1 | (***************************************************************************************************************)
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2 | (****** This is the FeynRules mod-file for the 331 model where beta is general ******)
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3 | (****** ******)
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4 | (****** Authors: Dongming Zhang ******)
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5 | (****** ******)
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6 | (****** Choose whether Feynman gauge is desired. ******)
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7 | (****** If set to False, unitary gauge is assumed. ****)
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8 | (****** Feynman gauge is especially useful for CalcHEP/CompHEP where the calculation is 10-100 times faster. ***)
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9 | (****** Feynman gauge is not supported in MadGraph and Sherpa. ****)
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10 | (***************************************************************************************************************)
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11 |
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12 | (* ************************** *)
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13 | (* ***** Information ***** *)
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14 | (* ************************** *)
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15 | M$ModelName = "331 Model";
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16 |
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17 | M$Information = {
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18 | Authors -> {"Dongming Zhang"},
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19 | Version -> "1.0.0",
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20 | Date -> "22. 01. 2014",
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21 | Institutions -> {"Peking University"},
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22 | Emails -> {"zhangdongming@pku.edu.cn"},
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23 | URLs -> "http://feynrules.irmp.ucl.ac.be/wiki/331"
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24 | };
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25 |
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26 | FeynmanGauge = True;
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27 |
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28 | (* ************************** *)
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29 | (* ***** Change log ***** *)
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30 | (* ************************** *)
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31 |
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32 | (* ************************** *)
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33 | (* ***** vevs ***** *)
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34 | (* ************************** *)
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35 | M$vevs = { {Rho[2],v}, {Phi[1],v2}, {Chi[3],v3} };
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36 |
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37 | (* ************************** *)
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38 | (* ***** Gauge groups ***** *)
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39 | (* ************************** *)
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40 | M$GaugeGroups = {
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41 | U1X == {
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42 | Abelian -> True,
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43 | CouplingConstant -> gx,
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44 | GaugeBoson -> K,
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45 | Charge -> X
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46 | },
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47 | SU3L == {
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48 | Abelian -> False,
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49 | CouplingConstant -> gw,
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50 | GaugeBoson -> Wi,
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51 | StructureConstant -> x,
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52 | Representations -> {Ta,SU3T},
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53 | Definitions -> {Ta[a_,b_,c_]->Gellmann[a,b,c]/2,FSU3L[i_,j_,k_]:> I x[i,j,k]},
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54 | SymmetricTensor -> dSUN
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55 | },
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56 | ASU3L == {
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57 | Abelian -> False,
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58 | CouplingConstant -> gw,
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59 | GaugeBoson -> WWi,
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60 | StructureConstant -> x,
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61 | Representations -> {Tb,ASU3T},
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62 | Definitions -> {Tb[a_,b_,c_]->-Gellmann[a,c,b]/2,FSU3L[i_,j_,k_]:> I x[i,j,k]},
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63 | SymmetricTensor -> dSUN
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64 | },
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65 | SU3C == {
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66 | Abelian -> False,
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67 | CouplingConstant -> gs,
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68 | GaugeBoson -> G,
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69 | StructureConstant -> f,
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70 | Representations -> {T,Colour},
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71 | SymmetricTensor -> dSUN
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72 | }
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73 | };
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74 |
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75 | (* ************************** *)
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76 | (* *** Gellmann matrices *** *)
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77 | (* ************************** *)
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78 |
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79 | Table[Gellmann[i, j, k] = 0, {i, 1, 8}, {j, 1, 3}, {k, 1, 3}] //
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80 | Flatten;
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81 |
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82 | Gellmann[1] = {{0, 1, 0}, {1, 0, 0}, {0, 0, 0}};
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83 | Gellmann[2] = {{0, -I, 0}, {I, 0, 0}, {0, 0, 0}};
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84 | Gellmann[3] = {{1, 0, 0}, {0, -1, 0}, {0, 0, 0}};
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85 | Gellmann[4] = {{0, 0, 1}, {0, 0, 0}, {1, 0, 0}};
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86 | Gellmann[5] = {{0, 0, -I}, {0, 0, 0}, {I, 0, 0}};
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87 | Gellmann[6] = {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}};
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88 | Gellmann[7] = {{0, 0, 0}, {0, 0, -I}, {0, I, 0}};
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89 | Gellmann[8] = 1/Sqrt[3] {{1, 0, 0}, {0, 1, 0}, {0, 0, -2}};
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90 |
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91 | Gellmann[1, 1, 2] = 1; Gellmann[1, 2, 1] = 1;
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92 | Gellmann[2, 1, 2] = -I; Gellmann[2, 2, 1] = I;
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93 | Gellmann[3, 1, 1] = 1; Gellmann[3, 2, 2] = -1;
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94 | Gellmann[4, 1, 3] = 1; Gellmann[4, 3, 1] = 1;
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95 | Gellmann[5, 1, 3] = -I; Gellmann[5, 3, 1] = I;
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96 | Gellmann[6, 2, 3] = 1; Gellmann[6, 3, 2] = 1;
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97 | Gellmann[7, 2, 3] = -I; Gellmann[7, 3, 2] = I;
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98 | Gellmann[8, 1, 1] = 1/Sqrt[3]; Gellmann[8, 2, 2] = 1/Sqrt[3];
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99 | Gellmann[8, 3, 3] = -2/Sqrt[3];
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100 |
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101 |
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102 | Gellmann[i_Integer, j_Integer, k_Integer] := Gellmann[i][[j, k]];
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103 | Gellmann[xx___, Index[_, i_Integer], yy___] := Gellmann[xx, i, yy];
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104 |
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105 | Gellmann /:
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106 | Gellmann[i1_, i2_, i3_?(Not[NumericQ[#]] &)] Gellmann[j1_, i3_,
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107 | j3_] :=
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108 | Gellmann[i1, i2, 1] Gellmann[j1, 1, j3] +
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109 | Gellmann[i1, i2, 2] Gellmann[j1, 2, j3] +
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110 | Gellmann[i1, i2, 3] Gellmann[j1, 3, j3];
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111 |
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112 | Table[x[i, j, k] = 0, {i, 1, 8}, {j, 1, 8}, {k, 1, 8}] // Flatten;
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113 | x[1, 2, 3] = 1; x[2, 3, 1] = 1; x[3, 1, 2] = 1;
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114 | x[2, 1, 3] = -1; x[1, 3, 2] = -1; x[3, 2, 1] = -1;
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115 | x[1, 5, 6] = -1/2; x[3, 6, 7] = -1/2; x[1, 7, 4] = -1/2;
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116 | x[2, 6, 4] = -1/2; x[2, 7, 5] = -1/2; x[3, 5, 4] = -1/2;
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117 | x[6, 1, 5] = -1/2; x[7, 3, 6] = -1/2; x[4, 1, 7] = -1/2;
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118 | x[4, 2, 6] = -1/2; x[5, 2, 7] = -1/2; x[4, 3, 5] = -1/2;
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119 | x[5, 6, 1] = -1/2; x[6, 7, 3] = -1/2; x[7, 4, 1] = -1/2;
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120 | x[6, 4, 2] = -1/2; x[7, 5, 2] = -1/2; x[5, 4, 3] = -1/2;
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121 | x[1, 6, 5] = 1/2; x[3, 7, 6] = 1/2; x[1, 4, 7] = 1/2;
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122 | x[2, 4, 6] = 1/2; x[2, 5, 7] = 1/2; x[3, 4, 5] = 1/2;
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123 | x[5, 1, 6] = 1/2; x[7, 6, 3] = 1/2; x[4, 7, 1] = 1/2;
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124 | x[4, 6, 2] = 1/2; x[5, 7, 2] = 1/2; x[4, 5, 3] = 1/2;
