# StandardModelScalars: SMScalar.tex

File SMScalar.tex, 6.0 KB (added by claudeduhr, 10 years ago) |
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1 | % |

2 | % |

3 | % This TeX-file has been automatcally generated by FeynRules. |

4 | % |

5 | % C. Duhr, 2008 |

6 | % |

7 | % |

8 | |

9 | \documentclass[11pt]{article} |

10 | |

11 | \usepackage{amsfonts} |

12 | \usepackage{amsmath} |

13 | |

14 | \newenvironment{respr}[0]{\sloppy\begin{flushleft}\hspace*{0.75cm}\(}{\)\end{flushleft}\fussy} |

15 | |

16 | \setlength{\topmargin}{-.2 cm} |

17 | \setlength{\evensidemargin}{.0 cm} |

18 | \setlength{\oddsidemargin}{.0 cm} |

19 | \setlength{\textheight}{8.5 in} |

20 | \setlength{\textwidth}{6.4 in} |

21 | |

22 | |

23 | \begin{document} |

24 | |

25 | |

26 | \section{Model description} |

27 | This file contains the Feynman rules for the model \verb+SM_Plus_Scalars+. |

28 | The Feynman rules have been generated automatically by FeynRules0.3. |

29 | |

30 | \subsection{Model information} |

31 | |

32 | Author(s) of the model file: \\ |

33 | \indent C. Duhr\\ |

34 | Institution(s):\\ |

35 | \indent Universite catholique de Louvain (CP3).\\ |

36 | Email:\\ |

37 | \indent claude.duhr@uclouvain.be\\ |

38 | Date: {05. 03. 2008}\\ |

39 | |

40 | \subsection{Index description} |

41 | |

42 | \begin{center}\begin{tabular}{|c|c|c|} |

43 | \hline |

44 | Index & Index range & Symbol\\ |

45 | \hline |

46 | Generation & 1 \ldots 3 & N/A\\ |

47 | \hline |

48 | Colour & 1 \ldots 3 & N/A\\ |

49 | \hline |

50 | Gluon & 1 \ldots 8 & N/A\\ |

51 | \hline |

52 | SU2W & 1 \ldots 3 & N/A\\ |

53 | \hline |

54 | SGen & 1 \ldots 4 & $ k $ |

55 | \\ \hline |

56 | \end{tabular}\end{center} |

57 | \subsection{Particle content of the model} |

58 | |

59 | \begin{enumerate} |

60 | \item |

61 | \begin{tabular}{ll} |

62 | Class: F(1) = $ \text{vl} $, & Fieldtype: Dirac Field.\\ |

63 | \multicolumn{2}{l}{Indices: Spin, Generation.}\\ |

64 | \multicolumn{2}{l}{Class Members: \text{ve}, vm, vt.} |

65 | \end{tabular} |

66 | \item |

67 | \begin{tabular}{ll} |

68 | Class: F(2) = $ l $, & Fieldtype: Dirac Field.\\ |

69 | \multicolumn{2}{l}{Indices: Spin, Generation.}\\ |

70 | \multicolumn{2}{l}{Class Members: e, m, tt.} |

71 | \end{tabular} |

72 | \item |

73 | \begin{tabular}{ll} |

74 | Class: F(3) = $ \text{uq} $, & Fieldtype: Dirac Field.\\ |

75 | \multicolumn{2}{l}{Indices: Spin, Generation, Colour.}\\ |

