HiggsEffectiveTheory: HiggsEffective.tex

File HiggsEffective.tex, 9.0 KB (added by claudeduhr, 8 years ago)

TeX file containing the model and the Feynman rules

Line 
1%
2%
3% This TeX-file has been automatically 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}
27This file contains the Feynman rules for the model \verb+Higgs_Effective_Couplings+.
28The Feynman rules have been generated automatically by FeynRules1.2.2.
29
30\subsection{Model information}
31
32Author(s) of the model file: \\
33\indent N. Christensen\\
34\indent C. Duhr\\
35Date: {04. 03. 2008}\\
36
37\subsection{Index description}
38
39\begin{center}\begin{tabular}{|c|c|c|}
40\hline
41Index & Index range & Symbol\\ 
42\hline
43Generation & 1 \ldots 3 & $ f $\\ 
44\hline
45Colour & 1 \ldots 3 & $ i $\\ 
46\hline
47Gluon & 1 \ldots 8 & $ a $\\ 
48\hline
49SU2W & 1 \ldots 3 & N/A
50\\ \hline
51\end{tabular}\end{center}
52\subsection{Particle content of the model}
53
54\begin{enumerate}
55\item 
56\begin{tabular}{ll}
57Class: F(1) = $ \text{vl} $, &  Fieldtype: Dirac Field.\\ 
58\multicolumn{2}{l}{Indices: Spin, Generation.}\\ 
59\multicolumn{2}{l}{Class Members: \text{ve}, vm, vt.}
60\end{tabular}
61\item 
62\begin{tabular}{ll}
63Class: F(2) = $ l $, &  Fieldtype: Dirac Field.\\ 
64\multicolumn{2}{l}{Indices: Spin, Generation.}\\ 
65\multicolumn{2}{l}{Class Members: e, m, tt.}
66\end{tabular}
67\item 
68\begin{tabular}{ll}
69Class: F(3) = $ \text{uq} $, &  Fieldtype: Dirac Field.\\ 
70\multicolumn{2}{l}{Indices: Spin, Generation, Colour.}\\ 
71\multicolumn{2}{l}{Class Members: u, c, t.}
72\end{tabular}
73\item 
74\begin{tabular}{ll}
75Class: F(4) = $ \text{dq} $, &  Fieldtype: Dirac Field.\\ 
76\multicolumn{2}{l}{Indices: Spin, Generation, Colour.}\\ 
77\multicolumn{2}{l}{Class Members: d, s, b.}
78\end{tabular}
79\item 
80\begin{tabular}{ll}
81Class: U(1) = $ \text{ghA} $, &  Fieldtype: Ghost Field.\\ 
82\multicolumn{2}{l}{Indices: N/A.}\\ 
83\end{tabular}
84\item 
85\begin{tabular}{ll}
86Class: U(2) = $ \text{ghZ} $, &  Fieldtype: Ghost Field.\\ 
87\multicolumn{2}{l}{Indices: N/A.}\\ 
88\end{tabular}
89\item 
90\begin{tabular}{ll}
91Class: U(31) = $ \text{ghWp} $, &  Fieldtype: Ghost Field.\\ 
92\multicolumn{2}{l}{Indices: N/A.}\\ 
93\end{tabular}
94\item 
95\begin{tabular}{ll}
96Class: U(32) = $ \text{ghWm} $, &  Fieldtype: Ghost Field.\\ 
97\multicolumn{2}{l}{Indices: N/A.}\\ 
98\end{tabular}
99\item 
100\begin{tabular}{ll}
101Class: U(4) = $ \text{ghG} $, &  Fieldtype: Ghost Field.\\ 
102\multicolumn{2}{l}{Indices: Gluon.}\\ 
103\end{tabular}
104\item 
105\begin{tabular}{ll}
106Class: U(5) = $ \text{ghWi} $, &  Fieldtype: Ghost Field (Unphysical).\\ 
107\multicolumn{2}{l}{Indices: SU2W.}\\ 
108\end{tabular}
109\item 
110\begin{tabular}{ll}
111Class: U(6) = $ \text{ghB} $, &  Fieldtype: Ghost Field (Unphysical).\\ 
112\multicolumn{2}{l}{Indices: N/A.}\\ 
113\end{tabular}
114\item 
115\begin{tabular}{ll}
116Class: V(1) = $ A $, &  Fieldtype: Real Vectorfield.\\ 
117\multicolumn{2}{l}{Indices: Lorentz.}\\ 
118\end{tabular}
119\item 
120\begin{tabular}{ll}
121Class: V(2) = $ Z $, &  Fieldtype: Real Vectorfield.\\ 
122\multicolumn{2}{l}{Indices: Lorentz.}\\ 
123\end{tabular}
124\item 
125\begin{tabular}{ll}
