StandardModelScalars: SMScalar.tex

File SMScalar.tex, 6.0 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 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}
27This file contains the Feynman rules for the model \verb+SM_Plus_Scalars+.
28The Feynman rules have been generated automatically by FeynRules0.3.
29
30\subsection{Model information}
31
32Author(s) of the model file: \\
33\indent C. Duhr\\
34Institution(s):\\
35\indent Universite catholique de Louvain (CP3).\\
36Email:\\
37\indent claude.duhr@uclouvain.be\\
38Date: {05. 03. 2008}\\
39
40\subsection{Index description}
41
42\begin{center}\begin{tabular}{|c|c|c|}
43\hline
44Index & Index range & Symbol\\ 
45\hline
46Generation & 1 \ldots 3 & N/A\\ 
47\hline
48Colour & 1 \ldots 3 & N/A\\ 
49\hline
50Gluon & 1 \ldots 8 & N/A\\ 
51\hline
52SU2W & 1 \ldots 3 & N/A\\ 
53\hline
54SGen & 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}
62Class: 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}
68Class: 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}
74Class: 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}
80Class: 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}
86Class: U(1) = $ \text{ghA} $, &  Fieldtype: Ghost Field.\\ 
87\multicolumn{2}{l}{Indices: N/A.}\\ 
88\end{tabular}
89\item 
90\begin{tabular}{ll}
91Class: U(2) = $ \text{ghZ} $, &  Fieldtype: Ghost Field.\\ 
92\multicolumn{2}{l}{Indices: N/A.}\\ 
93\end{tabular}
94\item 
95\begin{tabular}{ll}
96Class: U(31) = $ \text{ghWp} $, &  Fieldtype: Ghost Field.\\ 
97\multicolumn{2}{l}{Indices: N/A.}\\ 
98\end{tabular}
99\item 
100\begin{tabular}{ll}
101Class: U(32) = $ \text{ghWm} $, &  Fieldtype: Ghost Field.\\ 
102\multicolumn{2}{l}{Indices: N/A.}\\ 
103\end{tabular}
104\item 
105\begin{tabular}{ll}
106Class: U(4) = $ \text{ghG} $, &  Fieldtype: Ghost Field.\\ 
107\multicolumn{2}{l}{Indices: Gluon.}\\ 
108\end{tabular}
109\item 
110\begin{tabular}{ll}
111Class: U(5) = $ \text{ghWi} $, &  Fieldtype: Ghost Field (Unphysical).\\ 
112\multicolumn{2}{l}{Indices: SU2W.}\\ 
113\end{tabular}
114\item 
115\begin{tabular}{ll}
116Class: U(6) = $ \text{ghB} $, &  Fieldtype: Ghost Field (Unphysical).\\ 
117\multicolumn{2}{l}{Indices: N/A.}\\ 
118\end{tabular}
119\item 
120\begin{tabular}{ll}
121Class: V(1) = $ A $, &  Fieldtype: Real Vectorfield.\\ 
122\multicolumn{2}{l}{Indices: Lorentz.}\\ 
123\end{tabular}
124\item 
125\begin{tabular}{ll}
126Class: V(2) = $ Z $, &  Fieldtype: Real Vectorfield.\\ 
127\multicolumn{2}{l}{Indices: Lorentz.}\\ 
128\end{tabular}
129\item 
130\begin{tabular}{ll}
131Class: V(3) = $ W $, &  Fieldtype: Complex Vectorfield.\\ 
132\multicolumn{2}{l}{Indices: Lorentz.}\\ 
133\end{tabular}
134\item 
135\begin{tabular}{ll}
136Class: V(4) = $ G $, &  Fieldtype: Real Vectorfield.\\ 
137\multicolumn{2}{l}{Indices: Lorentz, Gluon.}\\ 
138\end{tabular}
139\item 
140\begin{tabular}{ll}
141Class: V(5) = $ \text{Wi} $, &  Fieldtype: Real Vectorfield (Unphysical).\\ 
142\multicolumn{2}{l}{Indices: Lorentz, SU2W.}\\ 
143\end{tabular}
144\item 
145\begin{tabular}{ll}
146Class: V(6) = $ B $, &  Fieldtype: Real Vectorfield (Unphysical).\\ 
147\multicolumn{2}{l}{Indices: Lorentz.}\\ 
148\end{tabular}
149\item 
150\begin{tabular}{ll}
151Class: S(1) = $ H $, &  Fieldtype: Real Scalar Field.\\ 
152\multicolumn{2}{l}{Indices: N/A.}\\ 
153\end{tabular}
154\item 
155\begin{tabular}{ll}
156Class: S(2) = $ \phi  $, &  Fieldtype: Real Scalar Field.\\ 
157\multicolumn{2}{l}{Indices: N/A.}\\ 
158\end{tabular}
159\item 
160\begin{tabular}{ll}
161Class: S(3) = $ \text{phi2} $, &  Fieldtype: Complex Scalar Field.\\ 
162\multicolumn{2}{l}{Indices: N/A.}\\ 
163\end{tabular}
164\item 
165\begin{tabular}{ll}
166Class: S(4) = $ \text{Sk} $, &  Fieldtype: Real Scalar Field.\\ 
167\multicolumn{2}{l}{Indices: SGen.}\\ 
168\multicolumn{2}{l}{Class Members: \text{S1}, S2, S3, S4.}
169\end{tabular}
170\end{enumerate}
171
172
173%%
174%% The Lagrangian
175%%
176
177\section{The lagrangian}
178
179
180%
181% NewSector
182%
183
184The lagrangian corresponding to \verb+NewSector+.
185
186\begin{respr}
187-\frac{1}{2} \text{MSk}^2 \text{Sk}.\text{Sk}-\frac{1}{16} H^2 \omega  \text{Sk}.\text{Sk}-\frac{1}{16} \phi ^2 \omega  \text{Sk}.\text{Sk}-\frac{1}{8} \text{phi2} \text{phi2}^{\dagger } \omega  \text{Sk}.\text{Sk}-\frac{1}{8} H v \omega  \text{Sk}.\text{Sk}-\frac{1}{16} v^2 \omega  \text{Sk}.\text{Sk}-\frac{1}{32} \text{$\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
198Vertex $\{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
207Vertex $\{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
211Vertex $\{\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
215Vertex $\{\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
219Vertex $\{\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}