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125 | x[6, 5, 1] = 1/2; x[6, 3, 7] = 1/2; x[7, 1, 4] = 1/2;
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126 | x[6, 2, 4] = 1/2; x[7, 2, 5] = 1/2; x[5, 3, 4] = 1/2;
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127 | x[4, 5, 8] = Sqrt[3]/2; x[6, 7, 8] = Sqrt[3]/2;
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128 | x[8, 4, 5] = Sqrt[3]/2; x[8, 6, 7] = Sqrt[3]/2;
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129 | x[5, 8, 4] = Sqrt[3]/2; x[7, 8, 6] = Sqrt[3]/2;
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130 | x[4, 8, 5] = -Sqrt[3]/2; x[6, 8, 7] = -Sqrt[3]/2;
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131 | x[5, 4, 8] = -Sqrt[3]/2;
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132 | x[7, 6, 8] = -Sqrt[3]/2; x[8, 7, 6] = -Sqrt[3]/2;
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133 | x[8, 5, 4] = -Sqrt[3]/2;
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134 |
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135 | x /: x[ii___, Except[Index[___] | _?NumericQ, jj_], kk___] f_[aa___,
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136 | Index[name_, jj_], cc___] :=
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137 | x[ii, Index[name, jj], kk] f[aa, Index[name, jj], cc];
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138 | x /: x[ii___, Except[Index[___] | _?NumericQ, jj_],
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139 | kk___] f_[aa___, Index[name_, jj_], cc___][ind___] :=
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140 | x[ii, Index[name, jj], kk] f[aa, Index[name, jj], cc][ind];
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141 | x /: x[ii___, Except[Index[___] | _?NumericQ, jj_], kk___] f_[aa___,
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142 | g_[xx___, Index[name_, jj_], yy___], cc___] :=
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143 | x[ii, Index[name, jj], kk] f[aa, g[xx, Index[name, jj], yy], cc];
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144 | x /: x[ii___, Except[Index[___] | _?NumericQ, jj_],
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145 | kk___] f_[aa___, g_[xx___, Index[name_, jj_], yy___], cc___][
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146 | ind___] :=
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147 | x[ii, Index[name, jj], kk] f[aa, g[xx, Index[name, jj], yy], cc][
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148 | ind];
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149 |
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150 | x[ii___, Except[_Index | _Done[Index] | _FV,
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151 | jj_?(Not[NumericQ[#]] &)], kk___, Index[name_, ll_], mm___] :=
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152 | x[ii, Index[name, jj], kk, Index[name, ll], mm];
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153 | x[ii___, Index[name_, ll_], kk___,
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154 | Except[_Index | _Done[Index] | _FV, jj_?(Not[NumericQ[#]] &)],
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155 | mm___] := x[ii, Index[name, ll], kk, Index[name, jj], mm];
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156 |
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157 | x /: x[i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
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158 | Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), j_, k_] x[
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159 | i_, m_, n_] :=
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160 | x[1, j, k] x[1, m, n] + x[2, j, k] x[2, m, n] +
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161 | x[3, j, k] x[3, m, n] + x[4, j, k] x[4, m, n] +
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162 | x[5, j, k] x[5, m, n] + x[6, j, k] x[6, m, n] +
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163 | x[7, j, k] x[7, m, n] + x[8, j, k] x[8, m, n];
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164 |
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165 | x /: x[i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
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166 | Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), j_, k_] x[
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167 | m_, n_, i_] := x[i, j, k] x[i, m, n];
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168 | x /: x[i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
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169 | Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), j_, k_] x[
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170 | m_, i_, n_] := x[i, j, k] x[i, n, m];
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171 | x /: x[j_,
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172 | i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
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173 | Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), k_] x[m_, i_,
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174 | n_] := x[i, k, j] x[i, n, m];
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175 | x /: x[j_,
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176 | i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
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177 | Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &), k_] x[m_, n_,
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178 | i_] := x[i, k, j] x[i, m, n];
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179 | x /: x[j_, k_,
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180 | i_?((Not[NumericQ[#]] && Not[MatchQ[#, Index[_, _?NumericQ]]] &&
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181 | Not[MatchQ[#, Done[Index][_, _?NumericQ]]]) &)] x[m_, n_,
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182 | i_] := x[i, j, k] x[i, m, n];
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183 |
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184 | x /: x[___, i_, ___, j_, ___] FV[a_, i_] FV[a_, j_] := 0;
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185 | x /: x[___, i_, ___, j_, ___] del[del[_, i_], j_] := 0;
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186 | x /: x[___, i_, ___, j_, ___] del[del[_, j_], i_] := 0;
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187 |
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188 | x[xx___, Index[name_, i_?NumericQ], yy___] := x[xx, i, yy];
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189 |
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190 | (* ************************** *)
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191 | (* ***** Indices ***** *)
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192 | (* ************************** *)
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193 |
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194 | IndexRange[Index[SU3W ]] = Unfold[Range[8]];
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195 | IndexRange[Index[ASU3W ]] = Unfold[Range[8]];
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196 | IndexRange[Index[ASU3T ]] = Unfold[Range[3]];
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197 | IndexRange[Index[SU3T ]] = Unfold[Range[3]];
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198 | IndexRange[Index[Gluon ]] = NoUnfold[Range[8]];
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199 | IndexRange[Index[Colour ]] = NoUnfold[Range[3]];
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200 | IndexRange[Index[Generation1]] = Range[3,3];
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201 | IndexRange[Index[Generation2]] = Range[2];
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202 | IndexRange[Index[Generation]] = Range[3];
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203 |
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204 | IndexStyle[SU3W, j];
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205 | IndexStyle[ASU3W, o];
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206 | IndexStyle[ASU3T, p];
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207 | IndexStyle[SU3T, k];
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208 | IndexStyle[Gluon, a];
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209 | IndexStyle[Colour, m];
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210 | IndexStyle[Generation1, r];
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211 | IndexStyle[Generation2, g];
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212 | IndexStyle[Generation, f];
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213 |
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214 |
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215 | (* ************************** *)
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216 | (* *** Interaction orders *** *)
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217 | (* *** (as used by mg5) *** *)
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218 | (* ************************** *)
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219 |
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220 | M$InteractionOrderHierarchy = {
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221 | {QCD, 1},
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222 | {QED, 2}
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223 | };
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224 |
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225 |
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226 | (* ************************** *)
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227 | (* **** Particle classes **** *)
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228 | (* ************************** *)
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229 | M$ClassesDescription = {
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230 |
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231 | (* Gauge bosons: physical vector fields *)
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232 | V[1] == {
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233 | ClassName -> A,
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234 | SelfConjugate -> True,
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235 | Mass -> 0,
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236 | Width -> 0,
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237 | ParticleName -> "a",
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238 | PDG -> 22,
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239 | PropagatorLabel -> "a",
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240 | PropagatorType -> W,
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241 | PropagatorArrow -> None,
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242 | FullName -> "Photon"
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243 | },
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244 | V[2] == {
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245 | ClassName -> Z,
