# Sextets: SextetDiquarks.fr

File SextetDiquarks.fr, 7.9 KB (added by BenjF, 5 years ago) |
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1 | |

2 | M$ModelName = "Sextet_Diquarks"; |

3 | |

4 | (* |

5 | |

6 | The convention and notations follow 0909.2666 |

7 | We also allow for non intergeneration couplings between quarks. |

8 | The mixing matrices are however implemented in general, and put diagonal via the independent |

9 | restriction file |

10 | |

11 | MFV.rst |

12 | |

13 | The new particles are |

14 | |

15 | six1 = (6, 1, 1/3) |

16 | six2 = (6, 1, -2/3) |

17 | six3 = (6, 1, 4/3) |

18 | |

19 | *) |

20 | |

21 | M$Information = {Authors -> {"C. Duhr"}, |

22 | Version -> "1.0", |

23 | Date -> "27. 10. 2010", |

24 | Institutions -> {"IPPP, Durham"}, |

25 | Emails -> {"claude.duhr@durham.ac.uk"}}; |

26 | |

27 | IndexRange[Index[Sextet]] = Range[6]; |

28 | IndexStyle[ Sextet, u]; |

29 | |

30 | AddGaugeRepresentation[SU3C -> {T6, Sextet}]; |

31 | |

32 | (* Coupling matrices are symmetric *) |

33 | |

34 | |

35 | SetAttributes[LQQR, Orderless]; |

36 | SetAttributes[LUDL, Orderless]; |

37 | SetAttributes[LUUL, Orderless]; |

38 | SetAttributes[LDDL, Orderless]; |

39 | |

40 | M$Parameters = { |

41 | |

42 | LQQRR == {Indices -> {Index[Generation], Index[Generation]}, |

43 | Value -> {LQQRR[1,1] -> 0.1, |

44 | LQQRR[2,2] -> 0.1, |

45 | LQQRR[3,3] -> 0.1, |

46 | LQQRR[i_, j_] :> 0 /; NumericQ[i] && NumericQ[j] && (i !=j)}, |

47 | InteractionOrder -> {QCD, 1}, |

48 | ParameterType -> External, |

49 | ComplexParameter -> False |

50 | }, |

51 | |

52 | LQQRI == {Indices -> {Index[Generation], Index[Generation]}, |

53 | Value -> {LQQRI[_,_] -> 0}, |

54 | InteractionOrder -> {QCD, 1}, |

55 | ParameterType -> External, |

56 | ComplexParameter -> False |

57 | }, |

58 | |

59 | LUDLR == {Indices -> {Index[Generation], Index[Generation]}, |

60 | Value -> {LUDLR[1,1] -> 0.1, |

61 | LUDLR[2,2] -> 0.1, |

62 | LUDLR[3,3] -> 0.1, |

63 | LUDLR[i_, j_] :> 0 /; NumericQ[i] && NumericQ[j] && (i !=j)}, |

64 | InteractionOrder -> {QCD, 1}, |

65 | ParameterType -> External, |

66 | ComplexParameter -> False |

67 | }, |

68 | |

69 | LUDLI == {Indices -> {Index[Generation], Index[Generation]}, |

70 | Value -> {LUDLI[_,_] -> 0}, |

71 | InteractionOrder -> {QCD, 1}, |

72 | ParameterType -> External, |

73 | ComplexParameter -> False |

74 | }, |

75 | |

76 | LUULR == {Indices -> {Index[Generation], Index[Generation]}, |

77 | Value -> {LUULR[1,1] -> 0.1, |

78 | LUULR[2,2] -> 0.1, |

79 | LUULR[3,3] -> 0.1, |

80 | LUULR[i_, j_] :> 0 /; NumericQ[i] && NumericQ[j] && (i !=j)}, |

81 | InteractionOrder -> {QCD, 1}, |

82 | ParameterType -> External, |

83 | ComplexParameter -> False |

84 | }, |

85 | |

86 | LUULI == {Indices -> {Index[Generation], Index[Generation]}, |

