle, prefactor=1, constant=0):
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| 65 |
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| 66 | self.particle = particle
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| 67 | HelasLib.LorentzObject.__init__(self, [], [], ['M%s' % particle], \
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| 68 | prefactor=prefactor, constant=constant)
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| 69 |
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| 70 |
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| 71 | def create_representation(self):
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| 72 | mass = HelasLib.ScalarVariable('M%s' % self.particle, self.tag)
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| 73 |
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| 74 | self.representation = HelasLib.LorentzObjectRepresentation(
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| 75 | mass, self.lorentz_ind, self.spin_ind, self.tag)
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| 76 |
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| 77 | #===============================================================================
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| 78 | # OverMass2
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| 79 | #===============================================================================
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| 80 | class OverMass2(HelasLib.LorentzObject):
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| 81 | """ Helas Object for 1/M**2 """
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| 82 |
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| 83 | def __init__(self, particle, prefactor=1, constant=0):
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| 84 |
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| 85 | self.particle = particle
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| 86 |
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| 87 | tag= ['mass%s' %particle, 'OM%s' % particle]
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| 88 | HelasLib.LorentzObject.__init__(self, [], [], tag, \
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| 89 | prefactor=prefactor, constant=constant)
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| 90 |
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| 91 |
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| 92 | def create_representation(self):
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| 93 | mass = HelasLib.ScalarVariable('OM%s' % self.particle, self.tag)
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| 94 |
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| 95 | self.representation = HelasLib.LorentzObjectRepresentation(
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| 96 | mass, self.lorentz_ind, self.spin_ind, self.tag)
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| 97 |
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| 98 | #===============================================================================
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| 99 | # Width
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| 100 | #===============================================================================
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| 101 | class Width(HelasLib.LorentzObject):
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| 102 | """ Helas Object for an Impulsion """
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| 103 |
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| 104 | def __init__(self, particle, prefactor=1, constant=0):
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| 105 |
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| 106 | self.particle = particle
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| 107 | HelasLib.LorentzObject.__init__(self, [], [], ['W%s' % particle], \
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| 108 | prefactor=prefactor, constant=constant)
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| 109 |
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| 110 | def create_representation(self):
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| 111 | width = HelasLib.ScalarVariable('W%s' % self.particle, self.tag)
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| 112 |
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| 113 | self.representation= HelasLib.LorentzObjectRepresentation(
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| 114 | width, self.lorentz_ind, self.spin_ind, self.tag)
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| 115 |
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| 116 | #===============================================================================
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| 117 | # Scalar
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| 118 | #===============================================================================
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| 119 | class Scalar(HelasLib.LorentzObject):
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| 120 | """ Helas Object for a Spinor"""
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| 121 |
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| 122 | def __init__(self, particle, prefactor=1, constant=0):
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| 123 |
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| 124 | self.particle = particle
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| 125 | HelasLib.LorentzObject.__init__(self, [], [], ['S%s' % particle], \
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| 126 | prefactor=prefactor,constant=constant)
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| 127 |
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| 128 |
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| 129 | def create_representation(self):
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| 130 | rep = HelasLib.ScalarVariable('S%s_1' % self.particle, self.tag)
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| 131 | self.representation= HelasLib.LorentzObjectRepresentation(
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| 132 | rep,
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| 133 | [],[],self.tag)
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| 134 |
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| 135 |
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| 136 | #===============================================================================
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| 137 | # Spinor
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| 138 | #===============================================================================
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| 139 | class Spinor(HelasLib.LorentzObject):
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| 140 | """ Helas Object for a Spinor"""
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| 141 |
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| 142 | def __init__(self, spin1, particle, prefactor=1, constant=0):
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| 143 |
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| 144 | self.particle = particle
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| 145 | HelasLib.LorentzObject.__init__(self, [], [spin1], ['F%s' % particle], \
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| 146 | prefactor=prefactor,constant=constant)
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| 147 |
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| 148 |
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| 149 | def create_representation(self):