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246 | SelfConjugate -> True,
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247 | Mass -> {MZ, 91.1876},
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248 | Width -> {WZ, 2.4952},
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249 | ParticleName -> "Z",
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250 | PDG -> 23,
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251 | PropagatorLabel -> "Z",
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252 | PropagatorType -> Sine,
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253 | PropagatorArrow -> None,
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254 | FullName -> "Z"
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255 | },
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256 | V[3] == {
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257 | ClassName -> ZP,
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258 | SelfConjugate -> True,
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259 | Mass -> {MZP, 6000},
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260 | Width -> {WZP, 10},
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261 | ParticleName -> "ZP",
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262 | PropagatorLabel -> "ZP",
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263 | PropagatorType -> Sine,
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264 | PropagatorArrow -> None,
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265 | FullName -> "ZP"
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266 | },
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267 | V[4] == {
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268 | ClassName -> W,
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269 | SelfConjugate -> False,
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270 | Mass -> {MW,Internal},
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271 | Width -> {WW, 2.085},
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272 | ParticleName -> "W+",
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273 | AntiParticleName -> "W-",
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274 | QuantumNumbers -> {Q -> 1},
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275 | PDG -> 24,
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276 | PropagatorLabel -> "W",
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277 | PropagatorType -> Sine,
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278 | PropagatorArrow -> Forward,
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279 | FullName -> "W"
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280 | },
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281 | V[5] == {
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282 | ClassName -> YY,
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283 | SelfConjugate -> False,
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284 | Mass -> {MY, Internal},
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285 | Width -> {WY, 10},
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286 | ParticleName -> "Y+",
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287 | AntiParticleName -> "Y-",
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288 | QuantumNumbers -> {Q -> -1/2-Sqrt[3] beta/2},
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289 | PropagatorLabel -> "YY",
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290 | PropagatorType -> Sine,
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291 | PropagatorArrow -> Forward,
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292 | FullName -> "YY"
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293 | },
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294 | V[6] == {
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295 | ClassName -> V,
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296 | SelfConjugate -> False,
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297 | Mass -> {MV, Internal},
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298 | Width -> {WV, 10},
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299 | ParticleName -> "V++",
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300 | AntiParticleName -> "V--",
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301 | QuantumNumbers -> {Q -> 1/2-Sqrt[3] beta/2},
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302 | PropagatorLabel -> "V",
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303 | PropagatorType -> Sine,
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304 | PropagatorArrow -> Forward,
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305 | FullName -> "V"
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306 | },
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307 | V[7] == {
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308 | ClassName -> G,
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309 | SelfConjugate -> True,
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310 | Indices -> {Index[Gluon]},
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311 | Mass -> 0,
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312 | Width -> 0,
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313 | ParticleName -> "g",
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314 | PDG -> 21,
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315 | PropagatorLabel -> "G",
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316 | PropagatorType -> C,
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317 | PropagatorArrow -> None,
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318 | FullName -> "G"
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319 | },
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320 |
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321 | (* Ghosts: related to physical gauge bosons *)
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322 | U[1] == {
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323 | ClassName -> ghA,
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324 | SelfConjugate -> False,
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325 | Ghost -> A,
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326 | QuantumNumbers -> {GhostNumber -> 1},
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327 | Mass -> 0,
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328 | Width -> 0,
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329 | PropagatorLabel -> "uA",
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330 | PropagatorType -> GhostDash,
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331 | PropagatorArrow -> Forward
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332 | },
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333 | U[2] == {
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334 | ClassName -> ghZ,
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335 | SelfConjugate -> False,
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336 | Ghost -> Z,
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337 | QuantumNumbers -> {GhostNumber -> 1},
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338 | Mass -> {MZ,91.1876},
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339 | Width -> {WZ, 2.4952},
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340 | PropagatorLabel -> "uZ",
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341 | PropagatorType -> GhostDash,
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342 | PropagatorArrow -> Forward
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343 | },
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344 | U[3] == {
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345 | ClassName -> ghZP,
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346 | SelfConjugate -> False,
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347 | Ghost -> ZP,
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348 | QuantumNumbers -> {GhostNumber -> 1},
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349 | Mass -> {MZP,6000},
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350 | Width -> {WZP, 10},
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351 | PropagatorLabel -> "uZP",
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352 | PropagatorType -> GhostDash,
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353 | PropagatorArrow -> Forward
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354 | },
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355 | U[41] == {
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356 | ClassName -> ghWp,
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357 | SelfConjugate -> False,
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358 | Ghost -> W,
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359 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1},
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360 | Mass -> {MW,Internal},
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361 | Width -> {WW, 2.085},
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362 | PropagatorLabel -> "uWp",
|
---|
363 | PropagatorType -> GhostDash,
|
---|
364 | PropagatorArrow -> Forward
|
---|
365 | },
|
---|
366 | U[42] == {
|
---|
367 | ClassName -> ghWm,
|
---|
368 | SelfConjugate -> False,
|
---|
369 | Ghost -> Wbar,
|
---|
370 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1},
|
---|
371 | Mass -> {MW,Internal},
|
---|
372 | Width -> {WW, 2.085},
|
---|
373 | PropagatorLabel -> "uWm",
|
---|
374 | PropagatorType -> GhostDash,
|
---|
375 | PropagatorArrow -> Forward
|
---|
376 | },
|
---|
377 | U[51] == {
|
---|
378 | ClassName -> ghYp,
|
---|
379 | SelfConjugate -> False,
|
---|
380 | Ghost -> YY,
|
---|
381 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1/2-Sqrt[3] beta/2},
|
---|
382 | Mass -> {MY, Internal},
|
---|
383 | Width -> {WY, 10},
|
---|
384 | PropagatorLabel -> "uYp",
|
---|
385 | PropagatorType -> GhostDash,
|
---|
386 | PropagatorArrow -> Forward
|
---|
387 | },
|
---|
388 | U[52] == {
|
---|
389 | ClassName -> ghYm,
|
---|
390 | SelfConjugate -> False,
|
---|
391 | Ghost -> YYbar,
|
---|
392 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1/2+Sqrt[3] beta/2},
|
---|
393 | Mass -> {MY, Internal},
|
---|
394 | Width -> {WY, 10},
|
---|
395 | PropagatorLabel -> "uYm",
|
---|
396 | PropagatorType -> GhostDash,
|
---|
397 | PropagatorArrow -> Forward
|
---|
398 | },
|
---|
399 | U[61] == {
|
---|
400 | ClassName -> ghVp,
|
---|
401 | SelfConjugate -> False,
|
---|
402 | Ghost -> V,
|
---|
403 | QuantumNumbers -> {GhostNumber -> 1, Q -> 1/2-Sqrt[3] beta/2},
|
---|
404 | Mass -> {MV,Internal},
|
---|
405 | Width -> {WV, 10},
|
---|
406 | PropagatorLabel -> "uVp",
|
---|
407 | PropagatorType -> GhostDash,
|
---|
408 | PropagatorArrow -> Forward
|
---|
409 | },
|
---|
410 | U[62] == {
|
---|
411 | ClassName -> ghVm,
|
---|
412 | SelfConjugate -> False,
|
---|
413 | Ghost -> Vbar,
|
---|
414 | QuantumNumbers -> {GhostNumber -> 1, Q -> -1/2+Sqrt[3] beta/2},
|
---|
415 | Mass -> {MV,Internal},
|
---|
416 | Width -> {WV, 10},
|
---|
417 | PropagatorLabel -> "uVm",
|
---|