126Class: V(3) = $ W $, &  Fieldtype: Complex Vectorfield.\\ 
127\multicolumn{2}{l}{Indices: Lorentz.}\\ 
128\end{tabular}
129\item 
130\begin{tabular}{ll}
131Class: V(4) = $ G $, &  Fieldtype: Real Vectorfield.\\ 
132\multicolumn{2}{l}{Indices: Lorentz, Gluon.}\\ 
133\end{tabular}
134\item 
135\begin{tabular}{ll}
136Class: V(5) = $ \text{Wi} $, &  Fieldtype: Real Vectorfield (Unphysical).\\ 
137\multicolumn{2}{l}{Indices: Lorentz, SU2W.}\\ 
138\end{tabular}
139\item 
140\begin{tabular}{ll}
141Class: V(6) = $ B $, &  Fieldtype: Real Vectorfield (Unphysical).\\ 
142\multicolumn{2}{l}{Indices: Lorentz.}\\ 
143\end{tabular}
144\item 
145\begin{tabular}{ll}
146Class: S(1) = $ H $, &  Fieldtype: Real Scalar Field.\\ 
147\multicolumn{2}{l}{Indices: N/A.}\\ 
148\end{tabular}
149\item 
150\begin{tabular}{ll}
151Class: S(2) = $ \phi  $, &  Fieldtype: Real Scalar Field.\\ 
152\multicolumn{2}{l}{Indices: N/A.}\\ 
153\end{tabular}
154\item 
155\begin{tabular}{ll}
156Class: S(3) = $ \text{phi2} $, &  Fieldtype: Complex Scalar Field.\\ 
157\multicolumn{2}{l}{Indices: N/A.}\\ 
158\end{tabular}
159\item 
160\begin{tabular}{ll}
161Class: S(4) = $ \text{h1} $, &  Fieldtype: Real Scalar Field.\\ 
162\multicolumn{2}{l}{Indices: N/A.}\\ 
163\end{tabular}
164\end{enumerate}
165
166
167%%
168%% The Vertices
169%%
170\section{Vertices}
171
172\subsection{ 3-point vertices}
173
174\begin{itemize}
175\item
176Vertex $\{H,1\} $, $\{A,2\} $, $\{A,3\} $
177\begin{respr}
178-i A_H \big(p_2^{\mu _3} p_3^{\mu _2}-\eta _{\mu _2,\mu _3} p_2.p_3\big)\end{respr}
179\item
180Vertex $\{H,1\} $, $\{G,2\} $, $\{G,3\} $
181\begin{respr}
182-i G_H \delta _{a_2,a_3} \big(p_2^{\mu _3} p_3^{\mu _2}-\eta _{\mu _2,\mu _3} p_2.p_3\big)\end{respr}
183\item
184Vertex $\{\text{h1},1\} $, $\{G,2\} $, $\{G,3\} $
185\begin{respr}
186\frac{1}{8} i G_h \big(\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\beta $2}} p_2^{\text{$\beta $2}} p_3^{\text{$\alpha $2}}+\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\delta $2}} p_2^{\text{$\delta $2}} p_3^{\text{$\alpha $2}}-\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\beta $2}} p_2^{\text{$\alpha $2}} p_3^{\text{$\beta $2}}-\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\beta $2}} p_2^{\text{$\gamma $2}} p_3^{\text{$\beta $2}}+\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\beta $2}} p_2^{\text{$\beta $2}} p_3^{\text{$\gamma $2}}+\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\delta $2}} p_2^{\text{$\delta $2}} p_3^{\text{$\gamma $2}}-\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\delta $2}} p_2^{\text{$\alpha $2}} p_3^{\text{$\delta $2}}-\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\delta $2}} p_2^{\text{$\gamma $2}} p_3^{\text{$\delta $2}}\big) \delta _{a_2,a_3}\end{respr}
187\item
188Vertex $\{\text{h1},1\} $, $\{A,2\} $, $\{A,3\} $
189\begin{respr}