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| 150 | self.sub0 = HelasLib.ScalarVariable('F%s_1' % self.particle, self.tag)
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| 151 | self.sub1 = HelasLib.ScalarVariable('F%s_2' % self.particle, self.tag)
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| 152 | self.sub2 = HelasLib.ScalarVariable('F%s_3' % self.particle, self.tag)
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| 153 | self.sub3 = HelasLib.ScalarVariable('F%s_4' % self.particle, self.tag)
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| 154 |
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| 155 | self.representation= HelasLib.LorentzObjectRepresentation(
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| 156 | [self.sub0, self.sub1, self.sub2, self.sub3],
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| 157 | [],self.spin_ind,self.tag)
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| 158 |
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| 159 | #===============================================================================
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| 160 | # Vector
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| 161 | #===============================================================================
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| 162 | class Vector(HelasLib.LorentzObject):
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| 163 | """ Helas Object for a Vector"""
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| 164 |
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| 165 | def __init__(self, lorentz, particle, prefactor=1, constant=0):
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| 166 |
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| 167 | self.particle = particle
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| 168 | HelasLib.LorentzObject.__init__(self, [lorentz], [], ['V%s' % particle], \
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| 169 | prefactor=prefactor,constant=constant)
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| 170 |
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| 171 |
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| 172 | def create_representation(self):
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| 173 | self.sub0 = HelasLib.ScalarVariable('V%s_1' % self.particle, self.tag)
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| 174 | self.sub1 = HelasLib.ScalarVariable('V%s_2' % self.particle, self.tag)
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| 175 | self.sub2 = HelasLib.ScalarVariable('V%s_3' % self.particle, self.tag)
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| 176 | self.sub3 = HelasLib.ScalarVariable('V%s_4' % self.particle, self.tag)
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| 177 |
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| 178 | self.representation= HelasLib.LorentzObjectRepresentation(
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| 179 | [self.sub0, self.sub1, self.sub2, self.sub3],
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| 180 | self.lorentz_ind, [], self.tag)
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| 181 |
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| 182 | #===============================================================================
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| 183 | # Spin2
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| 184 | #===============================================================================
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| 185 | class Spin2(HelasLib.LorentzObject):
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| 186 | """ Helas Object for a Spin2"""
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| 187 |
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| 188 | def __init__(self, lorentz1, lorentz2, particle, prefactor=1, constant=0):
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| 189 |
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| 190 | self.particle = particle
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| 191 | if lorentz2 < lorentz1:
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| 192 | lorentz1, lorentz2 = lorentz2, lorentz1
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| 193 |
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| 194 | HelasLib.LorentzObject.__init__(self, [lorentz1, lorentz2], [], \
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| 195 | ['G%s' % particle], prefactor=prefactor, \
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| 196 | constant=constant)
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| 197 |
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| 198 | def create_representation(self):
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| 199 |
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| 200 | self.sub00 = HelasLib.ScalarVariable('G%s_00' % self.particle, self.tag)
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| 201 | self.sub01 = HelasLib.ScalarVariable('G%s_01' % self.particle, self.tag)
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| 202 | self.sub02 = HelasLib.ScalarVariable('G%s_02' % self.particle, self.tag)
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| 203 | self.sub03 = HelasLib.ScalarVariable('G%s_03' % self.particle, self.tag)
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| 204 |
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| 205 | self.sub11 = HelasLib.ScalarVariable('G%s_11' % self.particle, self.tag)
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| 206 | self.sub22 = HelasLib.ScalarVariable('G%s_12' % self.particle, self.tag)
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| 207 | self.sub33 = HelasLib.ScalarVariable('G%s_13' % self.particle, self.tag)
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| 208 |
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| 209 | self.sub22 = HelasLib.ScalarVariable('G%s_22' % self.particle, self.tag)
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| 210 | self.sub23 = HelasLib.ScalarVariable('G%s_23' % self.particle, self.tag)
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| 211 |
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| 212 | self.sub33 = HelasLib.ScalarVariable('G%s_33' % self.particle, self.tag)
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| 213 |
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| 214 | rep = [[self.sub00, self.sub01, self.sub02, self.sub03], \
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| 215 | [self.sub01, self.sub11, self.sub12, self.sub13], \
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| 216 | [self.sub02, self.sub12, self.sub22, self.sub23], \
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| 217 | [self.sub03, self.sub13, self.sub22, self.sub23]]
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| 218 |
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| 219 | self.representation= HelasLib.LorentzObjectRepresentation( rep, \
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| 220 | self.lorentz_ind, [], self.tag)
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| 221 |
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| 222 | #===============================================================================
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| 223 | # Gamma
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| 224 | #===============================================================================
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| 225 | class Gamma(HelasLib.LorentzObject):
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| 226 | """ Gamma Matrices """
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| 227 |
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| 228 | gamma0 = [[0, 0, 1, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 1, 0, 0]]