418 | PropagatorType -> GhostDash,
|
---|
419 | PropagatorArrow -> Forward
|
---|
420 | },
|
---|
421 | U[7] == {
|
---|
422 | ClassName -> ghG,
|
---|
423 | SelfConjugate -> False,
|
---|
424 | Indices -> {Index[Gluon]},
|
---|
425 | Ghost -> G,
|
---|
426 | QuantumNumbers ->{GhostNumber -> 1},
|
---|
427 | Mass -> 0,
|
---|
428 | Width -> 0,
|
---|
429 | PropagatorLabel -> "uG",
|
---|
430 | PropagatorType -> GhostDash,
|
---|
431 | PropagatorArrow -> Forward
|
---|
432 | },
|
---|
433 |
|
---|
434 | (* Gauge bosons: unphysical vector fields *)
|
---|
435 | V[12] == {
|
---|
436 | ClassName -> K,
|
---|
437 | Unphysical -> True,
|
---|
438 | SelfConjugate -> True,
|
---|
439 | Definitions -> { K[mu_] -> c3 (cz ZP[mu]-sz Z[mu]) + s3 (-sw (cz Z[mu]+sz ZP[mu]) + cw A[mu])}
|
---|
440 | },
|
---|
441 | V[13] == {
|
---|
442 | ClassName -> Wi,
|
---|
443 | Unphysical -> True,
|
---|
444 | SelfConjugate -> True,
|
---|
445 | Indices -> {Index[SU3W]},
|
---|
446 | FlavorIndex -> SU3W,
|
---|
447 | Definitions -> {
|
---|
448 | Wi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], Wi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
|
---|
449 | Wi[mu_,4] -> (YYbar[mu]+YY[mu])/Sqrt[2], Wi[mu_,5] -> (YY[mu]-YYbar[mu])/(I*Sqrt[2]),
|
---|
450 | Wi[mu_,6] -> (Vbar[mu]+V[mu])/Sqrt[2], Wi[mu_,7] -> (V[mu]-Vbar[mu])/(I*Sqrt[2]),
|
---|
451 | Wi[mu_,3] -> cw (cz Z[mu]+sz ZP[mu]) + sw A[mu], Wi[mu_,8] -> -s3 (cz ZP[mu]-sz Z[mu]) + c3 (-sw (cz Z[mu]+sz ZP[mu]) +cw A[mu])}
|
---|
452 | },
|
---|
453 | V[14] == {
|
---|
454 | ClassName -> WWi,
|
---|
455 | Unphysical -> True,
|
---|
456 | SelfConjugate -> True,
|
---|
457 | Indices -> {Index[ASU3W]},
|
---|
458 | FlavorIndex -> ASU3W,
|
---|
459 | Definitions -> {
|
---|
460 | WWi[mu_,1] -> (Wbar[mu]+W[mu])/Sqrt[2], WWi[mu_,2] -> (Wbar[mu]-W[mu])/(I*Sqrt[2]),
|
---|
461 | WWi[mu_,4] -> (YYbar[mu]+YY[mu])/Sqrt[2], WWi[mu_,5] -> (YY[mu]-YYbar[mu])/(I*Sqrt[2]),
|
---|
462 | WWi[mu_,6] -> (Vbar[mu]+V[mu])/Sqrt[2], WWi[mu_,7] -> (V[mu]-Vbar[mu])/(I*Sqrt[2]),
|
---|
463 | WWi[mu_,3] -> cw (cz Z[mu]+sz ZP[mu]) + sw A[mu], WWi[mu_,8] -> -s3 (cz ZP[mu]-sz Z[mu])+c3 (-sw (cz Z[mu]+sz ZP[mu])+cw A[mu])}
|
---|
464 | },
|
---|
465 |
|
---|
466 | (* Ghosts: related to unphysical gauge bosons *)
|
---|
467 | U[12] == {
|
---|
468 | ClassName -> ghK,
|
---|
469 | Unphysical -> True,
|
---|
470 | SelfConjugate -> False,
|
---|
471 | Ghost -> K,
|
---|
472 | Definitions -> { ghK -> -c3 (cz ghZP-sz ghZ) + s3 (-sw (cz ghZ+sz ghZP) + cw ghA)}
|
---|
473 | },
|
---|
474 | U[13] == {
|
---|
475 | ClassName -> ghWi,
|
---|
476 | Unphysical -> True,
|
---|
477 | SelfConjugate -> False,
|
---|
478 | Ghost -> Wi,
|
---|
479 | Indices -> {Index[SU3W]},
|
---|
480 | FlavorIndex -> SU3W,
|
---|
481 | Definitions -> { ghWi[1] -> (ghWp+ghWm)/Sqrt[2], ghWi[2] -> (ghWm-ghWp)/(I*Sqrt[2]), ghWi[4] -> (ghYp+ghYm)/Sqrt[2], ghWi[5] -> (ghYp-ghYm)/(I*Sqrt[2]),ghWi[6] -> (ghVp+ghVm)/Sqrt[2], ghWi[7] -> (ghVp-ghVm)/(I*Sqrt[2]), ghWi[3] -> cw (cz ghZ+sz ghZP)+sw ghA, ghWi[8] -> -s3 (cz ghZP-sz ghZ)+c3 (-sw (cz ghZ+sz ghZP) + cw ghA)}
|
---|
482 | },
|
---|
483 |
|
---|
484 | (* Fermions: physical fields *)
|
---|
485 | F[1] == {
|
---|
486 | ClassName -> vl,
|
---|
487 | ClassMembers -> {ve,vm,vt},
|
---|
488 | Indices -> {Index[Generation]},
|
---|
489 | FlavorIndex -> Generation,
|
---|
490 | SelfConjugate -> False,
|
---|
491 | Mass -> 0,
|
---|
492 | Width -> 0,
|
---|
493 | QuantumNumbers -> {LeptonNumber -> 1},
|
---|
494 | PropagatorLabel -> {"v", "ve", "vm", "vt"} ,
|
---|
495 | PropagatorType -> S,
|
---|
496 | PropagatorArrow -> Forward,
|
---|
497 | PDG -> {12,14,16},
|
---|
498 | ParticleName -> {"ve","vm","vt"},
|
---|
499 | AntiParticleName -> {"ve~","vm~","vt~"},
|
---|
500 | FullName -> {"Electron-neutrino", "Mu-neutrino", "Tau-neutrino"}
|
---|
501 | },
|
---|
502 | F[2] == {
|
---|
503 | ClassName -> l,
|
---|
504 | ClassMembers -> {e, mu, ta},
|
---|
505 | Indices -> {Index[Generation]},
|
---|
506 | FlavorIndex -> Generation,
|
---|
507 | SelfConjugate -> False,
|
---|
508 | Mass -> {Ml, {Me,5.11*^-4}, {MMU,0.10566}, {MTA,1.777}},
|
---|
509 | Width -> 0,
|
---|
510 | QuantumNumbers -> {Q -> -1, LeptonNumber -> 1},
|
---|
511 | PropagatorLabel -> {"l", "e", "mu", "ta"},
|
---|
512 | PropagatorType -> Straight,
|
---|
513 | PropagatorArrow -> Forward,
|
---|
514 | PDG -> {11, 13, 15},
|
---|
515 | ParticleName -> {"e-", "mu-", "ta-"},
|
---|
516 | AntiParticleName -> {"e+", "mu+", "ta+"},
|
---|
517 | FullName -> {"Electron", "Muon", "Tau"}
|
---|
518 | },
|
---|
519 | F[3] == {
|
---|
520 | ClassName -> EE,
|
---|
521 | ClassMembers -> {Ee, Emu, Eta},
|
---|
522 | Indices -> {Index[Generation]},
|
---|
523 | FlavorIndex -> Generation,
|
---|
524 | SelfConjugate -> False,
|
---|
525 | Mass -> {ME, {MEE,1*^3}, {MEMU,1*^3}, {META,1*^3}},
|
---|
526 | Width -> {WE, {WEE,10},{WEMU,10},{WETA,10}},
|
---|
527 | QuantumNumbers -> {Q -> -1/2+Sqrt[3] beta/2, LeptonNumber -> 1},
|
---|
528 | PropagatorLabel -> {"E", "Ee", "Emu", "Eta"},
|
---|
529 | PropagatorType -> Straight,
|
---|
530 | PropagatorArrow -> Forward,
|
---|
531 | ParticleName -> {"Ee+", "Emu+", "Eta+"},
|
---|
532 | AntiParticleName -> {"Ee-", "Emu-", "Eta-"},
|
---|
533 | FullName -> {"HElectron", "HMuon", "HTau"}
|
---|
534 | },
|
---|
535 | F[4] == {
|
---|
536 | ClassName -> uq,
|
---|
537 | ClassMembers -> {u, c, t},
|
---|
538 | Indices -> {Index[Generation], Index[Colour]},
|
---|
539 | FlavorIndex -> Generation,
|
---|
540 | SelfConjugate -> False,
|
---|
541 | Mass -> {Mu, {MU, 2.55*^-3}, {MC,1.27}, {MT,172}},
|
---|
542 | Width -> {0, 0, {WT,1.50833649}},
|
---|
543 | QuantumNumbers -> {Q -> 2/3},
|
---|
544 | PropagatorLabel -> {"uq", "u", "c", "t"},
|
---|
545 | PropagatorType -> Straight,
|
---|
546 | PropagatorArrow -> Forward,
|
---|
547 | PDG -> {2, 4, 6},
|
---|
548 | ParticleName -> {"u", "c", "t" },
|
---|
549 | AntiParticleName -> {"u~", "c~", "t~"},
|
---|
550 | FullName -> {"u-quark", "c-quark", "t-quark"}
|
---|
551 | },
|
---|
552 | F[5] == {
|
---|
553 | ClassName -> dq,
|
---|
554 | ClassMembers -> {d, s, b},
|
---|
555 | Indices -> {Index[Generation], Index[Colour]},
|
---|
556 | FlavorIndex -> Generation,
|
---|
557 | SelfConjugate -> False,
|
---|
558 | Mass -> {Md, {MD,5.04*^-3}, {MS,0.101}, {MB,4.7}},
|
---|
559 | Width -> 0,
|
---|
560 | QuantumNumbers -> {Q -> -1/3},
|
---|
561 | PropagatorLabel -> {"dq", "d", "s", "b"},
|
---|
562 | PropagatorType -> Straight,
|
---|
563 | PropagatorArrow -> Forward,
|
---|
564 | PDG -> {1,3,5},
|
---|
565 | ParticleName -> {"d", "s", "b" },
|
---|
566 | AntiParticleName -> {"d~", "s~", "b~"},
|
---|
567 | FullName -> {"d-quark", "s-quark", "b-quark"}
|
---|
568 | },
|
---|
569 | F[6] == {
|
---|
570 | ClassName -> Jq12,
|
---|
571 | ClassMembers -> {Jd, Js},
|
---|
572 | Indices -> {Index[Generation2], Index[Colour]},
|
---|
573 | FlavorIndex -> Generation2,
|
---|
574 | SelfConjugate -> False,
|
---|
575 | Mass -> {MJ12, {MJD,1*^3}, {MJS,1*^3}},
|
---|
576 | Width -> {WJQ12,{WJD,10},{WJS,10}},
|
---|
577 | QuantumNumbers -> {Q -> 1/6-Sqrt[3] beta/2},
|
---|
578 | PropagatorLabel -> {"Jq12", "Jd", "Js"},
|
---|
579 | PropagatorType -> Straight,
|
---|
580 | PropagatorArrow -> Forward,
|
---|
581 | ParticleName -> {"Jd", "Js"},
|
---|
582 | AntiParticleName -> {"Jd~", "Js~"},
|
---|
583 | FullName -> {"Jd-quark", "Js-quark"}
|
---|
584 | },
|
---|
585 | F[7] == {
|
---|
586 | ClassName -> Jt,
|
---|
587 | Indices -> {Index[Colour]},
|
---|
588 | SelfConjugate -> False,
|
---|
589 | Mass -> {MJT,1*^3},
|
---|
590 | Width -> 10,
|
---|
591 | QuantumNumbers -> {Q -> 1/6+Sqrt[3] beta/2},
|
---|
592 | PropagatorLabel -> "Jt",
|
---|
593 | PropagatorType -> Straight,
|
---|
594 | PropagatorArrow -> Forward,
|
---|
595 | ParticleName -> "Jt",
|
---|
596 | AntiParticleName -> "Jt~",
|
---|
597 | FullName -> "Jt-quark"
|
---|
598 | },
|
---|
599 |
|
---|
600 |
|
---|
601 |
|
---|
602 | (* Fermions: unphysical fields *)
|
---|
603 | F[11] == {
|
---|
604 | ClassName -> LL,
|
---|
605 | Unphysical -> True,
|
---|
606 | Indices -> {Index[ASU3T], Index[Generation]},
|
---|
607 | FlavorIndex -> ASU3T,
|
---|
608 | SelfConjugate -> False,
|
---|
609 | QuantumNumbers -> {X -> -1/2+beta/(2 Sqrt[3])},
|
---|
610 | Definitions -> {
|
---|
611 | LL[sp1_,1,ff_] :> Module[{sp2}, ProjM[sp1,sp2] l[sp2,ff]],
|
---|
612 | LL[sp1_,2,ff_] :> -Module[{sp2}, ProjM[sp1,sp2] vl[sp2,ff]],
|
---|
613 | LL[sp1_,3,ff_] :> Module[{sp2}, ProjM[sp1,sp2] EE[sp2,ff]]}
|
---|
614 | },
|
---|
615 | F[12] == {
|
---|
616 | ClassName -> lR,
|
---|
617 | Unphysical -> True,
|
---|
618 | Indices -> {Index[Generation]},
|
---|
619 | FlavorIndex -> Generation,
|
---|
620 | SelfConjugate -> False,
|
---|
621 | QuantumNumbers -> {X -> -1},
|
---|
622 | Definitions -> { lR[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] l[sp2,ff]] }
|
---|
623 | },
|
---|
624 | F[13] == {
|
---|
625 | ClassName -> EER,
|
---|
626 | Unphysical -> True,
|
---|
627 | Indices -> {Index[Generation]},
|
---|
628 | FlavorIndex -> Generation,
|
---|
629 | SelfConjugate -> False,
|
---|
630 | QuantumNumbers -> {X -> -1/2+Sqrt[3] beta/2},
|
---|
631 | Definitions -> { EER[sp1_,ff_] :> Module[{sp2}, ProjP[sp1,sp2] EE[sp2,ff]] }
|
---|
632 | },
|
---|
633 | F[14] == {
|
---|
634 | ClassName -> QL12,
|
---|
635 | Unphysical -> True,
|
---|
636 | Indices -> {Index[SU3T], Index[Generation2], Index[Colour]},
|
---|
637 | FlavorIndex -> SU3T,
|
---|
638 | SelfConjugate -> False,
|
---|
639 | QuantumNumbers -> {X -> 1/6-beta/(2 Sqrt[3])},
|
---|
640 | Definitions -> {
|
---|
641 | QL12[sp1_,1,1,cc_] :> Module[{sp2,ff2}, RU[1,ff2] ProjM[sp1,sp2] uq[sp2,ff2,cc]],
|
---|
642 | QL12[sp1_,1,2,cc_] :> Module[{sp2,ff2}, RU[2,ff2] ProjM[sp1,sp2] uq[sp2,ff2,cc]],
|
---|
643 | QL12[sp1_,2,1,cc_] :> Module[{sp2,ff2}, CKM[1,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]],
|
---|
644 | QL12[sp1_,2,2,cc_] :> Module[{sp2,ff2}, CKM[2,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]],
|
---|
645 | QL12[sp1_,3,ff12_,cc_] :> Module[{sp2}, ProjM[sp1,sp2] Jq12[sp2,ff12,cc]]}
|
---|
646 | },
|
---|
647 | F[15] == {
|
---|
648 | ClassName -> QL3,
|
---|
649 | Unphysical -> True,
|
---|
650 | Indices -> {Index[ASU3T], Index[Generation1], Index[Colour]},
|
---|
651 | FlavorIndex -> ASU3T,
|
---|
652 | SelfConjugate -> False,
|
---|
653 | QuantumNumbers -> {X -> 1/6+beta/(2 Sqrt[3])},
|
---|
654 | Definitions -> {
|
---|
655 | QL3[sp1_,1,3,cc_] :> Module[{sp2,ff2}, CKM[3,ff2] ProjM[sp1,sp2] dq[sp2,ff2,cc]],
|
---|
656 | QL3[sp1_,2,3,cc_] :>-Module[{sp2,ff2}, RU[3,ff2] ProjM[sp1,sp2] uq[sp2,ff2,cc]],
|
---|
657 | QL3[sp1_,3,3,cc_] :> Module[{sp2}, ProjM[sp1,sp2] Jt[sp2,cc]]}
|
---|
658 | },
|
---|
659 | F[16] == {
|
---|
660 | ClassName -> QL,
|
---|
661 | Unphysical -> True,
|
---|
662 | Indices -> {Index[SU3T], Index[Generation], Index[Colour]},
|
---|
663 | FlavorIndex -> SU3T,
|
---|
664 | SelfConjugate -> False,
|
---|
665 | QuantumNumbers -> {X -> 1/6-beta/(2 Sqrt[3]), X -> 1/6-beta/(2 Sqrt[3]), X -> 1/6+beta/(2 Sqrt[3])},
|
---|
666 | Definitions -> {
|
---|
667 | QL[sp1_,1,1,cc_] :> QL12[sp1,1,1,cc],
|
---|
668 | QL[sp1_,1,2,cc_] :> QL12[sp1,1,2,cc],
|
---|
669 | QL[sp1_,1,3,cc_] :> QL3[sp1,1,3,cc],
|
---|
670 | QL[sp1_,2,1,cc_] :> QL12[sp1,2,1,cc],