87 | Value -> {LUULI[_,_] -> 0}, |

88 | InteractionOrder -> {QCD, 1}, |

89 | ParameterType -> External, |

90 | ComplexParameter -> False |

91 | }, |

92 | |

93 | LDDLR == {Indices -> {Index[Generation], Index[Generation]}, |

94 | Value -> {LDDLR[1,1] -> 0.1, |

95 | LDDLR[2,2] -> 0.1, |

96 | LDDLR[3,3] -> 0.1, |

97 | LDDLR[i_, j_] :> 0 /; NumericQ[i] && NumericQ[j] && (i !=j)}, |

98 | InteractionOrder -> {QCD, 1}, |

99 | ParameterType -> External, |

100 | ComplexParameter -> False |

101 | }, |

102 | |

103 | LDDLI == {Indices -> {Index[Generation], Index[Generation]}, |

104 | Value -> {LDDLI[_,_] -> 0}, |

105 | InteractionOrder -> {QCD, 1}, |

106 | ParameterType -> External, |

107 | ComplexParameter -> False |

108 | }, |

109 | |

110 | LHS1 == {InteractionOrder -> {QED, 2}, |

111 | Value -> 0.1, |

112 | ParameterType -> External |

113 | }, |

114 | |

115 | LHS2 == {InteractionOrder -> {QED, 2}, |

116 | Value -> 0.1, |

117 | ParameterType -> External |

118 | }, |

119 | |

120 | LHS3 == {InteractionOrder -> {QED, 2}, |

121 | Value -> 0.1, |

122 | ParameterType -> External |

123 | }, |

124 | |

125 | LSS11 == {InteractionOrder -> {QCD, 2}, |

126 | Value -> 0.1, |

127 | ParameterType -> External |

128 | }, |

129 | |

130 | LSS121 == {InteractionOrder -> {QCD, 2}, |

131 | Value -> 0.1, |

132 | ParameterType -> External |

133 | }, |

134 | |

135 | LSS122 == {InteractionOrder -> {QCD, 2}, |

136 | Value -> 0.1, |

137 | ParameterType -> External |

138 | }, |

139 | |

140 | LSS131 == {InteractionOrder -> {QCD, 2}, |

141 | Value -> 0.1, |

142 | ParameterType -> External |

143 | }, |

144 | |

145 | LSS132 == {InteractionOrder -> {QCD, 2}, |

146 | Value -> 0.1, |

147 | ParameterType -> External |

148 | }, |

149 | |

150 | LSS22 == {InteractionOrder -> {QCD, 2}, |

151 | Value -> 0.1, |

152 | ParameterType -> External |

153 | }, |

154 | |

155 | LSS231== {InteractionOrder -> {QCD, 2}, |

156 | Value -> 0.1, |

157 | ParameterType -> External |

158 | }, |

159 | |

160 | LSS232 == {InteractionOrder -> {QCD, 2}, |

161 | Value -> 0.1, |

162 | ParameterType -> External |

163 | }, |

164 | |

165 | LSS33 == {InteractionOrder -> {QCD, 2}, |

166 | Value -> 0.1, |

167 | ParameterType -> External |

168 | }, |

169 | |

170 | (* Internal parameters *) |

171 | |

172 | LQQR == {Indices -> {Index[Generation], Index[Generation]}, |

173 | Value -> {LQQR[i_,j_] :> LQQRR[i,j] + I LQQRI[i,j]}, |

174 | InteractionOrder -> {QCD, 1}, |

175 | ComplexParameter -> True |

176 | }, |

177 | |

178 | LUDL == {Indices -> {Index[Generation], Index[Generation]}, |

179 | Value -> {LUDL[i_,j_] :> LUDLR[i,j] + I LUDLI[i,j]}, |

180 | InteractionOrder -> {QCD, 1}, |

181 | ComplexParameter -> True |

182 | }, |

183 | |

184 | LUUL == {Indices -> {Index[Generation], Index[Generation]}, |