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| 229 | gamma1 = [[0, 0, 0, 1], [0, 0, 1, 0], [0, -1, 0, 0], [-1, 0, 0, 0]]
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| 230 | gamma2 = [[0, 0, 0, -complex(0,1)],[0, 0, complex(0,1), 0],
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| 231 | [0, complex(0,1), 0, 0], [-complex(0,1), 0, 0, 0]]
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| 232 | gamma3 = [[0, 0, 1, 0], [0, 0, 0, -1], [-1, 0, 0, 0], [0, 1, 0, 0]]
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| 233 |
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| 234 | gamma = [gamma0, gamma1, gamma2, gamma3]
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| 235 |
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| 236 |
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| 237 | def __init__(self, lorentz, spin1, spin2, prefactor=1, constant=0):
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| 238 | HelasLib.LorentzObject.__init__(self,[lorentz], [spin1, spin2], [])
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| 239 |
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| 240 | def create_representation(self):
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| 241 |
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| 242 | self.representation = HelasLib.LorentzObjectRepresentation(self.gamma,
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| 243 | self.lorentz_ind,self.spin_ind,[])
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| 244 |
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| 245 | #===============================================================================
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| 246 | # Sigma
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| 247 | #===============================================================================
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| 248 | class Sigma(HelasLib.LorentzObject):
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| 249 | """ Gamma Matrices """
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| 250 |
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| 251 | zero = [[0,0,0,0]]*4
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| 252 | i = complex(0,1)
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| 253 | sigma01 = [[ 0, -i, 0, 0], [-i, 0, 0, 0], [0, 0, 0, i], [0, 0, i, 0]]
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| 254 | sigma02 = [[ 0, -1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, -1, 0]]
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| 255 | sigma03 = [[-i, 0, 0, 0], [0, i, 0, 0], [0, 0, i, 0], [0, 0, 0, -i]]
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| 256 | sigma12 = [[1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 1, 0], [0, 0, 0, -1]]
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| 257 | sigma13 = [[0, i, 0, 0], [-i, 0, 0, 0], [0, 0, 0, i], [0, 0, -i, 0]]
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| 258 | sigma23 = [[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]
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| 259 |
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| 260 |
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| 261 | def inv(matrice):
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| 262 | out=[]
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| 263 | for i in range(4):
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| 264 | out2=[]
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| 265 | out.append(out2)
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| 266 | for j in range(4):
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| 267 | out2.append(-1*matrice[i][j])
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| 268 | return out
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| 269 |
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| 270 | sigma =[[zero, sigma01, sigma02, sigma03], \
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| 271 | [inv(sigma01), zero, sigma12, sigma13],\
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| 272 | [inv(sigma02), inv(sigma12), zero, sigma23],\
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| 273 | [inv(sigma03), inv(sigma13), inv(sigma23), zero]]
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| 274 |
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| 275 | def __init__(self, lorentz1, lorentz2, spin1, spin2, prefactor=1, constant=0):
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| 276 | if lorentz1 < lorentz2:
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| 277 | HelasLib.LorentzObject.__init__(self,[lorentz1, lorentz2], \
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| 278 | [spin1, spin2], [])
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| 279 | else:
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| 280 | HelasLib.LorentzObject.__init__(self,[lorentz2, lorentz1], [spin1, spin2], \
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| 281 | [], prefactor=-1)
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| 282 |
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| 283 | def create_representation(self):
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| 284 |
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| 285 | self.representation = HelasLib.LorentzObjectRepresentation(self.sigma,
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| 286 | self.lorentz_ind,self.spin_ind,[])
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| 287 |
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| 288 | #===============================================================================
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| 289 | # Gamma5
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| 290 | #===============================================================================
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| 291 | class Gamma5(HelasLib.LorentzObject):
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| 292 |
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| 293 | gamma5 = [[-1, 0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
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| 294 |
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| 295 | def __init__(self, spin1, spin2, prefactor=1, constant=0):
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| 296 | if spin1 < spin2:
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| 297 | HelasLib.LorentzObject.__init__(self,[], [spin1, spin2], [])
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| 298 | else:
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| 299 | HelasLib.LorentzObject.__init__(self,[], [spin2, spin1], [])
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| 300 |
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| 301 | def create_representation(self):
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| 302 |
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| 303 | self.representation = HelasLib.LorentzObjectRepresentation(self.gamma5,
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| 304 | self.lorentz_ind,self.spin_ind,[])
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| 305 |
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| 306 | #===============================================================================
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| 307 | # Metric
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| 308 | #===============================================================================
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| 309 | class Metric(HelasLib.LorentzObject):
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| 310 |
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| 311 | metric = [[1, 0, 0,0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]]