|
---|
671 | QL[sp1_,2,2,cc_] :> QL12[sp1,2,2,cc],
|
---|
672 | QL[sp1_,2,3,cc_] :> QL3[sp1,2,3,cc],
|
---|
673 | QL[sp1_,3,1,cc_] :> QL12[sp1,3,1,cc],
|
---|
674 | QL[sp1_,3,2,cc_] :> QL12[sp1,3,2,cc],
|
---|
675 | QL[sp1_,3,3,cc_] :> QL3[sp1,3,3,cc]}
|
---|
676 | },
|
---|
677 | F[17] == {
|
---|
678 | ClassName -> uR,
|
---|
679 | Unphysical -> True,
|
---|
680 | Indices -> {Index[Generation], Index[Colour]},
|
---|
681 | FlavorIndex -> Generation,
|
---|
682 | SelfConjugate -> False,
|
---|
683 | QuantumNumbers -> {X -> 2/3},
|
---|
684 | Definitions -> { uR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] uq[sp2,ff,cc]] }
|
---|
685 | },
|
---|
686 | F[18] == {
|
---|
687 | ClassName -> dR,
|
---|
688 | Unphysical -> True,
|
---|
689 | Indices -> {Index[Generation], Index[Colour]},
|
---|
690 | FlavorIndex -> Generation,
|
---|
691 | SelfConjugate -> False,
|
---|
692 | QuantumNumbers -> {X -> -1/3},
|
---|
693 | Definitions -> { dR[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] dq[sp2,ff,cc]] }
|
---|
694 | },
|
---|
695 | F[19] == {
|
---|
696 | ClassName -> JR12,
|
---|
697 | Unphysical -> True,
|
---|
698 | Indices -> {Index[Generation2], Index[Colour]},
|
---|
699 | FlavorIndex -> Generation2,
|
---|
700 | SelfConjugate -> False,
|
---|
701 | QuantumNumbers -> {X -> 1/6-Sqrt[3] beta/2},
|
---|
702 | Definitions -> { JR12[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] Jq12[sp2,ff,cc]] }
|
---|
703 | },
|
---|
704 | F[20] == {
|
---|
705 | ClassName -> JR3,
|
---|
706 | Unphysical -> True,
|
---|
707 | Indices -> {Index[Generation1], Index[Colour]},
|
---|
708 | FlavorIndex -> Generation1,
|
---|
709 | SelfConjugate -> False,
|
---|
710 | QuantumNumbers -> {X -> 1/6+Sqrt[3] beta/2},
|
---|
711 | Definitions -> { JR3[sp1_,ff_,cc_] :> Module[{sp2}, ProjP[sp1,sp2] Jt[sp2,cc]] }
|
---|
712 | },
|
---|
713 | F[21] == {
|
---|
714 | ClassName -> JR,
|
---|
715 | Unphysical -> True,
|
---|
716 | Indices -> {Index[Generation], Index[Colour]},
|
---|
717 | FlavorIndex -> Generation,
|
---|
718 | SelfConjugate -> False,
|
---|
719 | QuantumNumbers -> {X -> 1/6-Sqrt[3] beta/2, X -> 1/6-Sqrt[3] beta/2, X -> 1/6+Sqrt[3] beta/2},
|
---|
720 | Definitions -> { JR[sp1_,1,cc_] :> JR12[sp1,1,cc],
|
---|
721 | JR[sp1_,2,cc_] :> JR12[sp1,2,cc],
|
---|
722 | JR[sp1_,3,cc_] :> JR3[sp1,3,cc] }
|
---|
723 | },
|
---|
724 |
|
---|
725 | (* Higgs: physical scalars *)
|
---|
726 | S[1] == {
|
---|
727 | ClassName -> h,
|
---|
728 | SelfConjugate -> True,
|
---|
729 | Mass -> {Mh,125},
|
---|
730 | Width -> {Wh,0.00407},
|
---|
731 | PropagatorLabel -> "h",
|
---|
732 | PropagatorType -> D,
|
---|
733 | PropagatorArrow -> None,
|
---|
734 | PDG -> 25,
|
---|
735 | ParticleName -> "h",
|
---|
736 | FullName -> "h"
|
---|
737 | },
|
---|
738 | S[2] == {
|
---|
739 | ClassName -> H2,
|
---|
740 | SelfConjugate -> True,
|
---|
741 | Mass -> {MH2,Internal},
|
---|
742 | Width -> {WH2,10},
|
---|
743 | PropagatorLabel -> "H2",
|
---|
744 | PropagatorType -> D,
|
---|
745 | PropagatorArrow -> None,
|
---|
746 | ParticleName -> "H2",
|
---|
747 | FullName -> "H2"
|
---|
748 | },
|
---|
749 | S[3] == {
|
---|
750 | ClassName -> H3,
|
---|
751 | SelfConjugate -> True,
|
---|
752 | Mass -> {MH3,Internal},
|
---|
753 | Width -> {WH3,10},
|
---|
754 | PropagatorLabel -> "H3",
|
---|
755 | PropagatorType -> D,
|
---|
756 | PropagatorArrow -> None,
|
---|
757 | ParticleName -> "H3",
|
---|
758 | FullName -> "H3"
|
---|
759 | },
|
---|
760 | S[4] == {
|
---|
761 | ClassName -> H0,
|
---|
762 | SelfConjugate -> True,
|
---|
763 | Mass -> {MH0,Internal},
|
---|
764 | Width -> {WH0,10},
|
---|
765 | PropagatorLabel -> "H0",
|
---|
766 | PropagatorType -> D,
|
---|
767 | PropagatorArrow -> None,
|
---|
768 | ParticleName -> "H0",
|
---|
769 | FullName -> "H0"
|
---|
770 | },
|
---|
771 | S[5] == {
|
---|
772 | ClassName -> HW,
|
---|
773 | SelfConjugate -> False,
|
---|
774 | Mass -> {MHW,Internal},
|
---|
775 | Width -> {WHW,10},
|
---|
776 | ParticleName -> "HW+",
|
---|
777 | AntiParticleName -> "HW-",
|
---|
778 | QuantumNumbers -> {Q -> 1},
|
---|
779 | PropagatorLabel -> "HW",
|
---|
780 | PropagatorType -> D,
|
---|
781 | PropagatorArrow -> Forward,
|
---|
782 | FullName -> "HW"
|
---|
783 | },
|
---|
784 | S[6] == {
|
---|
785 | ClassName -> HY,
|
---|
786 | SelfConjugate -> False,
|
---|
787 | Mass -> {MHY,Internal},
|
---|
788 | Width -> {WHY,10},
|
---|
789 | ParticleName -> "HY+",
|
---|
790 | AntiParticleName -> "HY-",
|
---|
791 | QuantumNumbers -> {Q -> -1/2-Sqrt[3] beta/2},
|
---|
792 | PropagatorLabel -> "HY",
|
---|
793 | PropagatorType -> D,
|
---|
794 | PropagatorArrow -> Forward,
|
---|
795 | FullName -> "HY"
|
---|
796 | },
|
---|
797 | S[7] == {
|
---|
798 | ClassName -> HV,
|
---|
799 | SelfConjugate -> False,
|
---|
800 | Mass -> {MHV,Internal},
|
---|
801 | Width -> {WHV,10},
|
---|
802 | ParticleName -> "HV++",
|
---|
803 | AntiParticleName -> "HV--",
|
---|
804 | QuantumNumbers -> {Q -> 1/2-Sqrt[3] beta/2},
|
---|
805 | PropagatorLabel -> "HV",
|
---|
806 | PropagatorType -> D,
|
---|
807 | PropagatorArrow -> Forward,
|
---|
808 | FullName -> "HV"
|
---|
809 | },
|
---|
810 |
|
---|
811 |
|
---|
812 | (* Higgs: physical scalars *)
|
---|
813 | S[8] == {
|
---|
814 | ClassName -> GZ,
|
---|
815 | SelfConjugate -> True,
|
---|
816 | Goldstone -> Z,
|
---|
817 | Mass -> {MZ, 91.1876},
|
---|
818 | Width -> {WZ, 2.4952},
|
---|
819 | PropagatorLabel -> "GZ",
|
---|
820 | PropagatorType -> D,
|
---|
821 | PropagatorArrow -> None,
|
---|
822 | PDG -> 250,
|
---|
823 | ParticleName -> "GZ",
|
---|
824 | FullName -> "GZ"
|
---|
825 | },
|
---|
826 | S[9] == {
|
---|
827 | ClassName -> GZP,
|
---|
828 | SelfConjugate -> True,
|
---|
829 | Goldstone -> ZP,
|
---|
830 | Mass -> {MZP, 6000},
|
---|
831 | Width -> {WZP, 10},
|
---|
832 | PropagatorLabel -> "GZP",
|
---|
833 | PropagatorType -> D,
|
---|
834 | PropagatorArrow -> None,
|
---|
835 | ParticleName -> "GZP",
|
---|
836 | FullName -> "GZP"
|
---|
837 | },
|
---|
838 | S[10] == {
|
---|
839 | ClassName -> GW,
|
---|
840 | SelfConjugate -> False,
|
---|
841 | Goldstone -> W,
|
---|
842 | Mass -> {MW, Internal},
|
---|
843 | QuantumNumbers -> {Q -> 1},
|
---|
844 | Width -> {WW, 2.085},
|
---|
845 | PropagatorLabel -> "GW",
|
---|
846 | PropagatorType -> D,
|
---|
847 | PropagatorArrow -> None,
|
---|
848 | PDG -> 251,
|
---|
849 | ParticleName -> "GW+",
|
---|
850 | AntiParticleName -> "GW-",
|
---|
851 | FullName -> "GW"
|
---|
852 | },
|
---|
853 | S[11] == {
|
---|
854 | ClassName -> GY,
|
---|
855 | SelfConjugate -> False,
|
---|
856 | Goldstone -> YY,
|
---|
857 | Mass -> {MY, Internal},
|
---|
858 | QuantumNumbers -> {Q -> -1/2-Sqrt[3] beta/2},
|
---|
859 | Width -> {WY, 10},
|
---|
860 | PropagatorLabel -> "GY",
|
---|
861 | PropagatorType -> D,
|
---|
862 | PropagatorArrow -> None,
|
---|
863 | ParticleName -> "GY+",
|
---|
864 | AntiParticleName -> "GY-",
|
---|
865 | FullName -> "GY"
|
---|
866 | },
|
---|
867 | S[12] == {
|
---|
868 | ClassName -> GV,
|
---|
869 | SelfConjugate -> False,
|
---|
870 | Goldstone -> V,
|
---|
871 | Mass -> {MV, Internal},
|
---|
872 | QuantumNumbers -> {Q -> 1/2-Sqrt[3] beta/2},
|
---|
873 | Width -> {WV, 10},
|
---|
874 | PropagatorLabel -> "GV",
|
---|
875 | PropagatorType -> D,
|
---|
876 | PropagatorArrow -> None,
|
---|
877 | ParticleName -> "GV++",
|
---|
878 | AntiParticleName -> "GV--",
|
---|
879 | FullName -> "GV"
|
---|
880 | },
|
---|
881 |
|
---|
882 |
|
---|
883 | (* Higgs: unphysical scalars *)
|
---|
884 | S[13] == {
|
---|
885 | ClassName -> Rho,
|
---|
886 | Unphysical -> True,
|
---|
887 | Indices -> {Index[SU3T]},
|
---|
888 | FlavorIndex -> SU3T,
|
---|
889 | SelfConjugate -> False,
|
---|
890 | QuantumNumbers -> {X -> 1/2-beta/(2 Sqrt[3])},
|
---|
891 | Definitions -> { Rho[1] -> -I (HW svv2+GW cvv2), Rho[2] -> (v + UH11 h + UH12 H2 + UH13 H3 + I (Uh11 H0 + Uh12 GZ + Uh13 GZP))/Sqrt[2], Rho[3] -> -I (HV svv3+GV cvv3)}
|
---|
892 | },
|
---|
893 | S[14] == {
|
---|
894 | ClassName -> Phi,
|
---|
895 | Unphysical -> True,
|
---|
896 | Indices -> {Index[SU3T]},
|
---|
897 | FlavorIndex -> SU3T,
|
---|
898 | SelfConjugate -> False,
|
---|
899 | QuantumNumbers -> {X -> -1/2-beta/(2 Sqrt[3])},
|
---|
900 | Definitions -> { Phi[1] -> (v2 + UH21 h + UH22 H2 + UH23 H3 + I (Uh21 H0 + Uh23 GZP))/Sqrt[2], Phi[2] -> -I(GWbar svv2 -HWbar cvv2), Phi[3] -> -I(HY sv2v3+GY cv2v3) }
|
---|
901 | },
|
---|
902 | S[15] == {
|
---|
903 | ClassName -> Chi,
|
---|
904 | Unphysical -> True,
|
---|
905 | Indices -> {Index[SU3T]},
|
---|
906 | FlavorIndex -> SU3T,
|
---|
907 | SelfConjugate -> False,
|
---|
908 | QuantumNumbers -> {X -> beta/Sqrt[3]},
|
---|
909 | Definitions -> { Chi[1] -> -I (GYbar sv2v3-HYbar cv2v3), Chi[2] -> -I (GVbar svv3-HVbar cvv3), Chi[3] -> (v3 + UH31 h + UH32 H2 + UH33 H3 + I (Uh31 H0 + Uh32 GZ + Uh33 GZP))/Sqrt[2] }
|
---|
910 | },
|
---|
911 | S[16] == {
|
---|
912 | ClassName -> Su,
|
---|
913 | Unphysical -> True,
|
---|
914 | Indices -> {Index[Generation], Index[Generation],Index[SU3T]},
|
---|
915 | FlavorIndex -> SU3T,
|
---|
916 | SelfConjugate -> False,
|
---|
917 | Definitions -> {Su[1,1,kk_] -> Phi[kk], Su[1,2,kk_] -> 0, Su[1,3,kk_] -> 0, Su[2,1,kk_] -> 0, Su[2,2,kk_] -> Phi[kk], Su[2,3,kk_] -> 0, Su[3,1,kk_] -> 0, Su[3,2,kk_] -> 0, Su[3,3,kk_] -> -Rhobar[kk]}
|
---|
918 | },
|
---|
919 | S[17] == {
|
---|
920 | ClassName -> Sd,
|
---|
921 | Unphysical -> True,
|
---|
922 | Indices -> {Index[Generation], Index[Generation],Index[SU3T]},
|
---|
923 | FlavorIndex -> SU3T,
|
---|
924 | SelfConjugate -> False,
|
---|
925 | Definitions -> {Sd[1,1,kk_] -> Rho[kk], Sd[1,2,kk_] -> 0, Sd[1,3,kk_] -> 0, Sd[2,1,kk_] -> 0, Sd[2,2,kk_] -> Rho[kk], Sd[2,3,kk_] -> 0, Sd[3,1,kk_] -> 0, Sd[3,2,kk_] -> 0, Sd[3,3,kk_] -> Phibar[kk]}
|
---|
926 | },
|
---|
927 | S[18] == {
|
---|
928 | ClassName -> SJ,
|
---|
929 | Unphysical -> True,
|
---|
930 | Indices -> {Index[Generation], Index[Generation],Index[SU3T]},
|
---|
931 | FlavorIndex -> SU3T,
|
---|
932 | SelfConjugate -> False,
|
---|
933 | Definitions -> {SJ[1,1,kk_] -> Chi[kk], SJ[1,2,kk_] -> 0, SJ[1,3,kk_] -> 0, SJ[2,1,kk_] -> 0, SJ[2,2,kk_] -> Chi[kk], SJ[2,3,kk_] -> 0, SJ[3,1,kk_] -> 0, SJ[3,2,kk_] -> 0, SJ[3,3,kk_] -> Chibar[kk]}
|
---|
934 | }
|
---|
935 | };
|
---|
936 |
|
---|
937 |
|
---|
938 | (* ************************** *)
|
---|
939 | (* ***** Gauge ***** *)
|
---|
940 | (* ***** Parameters ***** *)
|
---|
941 | (* ***** (FeynArts) ***** *)
|
---|
942 | (* ************************** *)
|
---|
943 |
|
---|
944 | GaugeXi[ V[1] ] = GaugeXi[A];
|
---|
945 | GaugeXi[ V[2] ] = GaugeXi[Z];
|
---|
946 | GaugeXi[ V[3] ] = GaugeXi[ZP];
|
---|
947 | GaugeXi[ V[4] ] = GaugeXi[W];
|
---|
948 | GaugeXi[ V[5] ] = GaugeXi[YY];
|
---|
949 | GaugeXi[ V[6] ] = GaugeXi[V];
|
---|
950 | GaugeXi[ V[7] ] = GaugeXi[G];
|
---|
951 | GaugeXi[ S[1] ] = 1;
|
---|
952 | GaugeXi[ S[2] ] = 1;
|
---|
953 | GaugeXi[ S[3] ] = 1;
|
---|
954 | GaugeXi[ S[4] ] = 1;
|
---|
955 | GaugeXi[ S[5] ] = 1;
|
---|
956 | GaugeXi[ S[6] ] = 1;
|
---|
957 | GaugeXi[ S[7] ] = 1;
|
---|
958 | GaugeXi[ S[8] ] = GaugeXi[Z];
|
---|
959 | GaugeXi[ S[9] ] = GaugeXi[ZP];
|
---|
960 | GaugeXi[ S[10] ] = GaugeXi[W];
|
---|
961 | GaugeXi[ S[11] ] = GaugeXi[YY];