185 | Value -> {LUUL[i_,j_] :> LUULR[i,j] + I LUULI[i,j]}, |

186 | InteractionOrder -> {QCD, 1}, |

187 | ComplexParameter -> True |

188 | }, |

189 | |

190 | LDDL == {Indices -> {Index[Generation], Index[Generation]}, |

191 | Value -> {LDDL[i_,j_] :> LDDLR[i,j] + I LDDLI[i,j]}, |

192 | InteractionOrder -> {QCD, 1}, |

193 | ComplexParameter -> True |

194 | } |

195 | }; |

196 | |

197 | M$ClassesDescription = { |

198 | |

199 | S[100] == { |

200 | ClassName -> six1, |

201 | SelfConjugate -> False, |

202 | Indices -> {Index[Sextet]}, |

203 | Mass -> {MSIX1, 500}, |

204 | Width -> {WSIX1, 4.4108}, |

205 | QuantumNumbers -> {Q -> 1/3, Y -> 1/3} |

206 | }, |

207 | |

208 | S[200] == { |

209 | ClassName -> six2, |

210 | SelfConjugate -> False, |

211 | Indices -> {Index[Sextet]}, |

212 | Mass -> {MSIX2, 500}, |

213 | Width -> {WSIX2, 4.7740}, |

214 | QuantumNumbers -> {Q -> -2/3, Y -> -2/3} |

215 | }, |

216 | |

217 | S[300] == { |

218 | ClassName -> six3, |

219 | SelfConjugate -> False, |

220 | Indices -> {Index[Sextet]}, |

221 | Mass -> {MSIX3, 500}, |

222 | Width -> {WSIX3, 4.0647}, |

223 | QuantumNumbers -> {Q -> 4/3, Y -> 4/3} |

224 | } |

225 | }; |

226 | |

227 | |

228 | (* the Lagrangian *) |

229 | |

230 | |

231 | LSextetKin := DC[six1bar[k], mu]DC[six1[k],mu] - MSIX1^2 six1bar[k]six1[k] + |

232 | DC[six2bar[k], mu]DC[six2[k],mu] - MSIX2^2 six2bar[k]six2[k] + |

233 | DC[six3bar[k], mu]DC[six3[k],mu] - MSIX2^2 six3bar[k]six3[k]; |

234 | |

235 | LD11 := 2 Sqrt[2] (K6bar[k,i,j] six1[k] LQQR[n,m] ProjP[s,r] dqbar[s,n,i].CC[uq][r,m,j] + |

236 | K6bar[k,i,j] six1[k] LUDL[n,m] ProjM[s,r] dqbar[s,n,i].CC[uq][r,m,j]); |

237 | |

238 | LD1 := LD11 + HC[LD11]; |

239 | |

240 | LD21 := 2 Sqrt[2] K6bar[k,i,j] six2[k] LDDL[n,m] ProjM[s,r] dqbar[s,n,i].CC[dq][r,m,j]; |

241 | |

242 | LD2 := LD21 + HC[LD21]; |

243 | |

244 | LD31 := 2 Sqrt[2] K6bar[k,i,j] six3[k] LUUL[n,m] ProjM[s,r] uqbar[s,n,i].CC[uq][r,m,j]; |

245 | |

246 | LD3 := LD31 + HC[LD31]; |

247 | |

248 | LD := LD1 + LD2 + LD3; |

249 | |

250 | LPot := ExpandIndices[LHS1 Phibar[ii] Phi[ii] six1bar[k]six1[k] + |

251 | LHS2 Phibar[ii] Phi[ii] six2bar[k]six2[k] + |

252 | LHS3 Phibar[ii] Phi[ii] six3bar[k]six3[k] + |

253 | LSS11 six1bar[k1]six1[k1]six1bar[k2]six1[k2] + |

254 | LSS121 six1bar[k1]six1[k1]six2bar[k2]six2[k2] + |

255 | LSS122 six1bar[k1]six1[k2]six2bar[k2]six2[k1] + |

256 | LSS131 six1bar[k1]six1[k1]six3bar[k2]six3[k2] + |

257 | LSS132 six1bar[k1]six1[k2]six3bar[k2]six3[k1] + |

258 | LSS22 six2bar[k1]six2[k1]six2bar[k2]six2[k2] + |

259 | LSS231 six2bar[k1]six2[k1]six3bar[k2]six3[k2] + |

260 | LSS232 six2bar[k1]six2[k2]six3bar[k2]six3[k1] + |

261 | LSS33 six3bar[k1]six3[k1]six3bar[k2]six3[k2], FlavorExpand->{SU2W,SU2D}]; |

262 | |

263 | LSextet := LSextetKin + LD1 + LD2 + LD3 + LPot; |

264 | |

265 | |

266 | |

267 | |

268 | |

269 |