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| 312 |
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| 313 | def __init__(self, lorentz1, lorentz2, prefactor=1, constant=0):
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| 314 | if lorentz1 < lorentz2:
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| 315 | HelasLib.LorentzObject.__init__(self,[lorentz1, lorentz2], [], [])
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| 316 | else:
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| 317 | HelasLib.LorentzObject.__init__(self,[lorentz2, lorentz1], [], [])
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| 318 | def create_representation(self):
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| 319 |
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| 320 | self.representation = HelasLib.LorentzObjectRepresentation(self.metric,
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| 321 | self.lorentz_ind,self.spin_ind,[])
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| 322 |
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| 323 |
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| 324 |
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| 325 | #===============================================================================
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| 326 | # Identity
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| 327 | #===============================================================================
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| 328 | class Identity(HelasLib.LorentzObject):
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| 329 |
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| 330 | identity = [[1, 0, 0,0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
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| 331 |
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| 332 | def __init__(self, spin1, spin2, prefactor=1, constant=0):
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| 333 | if spin1 < spin2:
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| 334 | HelasLib.LorentzObject.__init__(self,[],[spin1, spin2], [])
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| 335 | else:
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| 336 | HelasLib.LorentzObject.__init__(self,[],[spin2, spin1], [])
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| 337 |
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| 338 | def create_representation(self):
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| 339 |
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| 340 | self.representation = HelasLib.LorentzObjectRepresentation(self.identity,
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| 341 | self.lorentz_ind,self.spin_ind,[])
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| 342 | ##===============================================================================
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| 343 | ## IdentityL (Commented since not use)
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| 344 | ##===============================================================================
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| 345 | #class IdentityL(HelasLib.LorentzObject):
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| 346 | #
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| 347 | # identity = [[1, 0, 0,0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
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| 348 | #
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| 349 | # def __init__(self, lorentz1, lorentz2, prefactor=1, constant=0):
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| 350 | # if lorentz1 < lorentz2:
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| 351 | # HelasLib.LorentzObject.__init__(self,[lorentz1, lorentz2], [], [])
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| 352 | # else:
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| 353 | # HelasLib.LorentzObject.__init__(self,[lorentz1, lorentz2], [], [])
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| 354 | #
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| 355 | # def create_representation(self):
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| 356 | #
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| 357 | # self.representation = HelasLib.LorentzObjectRepresentation(self.identity,
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| 358 | # self.lorentz_ind,self.spin_ind,[])
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| 359 | #
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| 360 | #===============================================================================
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| 361 | # ProjM
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| 362 | #===============================================================================
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| 363 | class ProjM(HelasLib.LorentzObject):
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| 364 | """ A object for (1-gamma5)/2 """
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| 365 |
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| 366 | projm = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]
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| 367 |
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| 368 | def __init__(self,spin1, spin2):
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| 369 | """Initialize the object"""
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| 370 | if spin1 < spin2:
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| 371 | HelasLib.LorentzObject.__init__(self,[], [spin1, spin2], [])
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| 372 | else:
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| 373 | HelasLib.LorentzObject.__init__(self,[], [spin2, spin1], [])
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| 374 |
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| 375 |
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| 376 | def create_representation(self):
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| 377 |
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| 378 | self.representation = HelasLib.LorentzObjectRepresentation(self.projm,
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| 379 | self.lorentz_ind,self.spin_ind,[])
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| 380 |
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| 381 |
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| 382 | #===============================================================================
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| 383 | # ProjP
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| 384 | #===============================================================================
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| 385 | class ProjP(HelasLib.LorentzObject):
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| 386 | """A object for (1+gamma5)/2 """
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| 387 |
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| 388 | projp = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
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| 389 |
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| 390 | def __init__(self,spin1, spin2):
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| 391 | """Initialize the object"""
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| 392 | if spin1 < spin2:
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| 393 | HelasLib.LorentzObject.__init__(self,[], [spin1, spin2], [])
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| 394 | else:
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| 395 | HelasLib.LorentzObject.__init__(self,[], [spin2, spin1], [])