76 | \multicolumn{2}{l}{Class Members: u, c, t.} |

77 | \end{tabular} |

78 | \item |

79 | \begin{tabular}{ll} |

80 | Class: F(4) = $ \text{dq} $, & Fieldtype: Dirac Field.\\ |

81 | \multicolumn{2}{l}{Indices: Spin, Generation, Colour.}\\ |

82 | \multicolumn{2}{l}{Class Members: d, s, b.} |

83 | \end{tabular} |

84 | \item |

85 | \begin{tabular}{ll} |

86 | Class: U(1) = $ \text{ghA} $, & Fieldtype: Ghost Field.\\ |

87 | \multicolumn{2}{l}{Indices: N/A.}\\ |

88 | \end{tabular} |

89 | \item |

90 | \begin{tabular}{ll} |

91 | Class: U(2) = $ \text{ghZ} $, & Fieldtype: Ghost Field.\\ |

92 | \multicolumn{2}{l}{Indices: N/A.}\\ |

93 | \end{tabular} |

94 | \item |

95 | \begin{tabular}{ll} |

96 | Class: U(31) = $ \text{ghWp} $, & Fieldtype: Ghost Field.\\ |

97 | \multicolumn{2}{l}{Indices: N/A.}\\ |

98 | \end{tabular} |

99 | \item |

100 | \begin{tabular}{ll} |

101 | Class: U(32) = $ \text{ghWm} $, & Fieldtype: Ghost Field.\\ |

102 | \multicolumn{2}{l}{Indices: N/A.}\\ |

103 | \end{tabular} |

104 | \item |

105 | \begin{tabular}{ll} |

106 | Class: U(4) = $ \text{ghG} $, & Fieldtype: Ghost Field.\\ |

107 | \multicolumn{2}{l}{Indices: Gluon.}\\ |

108 | \end{tabular} |

109 | \item |

110 | \begin{tabular}{ll} |

111 | Class: U(5) = $ \text{ghWi} $, & Fieldtype: Ghost Field (Unphysical).\\ |

112 | \multicolumn{2}{l}{Indices: SU2W.}\\ |

113 | \end{tabular} |

114 | \item |

115 | \begin{tabular}{ll} |

116 | Class: U(6) = $ \text{ghB} $, & Fieldtype: Ghost Field (Unphysical).\\ |

117 | \multicolumn{2}{l}{Indices: N/A.}\\ |

118 | \end{tabular} |

119 | \item |

120 | \begin{tabular}{ll} |

121 | Class: V(1) = $ A $, & Fieldtype: Real Vectorfield.\\ |

122 | \multicolumn{2}{l}{Indices: Lorentz.}\\ |

123 | \end{tabular} |

124 | \item |

125 | \begin{tabular}{ll} |

126 | Class: V(2) = $ Z $, & Fieldtype: Real Vectorfield.\\ |

127 | \multicolumn{2}{l}{Indices: Lorentz.}\\ |

128 | \end{tabular} |

129 | \item |

130 | \begin{tabular}{ll} |

131 | Class: V(3) = $ W $, & Fieldtype: Complex Vectorfield.\\ |

132 | \multicolumn{2}{l}{Indices: Lorentz.}\\ |

133 | \end{tabular} |

134 | \item |

135 | \begin{tabular}{ll} |

136 | Class: V(4) = $ G $, & Fieldtype: Real Vectorfield.\\ |

137 | \multicolumn{2}{l}{Indices: Lorentz, Gluon.}\\ |

138 | \end{tabular} |

139 | \item |

140 | \begin{tabular}{ll} |

141 | Class: V(5) = $ \text{Wi} $, & Fieldtype: Real Vectorfield (Unphysical).\\ |