190\frac{1}{8} i A_h \big(\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\beta $2}} p_2^{\text{$\beta $2}} p_3^{\text{$\alpha $2}}+\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\delta $2}} p_2^{\text{$\delta $2}} p_3^{\text{$\alpha $2}}-\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\beta $2}} p_2^{\text{$\alpha $2}} p_3^{\text{$\beta $2}}-\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\beta $2}} p_2^{\text{$\gamma $2}} p_3^{\text{$\beta $2}}+\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\beta $2}} p_2^{\text{$\beta $2}} p_3^{\text{$\gamma $2}}+\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\delta $2}} p_2^{\text{$\delta $2}} p_3^{\text{$\gamma $2}}-\epsilon _{\mu _2,\mu _3,\text{$\alpha $2},\text{$\delta $2}} p_2^{\text{$\alpha $2}} p_3^{\text{$\delta $2}}-\epsilon _{\mu _2,\mu _3,\text{$\gamma $2},\text{$\delta $2}} p_2^{\text{$\gamma $2}} p_3^{\text{$\delta $2}}\big)\end{respr}
191\end{itemize}
192
193\subsection{ 4-point vertices}
194
195\begin{itemize}
196\item
197Vertex $\{H,1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $
198\begin{respr}
199G_H g_s f_{a_2,a_3,a_4} \big(p_2^{\mu _4} \eta _{\mu _2,\mu _3}-p_3^{\mu _4} \eta _{\mu _2,\mu _3}-p_2^{\mu _3} \eta _{\mu _2,\mu _4}+p_4^{\mu _3} \eta _{\mu _2,\mu _4}+p_3^{\mu _2} \eta _{\mu _3,\mu _4}-p_4^{\mu _2} \eta _{\mu _3,\mu _4}\big)\end{respr}
200\item
201Vertex $\{\text{h1},1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $
202\begin{respr}
203\frac{1}{4} G_h g_s f_{a_2,a_3,a_4} \big(\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\alpha $2}} p_2^{\text{$\alpha $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\beta $2}} p_2^{\text{$\beta $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\gamma $2}} p_2^{\text{$\gamma $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\delta $2}} p_2^{\text{$\delta $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\alpha $2}} p_3^{\text{$\alpha $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\beta $2}} p_3^{\text{$\beta $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\gamma $2}} p_3^{\text{$\gamma $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\delta $2}} p_3^{\text{$\delta $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\alpha $2}} p_4^{\text{$\alpha $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\beta $2}} p_4^{\text{$\beta $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\gamma $2}} p_4^{\text{$\gamma $2}}+\epsilon _{\mu _2,\mu _3,\mu _4,\text{$\delta $2}} p_4^{\text{$\delta $2}}\big)\end{respr}
204\end{itemize}
205
206\subsection{ 5-point vertices}
207
208\begin{itemize}
209\item
210Vertex $\{H,1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $, $\{G,5\} $
211\begin{respr}
212i G_H g_s^2 \big(f_{a_2,a_4,\text{a1}} f_{a_3,a_5,\text{a1}} \eta _{\mu _2,\mu _5} \eta _{\mu _3,\mu _4}+f_{a_2,a_3,\text{a1}} f_{a_4,a_5,\text{a1}} \eta _{\mu _2,\mu _5} \eta _{\mu _3,\mu _4}+f_{a_2,a_5,\text{a1}} f_{a_3,a_4,\text{a1}} \eta _{\mu _2,\mu _4} \eta _{\mu _3,\mu _5}-f_{a_2,a_3,\text{a1}} f_{a_4,a_5,\text{a1}} \eta _{\mu _2,\mu _4} \eta _{\mu _3,\mu _5}-f_{a_2,a_5,\text{a1}} f_{a_3,a_4,\text{a1}} \eta _{\mu _2,\mu _3} \eta _{\mu _4,\mu _5}-f_{a_2,a_4,\text{a1}} f_{a_3,a_5,\text{a1}} \eta _{\mu _2,\mu _3} \eta _{\mu _4,\mu _5}\big)\end{respr}
213\item
214Vertex $\{\text{h1},1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $, $\{G,5\} $
215\begin{respr}
216-i G_h g_s^2 \epsilon _{\mu _2,\mu _3,\mu _4,\mu _5} \big(f_{a_2,a_5,\text{a1}} f_{a_3,a_4,\text{a1}}-f_{a_2,a_4,\text{a1}} f_{a_3,a_5,\text{a1}}+f_{a_2,a_3,\text{a1}} f_{a_4,a_5,\text{a1}}\big)\end{respr}
217\end{itemize}
218
219
220\end{document}