|
---|
962 | GaugeXi[ S[12] ] = GaugeXi[V];
|
---|
963 | GaugeXi[ U[1] ] = GaugeXi[A];
|
---|
964 | GaugeXi[ U[2] ] = GaugeXi[Z];
|
---|
965 | GaugeXi[ U[3] ] = GaugeXi[ZP];
|
---|
966 | GaugeXi[ U[41] ] = GaugeXi[W];
|
---|
967 | GaugeXi[ U[42] ] = GaugeXi[W];
|
---|
968 | GaugeXi[ U[51] ] = GaugeXi[YY];
|
---|
969 | GaugeXi[ U[52] ] = GaugeXi[YY];
|
---|
970 | GaugeXi[ U[61] ] = GaugeXi[V];
|
---|
971 | GaugeXi[ U[62] ] = GaugeXi[V];
|
---|
972 | GaugeXi[ U[7] ] = GaugeXi[G];
|
---|
973 |
|
---|
974 |
|
---|
975 | (* ************************** *)
|
---|
976 | (* ***** Parameters ***** *)
|
---|
977 | (* ************************** *)
|
---|
978 | M$Parameters = {
|
---|
979 |
|
---|
980 | (* External parameters *)
|
---|
981 | aEWM1 == {
|
---|
982 | ParameterType -> External,
|
---|
983 | BlockName -> SMINPUTS,
|
---|
984 | OrderBlock -> 1,
|
---|
985 | Value -> 127.9,
|
---|
986 | InteractionOrder -> {QED,-2},
|
---|
987 | Description -> "Inverse of the EW coupling constant at the Z pole"
|
---|
988 | },
|
---|
989 | Gf == {
|
---|
990 | ParameterType -> External,
|
---|
991 | BlockName -> SMINPUTS,
|
---|
992 | OrderBlock -> 2,
|
---|
993 | Value -> 1.16637*^-5,
|
---|
994 | InteractionOrder -> {QED,2},
|
---|
995 | TeX -> Subscript[G,f],
|
---|
996 | Description -> "Fermi constant"
|
---|
997 | },
|
---|
998 | aS == {
|
---|
999 | ParameterType -> External,
|
---|
1000 | BlockName -> SMINPUTS,
|
---|
1001 | OrderBlock -> 3,
|
---|
1002 | Value -> 0.1184,
|
---|
1003 | InteractionOrder -> {QCD,2},
|
---|
1004 | TeX -> Subscript[\[Alpha],s],
|
---|
1005 | Description -> "Strong coupling constant at the Z pole"
|
---|
1006 | },
|
---|
1007 | ymdo == {
|
---|
1008 | ParameterType -> External,
|
---|
1009 | BlockName -> YUKAWA,
|
---|
1010 | OrderBlock -> 1,
|
---|
1011 | Value -> 5.04*^-3,
|
---|
1012 | Description -> "Down Yukawa mass"
|
---|
1013 | },
|
---|
1014 | ymup == {
|
---|
1015 | ParameterType -> External,
|
---|
1016 | BlockName -> YUKAWA,
|
---|
1017 | OrderBlock -> 2,
|
---|
1018 | Value -> 2.55*^-3,
|
---|
1019 | Description -> "Up Yukawa mass"
|
---|
1020 | },
|
---|
1021 | yms == {
|
---|
1022 | ParameterType -> External,
|
---|
1023 | BlockName -> YUKAWA,
|
---|
1024 | OrderBlock -> 3,
|
---|
1025 | Value -> 0.101,
|
---|
1026 | Description -> "Strange Yukawa mass"
|
---|
1027 | },
|
---|
1028 | ymc == {
|
---|
1029 | ParameterType -> External,
|
---|
1030 | BlockName -> YUKAWA,
|
---|
1031 | OrderBlock -> 4,
|
---|
1032 | Value -> 1.27,
|
---|
1033 | Description -> "Charm Yukawa mass"
|
---|
1034 | },
|
---|
1035 | ymb == {
|
---|
1036 | ParameterType -> External,
|
---|
1037 | BlockName -> YUKAWA,
|
---|
1038 | OrderBlock -> 5,
|
---|
1039 | Value -> 4.7,
|
---|
1040 | Description -> "Bottom Yukawa mass"
|
---|
1041 | },
|
---|
1042 | ymt == {
|
---|
1043 | ParameterType -> External,
|
---|
1044 | BlockName -> YUKAWA,
|
---|
1045 | OrderBlock -> 6,
|
---|
1046 | Value -> 172,
|
---|
1047 | Description -> "Top Yukawa mass"
|
---|
1048 | },
|
---|
1049 | ymD == {
|
---|
1050 | ParameterType -> External,
|
---|
1051 | BlockName -> YUKAWA,
|
---|
1052 | OrderBlock -> 7,
|
---|
1053 | Value -> 1*^3,
|
---|
1054 | Description -> "Heavy Down Yukawa mass"
|
---|
1055 | },
|
---|
1056 | ymS == {
|
---|
1057 | ParameterType -> External,
|
---|
1058 | BlockName -> YUKAWA,
|
---|
1059 | OrderBlock -> 8,
|
---|
1060 | Value -> 1*^3,
|
---|
1061 | Description -> "Heavy Strange Yukawa mass"
|
---|
1062 | },
|
---|
1063 | ymT == {
|
---|
1064 | ParameterType -> External,
|
---|
1065 | BlockName -> YUKAWA,
|
---|
1066 | OrderBlock -> 9,
|
---|
1067 | Value -> 1*^3,
|
---|
1068 | Description -> "Heavy Top Yukawa mass"
|
---|
1069 | },
|
---|
1070 | yme == {
|
---|
1071 | ParameterType -> External,
|
---|
1072 | BlockName -> YUKAWA,
|
---|
1073 | OrderBlock -> 11,
|
---|
1074 | Value -> 5.11*^-4,
|
---|
1075 | Description -> "Electron Yukawa mass"
|
---|
1076 | },
|
---|
1077 | ymm == {
|
---|
1078 | ParameterType -> External,
|
---|
1079 | BlockName -> YUKAWA,
|
---|
1080 | OrderBlock -> 13,
|
---|
1081 | Value -> 0.10566,
|
---|
1082 | Description -> "Muon Yukawa mass"
|
---|
1083 | },
|
---|
1084 | ymtau == {
|
---|
1085 | ParameterType -> External,
|
---|
1086 | BlockName -> YUKAWA,
|
---|
1087 | OrderBlock -> 15,
|
---|
1088 | Value -> 1.777,
|
---|
1089 | Description -> "Tau Yukawa mass"
|
---|
1090 | },
|
---|
1091 | ymEe == {
|
---|
1092 | ParameterType -> External,
|
---|
1093 | BlockName -> YUKAWA,
|
---|
1094 | OrderBlock -> 16,
|
---|
1095 | Value -> 1*^3,
|
---|
1096 | Description -> "Heavy Electron Yukawa mass"
|
---|
1097 | },
|
---|
1098 | ymEm == {
|
---|
1099 | ParameterType -> External,
|
---|
1100 | BlockName -> YUKAWA,
|
---|
1101 | OrderBlock -> 17,
|
---|
1102 | Value -> 1*^3,
|
---|
1103 | Description -> "Heavy Muon Yukawa mass"
|
---|
1104 | },
|
---|
1105 | ymEtau == {
|
---|
1106 | ParameterType -> External,
|
---|
1107 | BlockName -> YUKAWA,
|
---|
1108 | OrderBlock -> 18,
|
---|
1109 | Value -> 1*^3,
|
---|
1110 | Description -> "Heavy Tau Yukawa mass"
|
---|
1111 | },
|
---|
1112 | cabi == {
|
---|
1113 | ParameterType -> External,
|
---|
1114 | BlockName -> CKMBLOCK,
|
---|
1115 | OrderBlock -> 1,
|
---|
1116 | Value -> 0.227736,
|
---|
1117 | TeX -> Subscript[\[Theta], c],
|
---|
1118 | Description -> "Cabibbo angle"
|
---|
1119 | },
|
---|
1120 | v2 == {
|
---|
1121 | ParameterType -> External,
|
---|
1122 | Value -> V2,
|
---|
1123 | InteractionOrder -> {QED,-1},
|
---|
1124 | Description -> "phi vacuum expectation value"
|
---|
1125 | },
|
---|
1126 | v3 == {
|
---|
1127 | ParameterType -> External,
|
---|
1128 | BlockName -> OTHERS,
|
---|
1129 | OrderBlock -> 1,
|
---|
1130 | Value -> V3,
|
---|
1131 | InteractionOrder -> {QED,-1},
|
---|
1132 | Description -> "Chi vaccum expectation value"
|
---|
1133 | },
|
---|
1134 | lam2 == {
|
---|
1135 | ParameterType -> External,
|
---|
1136 | BlockName -> OTHERS,
|
---|
1137 | OrderBlock -> 2,
|
---|
1138 | Value -> Lam2,
|
---|
1139 | InteractionOrder -> {QED, 2},
|
---|
1140 | TeX -> Subscript[\[Lambda], 2],
|
---|
1141 | Description -> "phi quartic coupling"
|
---|
1142 | },
|
---|
1143 | lam3 == {
|
---|
1144 | ParameterType -> External,
|
---|
1145 | BlockName -> OTHERS,
|
---|
1146 | OrderBlock -> 3,
|
---|
1147 | Value -> Lam3,
|
---|
1148 | InteractionOrder -> {QED, 2},
|
---|
1149 | TeX -> Subscript[\[Lambda], 3],
|
---|
1150 | Description -> "Chi quartic coupling"
|
---|
1151 | },
|
---|
1152 | lam12 == {
|
---|
1153 | ParameterType -> External,
|
---|
1154 | BlockName -> OTHERS,
|
---|
1155 | OrderBlock -> 4,
|
---|
1156 | Value -> Lam12,
|
---|
1157 | InteractionOrder -> {QED, 2},
|
---|
1158 | TeX -> Subscript[\[Lambda], 12],
|
---|
1159 | Description -> "Rho Rho and phi phi quartic coupling"
|
---|
1160 | },
|
---|
1161 | lam13 == {
|
---|
1162 | ParameterType -> External,
|
---|
1163 | BlockName -> OTHERS,
|
---|
1164 | OrderBlock -> 5,
|
---|
1165 | Value -> Lam13,
|
---|
1166 | InteractionOrder -> {QED, 2},
|
---|
1167 | TeX -> Subscript[\[Lambda], 13],
|
---|
1168 | Description -> "Rho Rho and Chi Chi quartic coupling"
|
---|
1169 | },
|
---|
1170 | lam23 == {
|
---|
1171 | ParameterType -> External,
|
---|
1172 | BlockName -> OTHERS,
|
---|
1173 | OrderBlock -> 6,
|
---|
1174 | Value -> Lam23,
|
---|
1175 | InteractionOrder -> {QED, 2},
|
---|
1176 | TeX -> Subscript[\[Lambda], 23],
|
---|
1177 | Description -> "Chi Chi and phi phi quartic coupling"
|
---|
1178 | },
|
---|
1179 | lam12P == {
|
---|
1180 | ParameterType -> External,
|
---|
1181 | BlockName -> OTHERS,
|
---|
1182 | OrderBlock -> 7,
|
---|
1183 | Value -> Lam12P,
|
---|
1184 | InteractionOrder -> {QED, 2},
|
---|
1185 | TeX -> Subscript[\[Lambda]', 12],
|
---|
1186 | Description -> "Rho phi and phi Rho quartic coupling"
|
---|
1187 | },
|
---|
1188 | lam13P == {
|
---|
1189 | ParameterType -> External,
|
---|
1190 | BlockName -> OTHERS,
|
---|
1191 | OrderBlock -> 8,
|
---|
1192 | Value -> Lam13P,
|
---|
1193 | InteractionOrder -> {QED, 2},
|
---|
1194 | TeX -> Subscript[\[Lambda]', 13],
|
---|
1195 | Description -> "Rho Chi and Chi Rho quartic coupling"
|
---|
1196 | },
|
---|
1197 | lam23P == {
|
---|
1198 | ParameterType -> External,
|
---|
1199 | BlockName -> OTHERS,
|
---|
1200 | OrderBlock -> 9,
|
---|
1201 | Value -> Lam23P,
|
---|
1202 | InteractionOrder -> {QED, 2},
|
---|
1203 | TeX -> Subscript[\[Lambda]', 23],
|
---|
1204 | Description -> "phi Chi and Chi phi quartic coupling"
|
---|
1205 | },
|
---|
1206 | UH11 == {
|
---|
1207 | ParameterType -> External,
|
---|
1208 | BlockName -> OTHERS,
|
---|
1209 | OrderBlock -> 10,
|
---|
1210 | Value -> U11,
|
---|
1211 | TeX -> Subsuperscript[U,11,H],
|
---|
1212 | Description -> "11 rotation-matrix element of Realscalar"
|
---|
1213 | },
|
---|
1214 | UH12 == {
|
---|
1215 | ParameterType -> External,
|
---|
1216 | BlockName -> OTHERS,
|
---|
1217 | OrderBlock -> 11,
|
---|
1218 | Value -> U12,
|
---|
1219 | TeX -> Subsuperscript[U,12,H],
|
---|
1220 | Description -> "12 rotation-matrix element of Realscalar"
|
---|
1221 | },
|
---|
1222 | UH13 == {
|
---|
1223 | ParameterType -> External,
|
---|
1224 | BlockName -> OTHERS,
|
---|
1225 | OrderBlock -> 12,
|
---|
1226 | Value -> U13,
|
---|
1227 | TeX -> Subsuperscript[U,13,H],
|
---|
1228 | Description -> "13 rotation-matrix element of Realscalar"
|
---|
1229 | },
|
---|
1230 | UH21 == {
|
---|
1231 | ParameterType -> External,
|
---|
1232 | BlockName -> OTHERS,
|
---|
1233 | OrderBlock -> 13,
|
---|
1234 | Value -> U21,
|
---|
1235 | TeX -> Subsuperscript[U,21,H],
|
---|
1236 | Description -> "21 rotation-matrix element of Realscalar"
|
---|
1237 | },
|
---|
1238 | UH22 == {
|
---|
1239 | ParameterType -> External,
|
---|
1240 | BlockName -> OTHERS,
|
---|
1241 | OrderBlock -> 14,
|
---|
1242 | Value -> U22,
|
---|
1243 | TeX -> Subsuperscript[U,22,H],
|
---|
1244 | Description -> "22 rotation-matrix element of Realscalar"
|
---|
1245 | },
|
---|
1246 | UH23 == {
|
---|
1247 | ParameterType -> External,
|
---|
1248 | BlockName -> OTHERS,
|
---|
1249 | OrderBlock -> 15,
|
---|
1250 | Value -> U23,
|
---|
1251 | TeX -> Subsuperscript[U,23,H],
|
---|
1252 | Description -> "23 rotation-matrix element of Realscalar"
|
---|
1253 | },
|
---|
1254 | UH31 == {
|
---|
1255 | ParameterType -> External,
|
---|
1256 | BlockName -> OTHERS,
|
---|
1257 | OrderBlock -> 16,
|
---|
1258 | Value -> U31,
|
---|
1259 | TeX -> Subsuperscript[U,31,H],
|
---|
1260 | Description -> "31 rotation-matrix element of Realscalar"
|
---|
1261 | },
|
---|
1262 | UH32 == {
|
---|
1263 | ParameterType -> External,
|
---|
1264 | BlockName -> OTHERS,
|
---|
1265 | OrderBlock -> 17,
|
---|
1266 | Value -> U32,
|
---|
1267 | TeX -> Subsuperscript[U,32,H],
|
---|
1268 | Description -> "32 rotation-matrix element of Realscalar"
|
---|
1269 | },
|
---|
1270 | UH33 == {
|
---|
1271 | ParameterType -> External,
|
---|
1272 | BlockName -> OTHERS,
|
---|
1273 | OrderBlock -> 18,
|
---|
1274 | Value -> U33,
|
---|
1275 | TeX -> Subsuperscript[U,33,H],
|
---|
1276 | Description -> "33 rotation-matrix element of Realscalar"
|
---|
1277 | },
|
---|
1278 | tz == {
|
---|
1279 | ParameterType -> External,
|
---|
1280 | BlockName -> OTHERS,
|
---|