142 | \multicolumn{2}{l}{Indices: Lorentz, SU2W.}\\ |

143 | \end{tabular} |

144 | \item |

145 | \begin{tabular}{ll} |

146 | Class: V(6) = $ B $, & Fieldtype: Real Vectorfield (Unphysical).\\ |

147 | \multicolumn{2}{l}{Indices: Lorentz.}\\ |

148 | \end{tabular} |

149 | \item |

150 | \begin{tabular}{ll} |

151 | Class: S(1) = $ H $, & Fieldtype: Real Scalar Field.\\ |

152 | \multicolumn{2}{l}{Indices: N/A.}\\ |

153 | \end{tabular} |

154 | \item |

155 | \begin{tabular}{ll} |

156 | Class: S(2) = $ \phi $, & Fieldtype: Real Scalar Field.\\ |

157 | \multicolumn{2}{l}{Indices: N/A.}\\ |

158 | \end{tabular} |

159 | \item |

160 | \begin{tabular}{ll} |

161 | Class: S(3) = $ \text{phi2} $, & Fieldtype: Complex Scalar Field.\\ |

162 | \multicolumn{2}{l}{Indices: N/A.}\\ |

163 | \end{tabular} |

164 | \item |

165 | \begin{tabular}{ll} |

166 | Class: S(4) = $ \text{Sk} $, & Fieldtype: Real Scalar Field.\\ |

167 | \multicolumn{2}{l}{Indices: SGen.}\\ |

168 | \multicolumn{2}{l}{Class Members: \text{S1}, S2, S3, S4.} |

169 | \end{tabular} |

170 | \end{enumerate} |

171 | |

172 | |

173 | %% |

174 | %% The Lagrangian |

175 | %% |

176 | |

177 | \section{The lagrangian} |

178 | |

179 | |

180 | % |

181 | % NewSector |

182 | % |

183 | |

184 | The lagrangian corresponding to \verb+NewSector+. |

185 | |

186 | \begin{respr} |

187 | -\frac{1}{2} \text{MSk}^2 \text{Sk}.\text{Sk}-\frac{1}{16} H^2 \omega \text{Sk}.\text{Sk}-\frac{1}{16} \phi ^2 \omega \text{Sk}.\text{Sk}-\frac{1}{8} \text{phi2} \text{phi2}^{\dagger } \omega \text{Sk}.\text{Sk}-\frac{1}{8} H v \omega \text{Sk}.\text{Sk}-\frac{1}{16} v^2 \omega \text{Sk}.\text{Sk}-\frac{1}{32} \text{$\lambda $S} (\text{Sk}.\text{Sk})^2+\frac{1}{2} \partial _{\mu }(\text{Sk}).\partial _{\mu }(\text{Sk})\end{respr} |

188 | |

189 | %% |

190 | %% The Vertices |

191 | %% |

192 | \section{Vertices} |

193 | |

194 | \subsection{ 3-point vertices} |

195 | |

196 | \begin{itemize} |

197 | \item |

198 | Vertex $\{H,1\} $, $\{\text{Sk},2\} $, $\{\text{Sk},3\} $ |

199 | \begin{respr} |

200 | -\frac{1}{4} i v \omega \delta _{k_2,k_3}\end{respr} |

201 | \end{itemize} |

202 | |

203 | \subsection{ 4-point vertices} |

204 | |

205 | \begin{itemize} |

206 | \item |

207 | Vertex $\{H,1\} $, $\{H,2\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $ |

208 | \begin{respr} |

209 | -\frac{1}{4} i \omega \delta _{k_3,k_4}\end{respr} |

210 | \item |

211 | Vertex $\{\phi ,1\} $, $\{\phi ,2\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $ |

212 | \begin{respr} |

213 | -\frac{1}{4} i \omega \delta _{k_3,k_4}\end{respr} |

214 | \item |

215 | Vertex $\{\text{phi2},1\} $, $\big\{\text{phi2}^{\dagger },2\big\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $ |

216 | \begin{respr} |

217 | -\frac{1}{4} i \omega \delta _{k_3,k_4}\end{respr} |

218 | \item |

219 | Vertex $\{\text{Sk},1\} $, $\{\text{Sk},2\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $ |

220 | \begin{respr} |

221 | -\frac{1}{4} i \text{$\lambda $S} \big(\delta _{k_1,k_4} \delta _{k_2,k_3}+\delta _{k_1,k_3} \delta _{k_2,k_4}+\delta _{k_1,k_2} \delta _{k_3,k_4}\big)\end{respr} |

222 | \end{itemize} |

223 | |

224 | |

225 | \end{document} |