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| 396 |
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| 397 |
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| 398 | def create_representation(self):
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| 399 |
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| 400 | self.representation = HelasLib.LorentzObjectRepresentation(self.projp,
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| 401 | self.lorentz_ind, self.spin_ind, [])
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| 402 |
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| 403 | #===============================================================================
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| 404 | # Denominator Propagator
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| 405 | #===============================================================================
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| 406 | class DenominatorPropagator(HelasLib.LorentzObject):
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| 407 | """The Denominator of the Propagator"""
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| 408 |
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| 409 | def __init__(self, particle):
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| 410 | """Initialize the object"""
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| 411 |
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| 412 | self.particle = particle
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| 413 | tag=['M%s' % particle,'W%s' % particle, 'P%s' % particle]
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| 414 | HelasLib.LorentzObject.__init__(self, [], [], tag)
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| 415 |
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| 416 | def simplify(self):
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| 417 | """Return the Denominator in a abstract way"""
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| 418 |
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| 419 | mass = Mass(self.particle)
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| 420 | width = Width(self.particle)
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| 421 | denominator = P('i1', self.particle) * P('i1', self.particle) - \
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| 422 | mass * mass + complex(0,1) * mass* width
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| 423 |
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| 424 | return denominator
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| 425 |
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| 426 | def create_representation(self):
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| 427 | """Create the representation for the Vector propagator"""
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| 428 |
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| 429 | object = self.simplify()
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| 430 | self.representation = object.expand()
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| 431 |
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| 432 |
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| 433 |
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| 434 | #===============================================================================
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| 435 | # Numerator Propagator
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| 436 | #===============================================================================
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| 437 |
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| 438 |
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| 439 | SpinorPropagator = lambda spin1, spin2, particle: complex(0,1) * (Gamma('mu', spin1, spin2) * \
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| 440 | P('mu', particle) + Mass(particle) * Identity(spin1, spin2))
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| 441 |
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| 442 | VectorPropagator = lambda l1, l2, part: complex(0,1) * (-1 * Metric(l1, l2) + OverMass2(part) * \
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| 443 | Metric(l1,'I3')* P('I3', part) * P(l2, part))
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| 444 |
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| 445 | Spin2masslessPropagator = lambda l1, l2, l3, l4: 1/2 *( Metric(l1, l2)* \
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| 446 | Metric(l3, l4) + Metric(l1, l4) * Metric(l2, l3) - Metric(l1, l2) * Metric(l3, l4))
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| 447 |
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| 448 |
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| 449 |
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| 450 | Spin2Propagator = lambda l1, l2, l3, l4, part: Spin2masslessPropagator(l1, l2, l3, l4) + \
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| 451 | -1/2 * OverMass2(part) * (Metric(l1,l2)* P(l3, part) * P(l4, part) + \
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| 452 | Metric(l3, l4) * P(l1, part) * P(l2, part) + \
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| 453 | Metric(l1, l4) * P(l2, part) * P(l3, part) + \
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| 454 | Metric(l3, l2) * P(l1, part) * P(l4 , part) )+ \
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| 455 | 1/6 * (Metric(l1,l3) + 2 * OverMass2(part) * P(l1, part) * P(l3, part)) * \
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| 456 | (Metric(l2,l4) + 2 * OverMass2(part) * P(l2, part) * P(l4, part))
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| 457 |
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| 458 |
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| 459 |
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| 460 | if __name__ == '__main__':
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| 461 |
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| 462 | # Input as coming from FR!!!
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| 463 | obj = 1/DenominatorPropagator(2)
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| 464 | #Gamma(2,1,2)*Gamma(4,4,6)# * VectorPropagator(2,3,2) #/DenominatorPropagator(3)
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| 465 | print type(obj)
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| 466 | # Analysis
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| 467 | obj = obj.simplify() # -> Simplify sum
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| 468 | print obj
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| 469 |
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| 470 | # expand
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| 471 |
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| 472 |
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| 473 | low_level = obj.expand()
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| 474 | print type(low_level)
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| 475 | low_level = low_level.simplify()
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| 476 |
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| 477 | print 'all is done'
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| 478 | print low_level
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| 479 |
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| 480 | #writing the object in a file
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| 481 | #low_level.create_output('Fortran','test.f')
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| 482 |
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