1281 | OrderBlock -> 19,
|
---|
1282 | Definitions -> {tz->0},
|
---|
1283 | Description -> "Tan of z zp mixing angle"
|
---|
1284 | },
|
---|
1285 | lam1 == {
|
---|
1286 | ParameterType -> External,
|
---|
1287 | BlockName -> OTHERS,
|
---|
1288 | OrderBlock -> 20,
|
---|
1289 | Value -> Lam1,
|
---|
1290 | InteractionOrder -> {QED, 2},
|
---|
1291 | TeX -> Subscript[\[Lambda], 1],
|
---|
1292 | Description -> "Rho quartic coupling"
|
---|
1293 | },
|
---|
1294 | lamWS == {
|
---|
1295 | ParameterType -> External,
|
---|
1296 | BlockName -> WOLFENSTEIN,
|
---|
1297 | OrderBlock -> 1,
|
---|
1298 | Value -> 0.2253,
|
---|
1299 | TeX -> \[Lambda],
|
---|
1300 | Description -> "Wolfenstein variable lam"
|
---|
1301 | },
|
---|
1302 | AWS == {
|
---|
1303 | ParameterType -> External,
|
---|
1304 | BlockName -> WOLFENSTEIN,
|
---|
1305 | OrderBlock -> 2,
|
---|
1306 | Value -> 0.808,
|
---|
1307 | TeX -> A,
|
---|
1308 | Description -> "Wolfenstein variable A"
|
---|
1309 | },
|
---|
1310 | rhoWS == {
|
---|
1311 | ParameterType -> External,
|
---|
1312 | BlockName -> WOLFENSTEIN,
|
---|
1313 | OrderBlock -> 3,
|
---|
1314 | Value -> 0.132,
|
---|
1315 | TeX -> \[Rho],
|
---|
1316 | Description -> "Wolfenstein variable rho"
|
---|
1317 | },
|
---|
1318 | etaWS == {
|
---|
1319 | ParameterType -> External,
|
---|
1320 | BlockName -> WOLFENSTEIN,
|
---|
1321 | OrderBlock -> 4,
|
---|
1322 | Value -> 0.341,
|
---|
1323 | TeX -> \[Eta],
|
---|
1324 | Description -> "Wolfenstein variable eta"
|
---|
1325 | },
|
---|
1326 |
|
---|
1327 |
|
---|
1328 | (* Internal Parameters *)
|
---|
1329 | beta == {
|
---|
1330 | ParameterType -> Internal,
|
---|
1331 | Value -> Bet,
|
---|
1332 | TeX -> \[Beta],
|
---|
1333 | Description -> "beta"
|
---|
1334 | },
|
---|
1335 | aEW == {
|
---|
1336 | ParameterType -> Internal,
|
---|
1337 | Value -> 1/aEWM1,
|
---|
1338 | InteractionOrder -> {QED,2},
|
---|
1339 | TeX -> Subscript[\[Alpha], EW],
|
---|
1340 | Description -> "Electroweak coupling contant"
|
---|
1341 | },
|
---|
1342 | MW == {
|
---|
1343 | ParameterType -> Internal,
|
---|
1344 | Value -> Sqrt[MZ^2/2+Sqrt[MZ^4/4-Pi/Sqrt[2]*aEW/Gf*MZ^2]],
|
---|
1345 | TeX -> Subscript[M,W],
|
---|
1346 | Description -> "W mass"
|
---|
1347 | },
|
---|
1348 | sw2 == {
|
---|
1349 | ParameterType -> Internal,
|
---|
1350 | Value -> 1-(MW/MZ)^2,
|
---|
1351 | Description -> "Squared Sin of the Weinberg angle"
|
---|
1352 | },
|
---|
1353 | ee == {
|
---|
1354 | ParameterType -> Internal,
|
---|
1355 | Value -> Sqrt[4 Pi aEW],
|
---|
1356 | InteractionOrder -> {QED,1},
|
---|
1357 | TeX -> e,
|
---|
1358 | Description -> "Electric coupling constant"
|
---|
1359 | },
|
---|
1360 | cw == {
|
---|
1361 | ParameterType -> Internal,
|
---|
1362 | Value -> Sqrt[1-sw2],
|
---|
1363 | TeX -> Subscript[c,w],
|
---|
1364 | Description -> "Cosine of the Weinberg angle"
|
---|
1365 | },
|
---|
1366 | sw == {
|
---|
1367 | ParameterType -> Internal,
|
---|
1368 | Value -> Sqrt[sw2],
|
---|
1369 | TeX -> Subscript[s,w],
|
---|
1370 | Description -> "Sine of the Weinberg angle"
|
---|
1371 | },
|
---|
1372 | c3 == {
|
---|
1373 | ParameterType -> Internal,
|
---|
1374 | Definitions -> {c3->beta sw/cw},
|
---|
1375 | TeX -> Subscript[c,3],
|
---|
1376 | Description -> "Cosine of the 331 angle"
|
---|
1377 | },
|
---|
1378 | s3 == {
|
---|
1379 | ParameterType -> Internal,
|
---|
1380 | Definitions -> {s3->Sqrt[1-(1+beta^2)*sw^2]/cw},
|
---|
1381 | TeX -> Subscript[s,3],
|
---|
1382 | Description -> "Sine of the 331 angle"
|
---|
1383 | },
|
---|
1384 | gw == {
|
---|
1385 | ParameterType -> Internal,
|
---|
1386 | Definitions -> {gw->ee/sw},
|
---|
1387 | InteractionOrder -> {QED,1},
|
---|
1388 | TeX -> Subscript[g,w],
|
---|
1389 | Description -> "Weak coupling constant at the Z pole"
|
---|
1390 | },
|
---|
1391 | gx == {
|
---|
1392 | ParameterType -> Internal,
|
---|
1393 | Definitions -> {gx->gw sw/Sqrt[1-(1+beta^2)*sw^2]},
|
---|
1394 | InteractionOrder -> {QED,1},
|
---|
1395 | TeX -> Subscript[g,x],
|
---|
1396 | Description -> "U(1)X coupling constant at the Z pole"
|
---|
1397 | },
|
---|
1398 | gs == {
|
---|
1399 | ParameterType -> Internal,
|
---|
1400 | Value -> Sqrt[4 Pi aS],
|
---|
1401 | InteractionOrder -> {QCD,1},
|
---|
1402 | TeX -> Subscript[g,s],
|
---|
1403 | ParameterName -> G,
|
---|
1404 | Description -> "Strong coupling constant at the Z pole"
|
---|
1405 | },
|
---|
1406 | v == {
|
---|
1407 | ParameterType -> Internal,
|
---|
1408 | Value -> Sqrt[4*MW^2*sw2/(ee^2)-v2^2],
|
---|
1409 | InteractionOrder -> {QED,-1},
|
---|
1410 | Description -> "Rho vaccum expectation value"
|
---|
1411 | },
|
---|
1412 | v3 == {
|
---|
1413 | ParameterType -> Internal,
|
---|
1414 | Value -> MZP Sqrt[3*(1-(1+beta^2)*sw^2)]/(gw*cw),
|
---|
1415 | InteractionOrder -> {QED,-1},
|
---|
1416 | Description -> "Chi vaccum expectation value"
|
---|
1417 | },
|
---|
1418 | cz == {
|
---|
1419 | ParameterType -> Internal,
|
---|
1420 | Definitions -> {cz->1/Sqrt[1+tz^2]},
|
---|
1421 | Description -> "Cosin of z zp mixing angle"
|
---|
1422 | },
|
---|
1423 | sz == {
|
---|
1424 | ParameterType -> Internal,
|
---|
1425 | Definitions -> {sz->-tz/Sqrt[1+tz^2]},
|
---|
1426 | Description -> "Sin of z zp mixing angle"
|
---|
1427 | },
|
---|
1428 | svv2 == {
|
---|
1429 | ParameterType -> Internal,
|
---|
1430 | Value -> 1/Sqrt[1+(v/v2)^2],
|
---|
1431 | TeX -> Subscript[s,vv2],
|
---|
1432 | Description -> "Sine of the vv2 angle"
|
---|
1433 | },
|
---|
1434 | cvv2 == {
|
---|
1435 | ParameterType -> Internal,
|
---|
1436 | Value -> Sqrt[1-svv2^2],
|
---|
1437 | TeX -> Subscript[c,vv2],
|
---|
1438 | Description -> "Cosine of the vv2 angle"
|
---|
1439 | },
|
---|
1440 | svv3 == {
|
---|
1441 | ParameterType -> Internal,
|
---|
1442 | Value -> 1/Sqrt[1+(v/v3)^2],
|
---|
1443 | TeX -> Subscript[s,vv3],
|
---|
1444 | Description -> "Sine of the vv3 angle"
|
---|
1445 | },
|
---|
1446 | cvv3 == {
|
---|
1447 | ParameterType -> Internal,
|
---|
1448 | Value -> Sqrt[1-svv3^2],
|
---|
1449 | TeX -> Subscript[c,vv3],
|
---|
1450 | Description -> "Cosine of the vv3 angle"
|
---|
1451 | },
|
---|
1452 | sv2v3 == {
|
---|
1453 | ParameterType -> Internal,
|
---|
1454 | Value -> 1/Sqrt[1+(v2/v3)^2],
|
---|
1455 | TeX -> Subscript[s,v2v3],
|
---|
1456 | Description -> "Sine of the v2v3 angle"
|
---|
1457 | },
|
---|
1458 | cv2v3 == {
|
---|
1459 | ParameterType -> Internal,
|
---|
1460 | Value -> Sqrt[1-sv2v3^2],
|
---|
1461 | TeX -> Subscript[c,v2v3],
|
---|
1462 | Description -> "Cosine of the v2v3 angle"
|
---|
1463 | },
|
---|
1464 | ff == {
|
---|
1465 | ParameterType -> Internal,
|
---|
1466 | Value -> F,
|
---|
1467 | InteractionOrder -> {QED,1},
|
---|
1468 | TeX -> f,
|
---|
1469 | Description -> "Coefficient of the cubic piece of the Higgs potential"
|
---|
1470 | },
|
---|
1471 | mu1 == {
|
---|
1472 | ParameterType -> Internal,
|
---|
1473 | Definitions -> {mu1->Sqrt[-lam1*v^2-lam12*v2^2/2-lam13*v3^2/2+ff*v3*v2/v]},
|
---|
1474 | Description -> "Coefficient of the quadratic piece of the Rho potential"
|
---|
1475 | },
|
---|
1476 | mu2 == {
|
---|
1477 | ParameterType -> Internal,
|
---|
1478 | Definitions -> {mu2->Sqrt[-lam2*v2^2-lam12*v^2/2-lam23*v3^2/2+ff*v3*v/v2]},
|
---|
1479 | Description -> "Coefficient of the quadratic piece of the phi potential"
|
---|
1480 | },
|
---|
1481 | mu3 == {
|
---|
1482 | ParameterType -> Internal,
|
---|
1483 | Definitions -> {mu3->Sqrt[-lam3*v3^2-lam13*v^2/2-lam23*v2^2/2+ff*v*v2/v3]},
|
---|
1484 | Description -> "Coefficient of the quadratic piece of the Chi potential"
|
---|
1485 | },
|
---|
1486 | yl == {
|
---|
1487 | ParameterType -> Internal,
|
---|
1488 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1489 | Definitions -> {yl[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1490 | Value -> {yl[1,1] -> Sqrt[2] yme / v2, yl[2,2] -> Sqrt[2] ymm / v2, yl[3,3] -> Sqrt[2] ymtau / v2},
|
---|
1491 | InteractionOrder -> {QED, 1},
|
---|
1492 | ParameterName -> {yl[1,1] -> ye, yl[2,2] -> ym, yl[3,3] -> ytau},
|
---|
1493 | TeX -> Superscript[y, l],
|
---|
1494 | Description -> "Lepton Yukawa couplings"
|
---|
1495 | },
|
---|
1496 | yE == {
|
---|
1497 | ParameterType -> Internal,
|
---|
1498 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1499 | Definitions -> {yE[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1500 | Value -> {yE[1,1] -> Sqrt[2] ymEe / v3, yE[2,2] -> Sqrt[2] ymEm / v3, yE[3,3] -> Sqrt[2] ymEtau / v3},
|
---|
1501 | InteractionOrder -> {QED, 1},
|
---|
1502 | ParameterName -> {yE[1,1] -> yEe, yl[2,2] -> yEm, yl[3,3] -> yEtau},
|
---|
1503 | TeX -> Superscript[y, E],
|
---|
1504 | Description -> "Heavy Lepton Yukawa couplings"
|
---|
1505 | },
|
---|
1506 | yu == {
|
---|
1507 | ParameterType -> Internal,
|
---|
1508 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1509 | Definitions -> {yu[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1510 | Value -> {yu[1,1] -> Sqrt[2] ymup/v2, yu[2,2] -> Sqrt[2] ymc/v2, yu[3,3] -> Sqrt[2] ymt/v2},
|
---|
1511 | InteractionOrder -> {QED, 1},
|
---|
1512 | ParameterName -> {yu[1,1] -> yup, yu[2,2] -> yc, yu[3,3] -> yt},
|
---|
1513 | TeX -> Superscript[y, u],
|
---|
1514 | Description -> "Up-type Yukawa couplings"
|
---|
1515 | },
|
---|
1516 | yd == {
|
---|
1517 | ParameterType -> Internal,
|
---|
1518 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1519 | Definitions -> {yd[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1520 | Value -> {yd[1,1] -> Sqrt[2] ymdo/v, yd[2,2] -> Sqrt[2] yms/v, yd[3,3] -> Sqrt[2] ymb/v},
|
---|
1521 | InteractionOrder -> {QED, 1},
|
---|
1522 | ParameterName -> {yd[1,1] -> ydo, yd[2,2] -> ys, yd[3,3] -> yb},
|
---|
1523 | TeX -> Superscript[y, d],
|
---|
1524 | Description -> "Down-type Yukawa couplings"
|
---|
1525 | },
|
---|
1526 | yJ == {
|
---|
1527 | ParameterType -> Internal,
|
---|
1528 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1529 | Definitions -> {yJ[i_?NumericQ, j_?NumericQ] :> 0 /; (i =!= j)},
|
---|
1530 | Value -> {yJ[1,1] -> Sqrt[2] ymD/v3, yJ[2,2] -> Sqrt[2] ymS/v3, yJ[3,3] -> Sqrt[2] ymT/v3},
|
---|
1531 | InteractionOrder -> {QED, 1},
|
---|
1532 | ParameterName -> {yJ[1,1] -> yD, yJ[2,2] -> yS, yJ[3,3] -> yT},
|
---|
1533 | TeX -> Superscript[y, J],
|
---|
1534 | Description -> "Heavy-type Yukawa couplings"
|
---|
1535 | },
|
---|
1536 | MY == {
|
---|
1537 | ParameterType -> Internal,
|
---|
1538 | Value -> 1/2 gw Sqrt[v3^2+v2^2],
|
---|
1539 | TeX -> Subscript[M,Y],
|
---|
1540 | Description -> "YY mass"
|
---|
1541 | },
|
---|
1542 | MV == {
|
---|
1543 | ParameterType -> Internal,
|
---|
1544 | Value -> 1/2 gw Sqrt[v3^2+v^2],
|
---|
1545 | TeX -> Subscript[M,V],
|
---|
1546 | Description -> "V mass"
|
---|
1547 | },
|
---|
1548 | MH2 == {
|
---|
1549 | ParameterType -> Internal,
|
---|
1550 | Value -> Sqrt[2] Sqrt[ff UH22 UH32 v-lam1 UH12^2 v^2+ff UH12 UH32 v2-lam12 UH12 UH22 v v2-lam2 UH22^2 v2^2-(ff UH32^2 v v2)/(2 v3)+ff UH12 UH22 v3-lam13 UH12 UH32 v v3-(ff UH22^2 v v3)/(2 v2)-lam23 UH22 UH32 v2 v3-(ff UH12^2 v2 v3)/(2 v)-lam3 UH32^2 v3^2],
|
---|
1551 | TeX -> Subscript[M,H2],
|
---|
1552 | Description -> "H2 mass"
|
---|
1553 | },
|
---|
1554 | MH3 == {
|
---|
1555 | ParameterType -> Internal,
|
---|
1556 | Value -> Sqrt[2] Sqrt[ff UH23 UH33 v-lam1 UH13^2 v^2+ff UH13 UH33 v2-lam12 UH13 UH23 v v2-lam2 UH23^2 v2^2-(ff UH33^2 v v2)/(2 v3)+ff UH13 UH23 v3-lam13 UH13 UH33 v v3-(ff UH23^2 v v3)/(2 v2)-lam23 UH23 UH33 v2 v3-(ff UH13^2 v2 v3)/(2 v)-lam3 UH33^2 v3^2],
|
---|
1557 | TeX -> Subscript[M,H3],
|
---|
1558 | Description -> "H3 mass"
|
---|
1559 | },
|
---|
1560 | Uh11 == {
|
---|
1561 | ParameterType -> Internal,
|
---|
1562 | Value -> v3/(v Sqrt[1 + (1/v^2 + 1/v2^2) v3^2]),
|
---|
1563 | TeX -> Subsuperscript[U, 11, h],
|
---|
1564 | Description -> "11 rotation-matrix element of Pseudoscalar"
|
---|
1565 | },
|
---|
1566 | Uh12 == {
|
---|
1567 | ParameterType -> Internal,
|
---|
1568 | Value -> -v/(Sqrt[1 + v^2/v3^2] v3),
|
---|
1569 | TeX -> Subsuperscript[U, 12, h],
|
---|
1570 | Description -> "12 rotation-matrix element of Pseudoscalar"
|
---|
1571 | },
|
---|
1572 | Uh13 == {
|
---|
1573 | ParameterType -> Internal,
|
---|
1574 | Value -> -(v v2 v3^2 (v^2 + v3^2))/(Sqrt[
|
---|
1575 | v2^2 (v^2 + v3^2)^2] Sqrt[(v^2 + v3^2) (v2^2 v3^2 +
|
---|
1576 | v^2 (v2^2 + v3^2))]),
|
---|
1577 | TeX -> Subsuperscript[U, 13, h],
|
---|
1578 | Description -> "13 rotation-matrix element of Pseudoscalar"
|
---|
1579 | },
|
---|
1580 | Uh21 == {
|
---|
1581 | ParameterType -> Internal,
|
---|
1582 | Value -> v3/(v2 Sqrt[1 + (1/v^2 + 1/v2^2) v3^2]),
|
---|
1583 | TeX -> Subsuperscript[U, 21, h],
|
---|
1584 | Description -> "21 rotation-matrix element of Pseudoscalar"
|
---|
1585 | },
|
---|
1586 | Uh23 == {
|
---|
1587 | ParameterType -> Internal,
|
---|
1588 | Value -> Sqrt[
|
---|
1589 | v2^2 (v^2 + v3^2)^2]/Sqrt[(v^2 + v3^2) (v2^2 v3^2 +
|
---|
1590 | v^2 (v2^2 + v3^2))],
|
---|
1591 | TeX -> Subsuperscript[U, 23, h],
|
---|
1592 | Description -> "23 rotation-matrix element of Pseudoscalar"
|
---|
1593 | },
|
---|
1594 | Uh31 == {
|
---|
1595 | ParameterType -> Internal,
|
---|
1596 | Value -> 1/Sqrt[1 + (1/v^2 + 1/v2^2) v3^2],
|
---|
1597 | TeX -> Subsuperscript[U, 31, h],
|
---|
1598 | Description -> "31 rotation-matrix element of Pseudoscalar"
|
---|
1599 | },
|
---|
1600 | Uh32 == {
|
---|
1601 | ParameterType -> Internal,
|
---|
1602 | Value -> 1/Sqrt[1 + v^2/v3^2],
|
---|
1603 | TeX -> Subsuperscript[U, 32, h],
|
---|
1604 | Description -> "32 rotation-matrix element of Pseudoscalar"
|
---|
1605 | },
|
---|
1606 | Uh33 == {
|
---|
1607 | ParameterType -> Internal,
|
---|
1608 | Value -> -(v^2 v2 v3 (v^2 + v3^2))/(Sqrt[
|
---|
1609 | v2^2 (v^2 + v3^2)^2] Sqrt[(v^2 + v3^2) (v2^2 v3^2 +
|
---|
1610 | v^2 (v2^2 + v3^2))]),
|
---|
1611 | TeX -> Subsuperscript[U, 33, h],
|
---|
1612 | Description -> "33 rotation-matrix element of Pseudoscalar"
|
---|
1613 | },
|
---|
1614 | Mh == {
|
---|
1615 | ParameterType -> Internal,
|
---|
1616 | Value -> Sqrt[2] Sqrt[-ff Uh21 Uh31 v-ff Uh11 Uh31 v2-(ff Uh31^2 v v2)/(2 v3)-ff Uh11 Uh21 v3-(ff Uh21^2 v v3)/(2 v2)-(ff Uh11^2 v2 v3)/(2 v)],
|
---|
1617 | TeX -> Subscript[M,h],
|
---|
1618 | Description -> "h mass"
|
---|
1619 | },
|
---|
1620 | MHW == {
|
---|
1621 | ParameterType -> Internal,
|
---|
1622 | Value -> Sqrt[ (v^2+v2^2) ((-ff v3)/(v v2)-lam12P/2)],
|
---|
1623 | TeX -> Subscript[M,HW],
|
---|
1624 | Description -> "HW mass"
|
---|
1625 | },
|
---|
1626 | MHY == {
|
---|
1627 | ParameterType -> Internal,
|
---|
1628 | Value -> Sqrt[ (v2^2+v3^2) ((-ff v)/(v2 v3)-lam23P/2)],
|
---|
1629 | TeX -> Subscript[M,HY],
|
---|
1630 | Description -> "HY mass"
|
---|
1631 | },
|
---|
1632 | MHV == {
|
---|
1633 | ParameterType -> Internal,
|
---|
1634 | Value -> Sqrt[ (v^2+v3^2) ((-ff v2)/(v v3)-lam13P/2)],
|
---|
1635 | TeX -> Subscript[M,HV],
|
---|
1636 | Description -> "HV mass"
|
---|
1637 | },
|
---|
1638 |
|
---|
1639 |
|
---|
1640 |
|
---|
1641 |
|
---|
1642 | (* N. B. : only Cabibbo mixing! *)
|
---|
1643 | CKM == {
|
---|
1644 | ParameterType -> Internal,
|
---|
1645 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1646 | Unitary -> True,
|
---|
1647 | Value -> {CKM[1,1] -> 1-lamWS^2/2, CKM[1,2] -> lamWS, CKM[1,3] -> AWS*lamWS^3*(rhoWS-I*etaWS), CKM[2,1] -> -lamWS, CKM[2,2] -> 1-lamWS^2/2, CKM[2,3] -> AWS*lamWS^2, CKM[3,1] -> AWS*lamWS^3*(1-rhoWS-I*etaWS), CKM[3,2] -> -AWS*lamWS^2, CKM[3,3] -> 1},
|
---|
1648 | TeX -> Superscript[V,CKM],
|
---|
1649 | Description -> "CKM-Matrix"
|
---|
1650 | },
|
---|
1651 | RU == {
|
---|
1652 | ParameterType -> Internal,
|
---|
1653 | Indices -> {Index[Generation], Index[Generation]},
|
---|
1654 | Unitary -> True,
|
---|
1655 | Definitions -> {RU[1,1] -> 1, RU[1,2] -> 0, RU[1,3] -> 0, RU[2,1] -> 0, RU[2,2] -> 1, RU[2,3] -> 0, RU[3,1] -> 0, RU[3,2] -> 0, RU[3,3] -> 1},
|
---|
1656 | TeX -> Superscript[R,u],
|
---|
1657 | Description -> "RU-Matrix"
|
---|
1658 | }
|
---|
1659 |
|
---|
1660 | };
|
---|
1661 |
|
---|
1662 | (* ************************** *)
|
---|
1663 | (* ***** Lagrangian ***** *)
|
---|
1664 | (* ************************** *)
|
---|
1665 |
|
---|
1666 | LGauge := Block[{mu,nu,ii,aa},
|
---|
1667 |
|
---|
1668 | ExpandIndices[-1/4 FS[K,mu,nu] FS[K,mu,nu] - 1/4 FS[Wi,mu,nu,ii]FS[Wi,mu,nu,ii] - 1/4 FS[G,mu,nu,aa] FS[G,mu,nu,aa], FlavorExpand->SU3W]];
|
---|
1669 |
|
---|
1670 |
|
---|
1671 | LFermions := Block[{mu,fermi},
|
---|
1672 |
|
---|
1673 | fermi=ExpandIndices[I*(
|
---|
1674 | QL12bar.Ga[mu].DC[QL12, mu] + QL3bar.Ga[mu].DC[QL3, mu] + LLbar.Ga[mu].DC[LL, mu] + uRbar.Ga[mu].DC[uR, mu] + dRbar.Ga[mu].DC[dR, mu] + JR12bar.Ga[mu].DC[JR12,mu] + JR3bar.Ga[mu].DC[JR3,mu] + lRbar.Ga[mu].DC[lR, mu] + EERbar.Ga[mu].DC[EER, mu]),
|
---|
1675 | FlavorExpand->{SU3W,SU3T,ASU3W,ASU3T}];
|
---|
1676 | fermi = ExpandIndices[fermi]];
|
---|
1677 |
|
---|
1678 | LHiggs := Block[{ii,mu, feynmangaugerules},
|
---|
1679 | feynmangaugerules = If[Not[FeynmanGauge], {GZ|GZP|GW|GWbar|GY|GYbar|GV|GVbar ->0}, {}];
|
---|
1680 |
|
---|
1681 | ExpandIndices[DC[Rhobar[ii],mu] DC[Rho[ii],mu] + DC[Phibar[ii],mu] DC[Phi[ii],mu] + DC[Chibar[ii],mu] DC[Chi[ii],mu] + mu1^2 Rhobar[ii] Rho[ii] + lam1 Rhobar[ii] Rho[ii] Rhobar[jj] Rho[jj] + mu2^2 Phibar[ii] Phi[ii] + lam2 Phibar[ii] Phi[ii] Phibar[jj] Phi[jj] + mu3^2 Chibar[ii] Chi[ii] + lam3 Chibar[ii] Chi[ii] Chibar[jj] Chi[jj] + lam12 Rhobar[ii] Rho[ii] Phibar[jj] Phi[jj] + lam13 Rhobar[ii] Rho[ii] Chibar[jj] Chi[jj] + lam23 Phibar[ii] Phi[ii] Chibar[jj] Chi[jj] + lam12P Rhobar[ii] Phi[ii] Phibar[jj] Rho[jj] + lam13P Rhobar[ii] Chi[ii] Chibar[jj] Rho[jj] + lam23P Phibar[ii] Chi[ii] Chibar[jj] Phi[jj] + Sqrt[2] ff Eps[ii,jj,kk] Rho[ii] Phi[jj] Chi[kk] + Sqrt[2] ff HC[Eps[ii,jj,kk] Rho[ii] Phi[jj] Chi[kk]], FlavorExpand->{SU3T,SU3W}]/.feynmangaugerules
|
---|
1682 | ];
|
---|
1683 |
|
---|
1684 | LYukawa := Block[{sp,ii,cc,ff1,ff3,ff4,yuk,feynmangaugerules},
|
---|
1685 | feynmangaugerules = If[Not[FeynmanGauge], {GZ|GZP|GW|GWbar|GY|GYbar|GV|GVbar ->0}, {}];
|
---|
1686 |
|
---|
1687 | yuk = ExpandIndices[
|
---|
1688 | -yl[ff1, ff3] LLbar[sp, ii, ff1].lR [sp, ff3] Phibar[ii]
|
---|
1689 | -yE[ff1, ff3] LLbar[sp, ii, ff1].EER [sp, ff3] Chibar[ii]
|
---|
1690 | -yu[ff1, ff3] RU[ff2, ff1] QLbar[sp, ii, ff4, cc].uR [sp, ff3, cc] Su[ff4, ff2, ii]
|
---|
1691 | -yd[ff1, ff3] CKM[ff2, ff1] QLbar[sp, ii, ff4, cc].dR [sp, ff3, cc] Sd[ff4, ff2, ii]
|
---|
1692 | -yJ[ff1, ff3] QLbar[sp, ii, ff2, cc].JR[sp, ff3, cc] SJ[ff2, ff1, ii],
|
---|
1693 | FlavorExpand -> {SU3T}];
|
---|
1694 | yuk = ExpandIndices[yuk] /.{CKM[a_, b_] Conjugate[CKM[a_, c_]] -> 1/3 IndexDelta[b, c],CKM[b_, a_] Conjugate[CKM[c_, a_]] -> 1/3 IndexDelta[b, c]};
|
---|
1695 | yuk+HC[yuk]/.feynmangaugerules
|
---|
1696 | ];
|
---|
1697 |
|
---|
1698 | LGhost := Block[{LGh1,LGhw,LGhs,LGhhiggs,LGhrho,LGhphi,LGhchi,mu, generators,gh,ghbar,Vectorize,rho1,rho2,rho3,rho4,phi1,phi2,phi3,phi4,chi1,chi2,chi3,chi4,togoldstones,rho,rho0,phi,phi0,chi,chi0},
|
---|
1699 | (* Pure gauge piece *)
|
---|
1700 | LGh1 = -ghKbar.del[DC[ghK,mu],mu];
|
---|
1701 | LGhw = -ghWibar.del[DC[ghWi,mu],mu];
|
---|
1702 | LGhs = -ghGbar.del[DC[ghG,mu],mu];
|
---|
1703 |
|
---|
1704 | (* Scalar pieces: see Peskin pages 739-742 *)
|
---|
1705 | (* rho1, rho2, rho3 and rho4 are the real degrees of freedom of HW and GW *)
|
---|
1706 | (* Vectorize transforms a triplet in a vector in the phi-basis, i.e. the basis of real degrees of freedom *)
|
---|
1707 | gh = {ghK, ghWi[1], ghWi[2], ghWi[3], ghWi[4], ghWi[5], ghWi[6], ghWi[7], ghWi[8]};
|
---|
1708 | ghbar = {ghKbar, ghWibar[1], ghWibar[2], ghWibar[3], ghWibar[4], ghWibar[5], ghWibar[6], ghWibar[7], ghWibar[8]};
|
---|
1709 | generators = {-I/2 gx IdentityMatrix[3], -I/2 gw Gellmann[1], -I/2 gw Gellmann[2], -I/2 gw Gellmann[3], -I/2 gw Gellmann[4], -I/2 gw Gellmann[5], -I/2 gw Gellmann[6], -I/2 gw Gellmann[7], -I/2 gw Gellmann[8]};
|
---|
1710 | rho = Expand[{(-I rho1 - rho2)/Sqrt[2], (UH11 h + UH12 H2 + UH13 H3 + I (Uh11 H0 + Uh12 GZ + Uh13 GZP))/Sqrt[2], (-I rho3 - rho4)/Sqrt[2] } ];
|
---|
1711 | rho0 = {0, v/Sqrt[2], 0};
|
---|
1712 | phi = Expand[{(UH21 h + UH22 H2 + UH23 H3 + I (Uh21 H0 + Uh23 GZP))/Sqrt[2], (-I phi1 - phi2)/Sqrt[2], (-I phi3 - phi4)/Sqrt[2] } ];
|
---|
1713 | phi0 = {v2/Sqrt[2], 0, 0};
|
---|
1714 | chi = Expand[{(-I chi1 - chi2)/Sqrt[2], (-I chi3 - chi4)/Sqrt[2], (UH31 h + UH32 H2 + UH33 H3 + I (Uh31 H0 + Uh32 GZ + Uh33 GZP))/Sqrt[2] } ];
|
---|
1715 | chi0 = {0, 0, v3/Sqrt[2]};
|
---|
1716 | Vectorize[{a_, b_, c_}]:= Simplify[{Sqrt[2] Re[Expand[a]], Sqrt[2] Im[Expand[a]], Sqrt[2] Re[Expand[b]], Sqrt[2] Im[Expand[b]], Sqrt[2] Re[Expand[c]], Sqrt[2] Im[Expand[c]]}/.{Im[_]->0, Re[num_]->num}];
|
---|
1717 | togoldstones := {
|
---|
1718 | rho1 -> (HW svv2 + GW cvv2 + HWbar svv2 + GWbar cvv2)/Sqrt[2],
|
---|
1719 | rho2 -> (- HW svv2 - GW cvv2 + HWbar svv2 + GWbar cvv2)/(I Sqrt[2]),
|
---|
1720 | rho3 -> (GV cvv3 + HV svv3 + GVbar cvv3 + HVbar svv3)/Sqrt[2],
|
---|
1721 | rho4 -> (- GV cvv3 - HV svv3 + GVbar cvv3 + HVbar svv3)/(I Sqrt[2]),
|
---|
1722 | phi1 -> (- HW cvv2 + GW svv2 - HWbar cvv2 + GWbar svv2)/Sqrt[2],
|
---|
1723 | phi2 -> (HWbar cvv2 - GWbar svv2 - HW cvv2 + GW svv2)/(I Sqrt[2]),
|
---|
1724 | phi3 -> (GY cv2v3 + HY sv2v3 + GYbar cv2v3 + HYbar sv2v3)/Sqrt[2],
|
---|
1725 | phi4 -> (- GY cv2v3 - HY sv2v3 + GYbar cv2v3 + HYbar sv2v3)/(I Sqrt[2]),
|
---|
1726 | chi1 -> (- HY cv2v3 + GY sv2v3 - HYbar cv2v3 + GYbar sv2v3)/Sqrt[2],
|
---|
1727 | chi2 -> (HYbar cv2v3 - GYbar sv2v3 - HY cv2v3 + GY sv2v3)/(I Sqrt[2]),
|
---|
1728 | chi3 -> (- HV cvv3 + GV svv3 - HVbar cvv3 + GVbar svv3)/Sqrt[2],
|
---|
1729 | chi4 -> (HVbar cvv3 - GVbar svv3 - HV cvv3 + GV svv3)/(I Sqrt[2])};
|
---|
1730 | LGhrho=
|
---|
1731 | Plus@@Flatten[Table[-ghbar[[kkk]].gh[[lll]] Vectorize[generators[[kkk]].(rho0)].Vectorize[generators[[lll]].(rho + rho0)],{kkk,9},{lll,9}]];
|
---|
1732 | LGhphi=
|
---|
1733 | Plus@@Flatten[Table[-ghbar[[kkkk]].gh[[llll]] Vectorize[generators[[kkkk]].(phi0)].Vectorize[generators[[llll]].(phi + phi0)],{kkkk,9},{llll,9}]];
|
---|
1734 | LGhchi=
|
---|
1735 | Plus@@Flatten[Table[-ghbar[[kkkkk]].gh[[lllll]] Vectorize[generators[[kkkkk]].(chi0)].Vectorize[generators[[lllll]].(chi + chi0)],{kkkkk,9},{lllll,9}]];
|
---|
1736 |
|
---|
1737 | LGhhiggs=LGhrho+ LGhphi+ LGhchi /.togoldstones;
|
---|
1738 |
|
---|
1739 | ExpandIndices[ LGhs + If[FeynmanGauge, LGhw +LGh1 + LGhhiggs ,0], FlavorExpand->SU3W]];
|
---|
1740 |
|
---|
1741 | LThree:= LHiggs+LFermions+LYukawa+LGhost+LGauge;
|
---|