StandardModelScalars: SMScalar.tex

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% This TeX-file has been automatcally generated by FeynRules.
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% C. Duhr, 2008
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\begin{document}


\section{Model description}
This file contains the Feynman rules for the model \verb+SM_Plus_Scalars+.
The Feynman rules have been generated automatically by FeynRules0.3.

\subsection{Model information}

Author(s) of the model file: \\
\indent C. Duhr\\
Institution(s):\\
\indent Universite catholique de Louvain (CP3).\\
Email:\\
\indent claude.duhr@uclouvain.be\\
Date: {05. 03. 2008}\\

\subsection{Index description}

\begin{center}\begin{tabular}{|c|c|c|}
\hline
Index & Index range & Symbol\\ 
\hline
Generation & 1 \ldots 3 & N/A\\ 
\hline
Colour & 1 \ldots 3 & N/A\\ 
\hline
Gluon & 1 \ldots 8 & N/A\\ 
\hline
SU2W & 1 \ldots 3 & N/A\\ 
\hline
SGen & 1 \ldots 4 & $ k $
\\ \hline
\end{tabular}\end{center}
\subsection{Particle content of the model}

\begin{enumerate}
\item 
\begin{tabular}{ll}
Class: F(1) = $ \text{vl} $, &  Fieldtype: Dirac Field.\\ 
\multicolumn{2}{l}{Indices: Spin, Generation.}\\ 
\multicolumn{2}{l}{Class Members: \text{ve}, vm, vt.}
\end{tabular}
\item 
\begin{tabular}{ll}
Class: F(2) = $ l $, &  Fieldtype: Dirac Field.\\ 
\multicolumn{2}{l}{Indices: Spin, Generation.}\\ 
\multicolumn{2}{l}{Class Members: e, m, tt.}
\end{tabular}
\item 
\begin{tabular}{ll}
Class: F(3) = $ \text{uq} $, &  Fieldtype: Dirac Field.\\ 
\multicolumn{2}{l}{Indices: Spin, Generation, Colour.}\\ 
\multicolumn{2}{l}{Class Members: u, c, t.}
\end{tabular}
\item 
\begin{tabular}{ll}
Class: F(4) = $ \text{dq} $, &  Fieldtype: Dirac Field.\\ 
\multicolumn{2}{l}{Indices: Spin, Generation, Colour.}\\ 
\multicolumn{2}{l}{Class Members: d, s, b.}
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(1) = $ \text{ghA} $, &  Fieldtype: Ghost Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(2) = $ \text{ghZ} $, &  Fieldtype: Ghost Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(31) = $ \text{ghWp} $, &  Fieldtype: Ghost Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(32) = $ \text{ghWm} $, &  Fieldtype: Ghost Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(4) = $ \text{ghG} $, &  Fieldtype: Ghost Field.\\ 
\multicolumn{2}{l}{Indices: Gluon.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(5) = $ \text{ghWi} $, &  Fieldtype: Ghost Field (Unphysical).\\ 
\multicolumn{2}{l}{Indices: SU2W.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: U(6) = $ \text{ghB} $, &  Fieldtype: Ghost Field (Unphysical).\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: V(1) = $ A $, &  Fieldtype: Real Vectorfield.\\ 
\multicolumn{2}{l}{Indices: Lorentz.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: V(2) = $ Z $, &  Fieldtype: Real Vectorfield.\\ 
\multicolumn{2}{l}{Indices: Lorentz.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: V(3) = $ W $, &  Fieldtype: Complex Vectorfield.\\ 
\multicolumn{2}{l}{Indices: Lorentz.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: V(4) = $ G $, &  Fieldtype: Real Vectorfield.\\ 
\multicolumn{2}{l}{Indices: Lorentz, Gluon.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: V(5) = $ \text{Wi} $, &  Fieldtype: Real Vectorfield (Unphysical).\\ 
\multicolumn{2}{l}{Indices: Lorentz, SU2W.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: V(6) = $ B $, &  Fieldtype: Real Vectorfield (Unphysical).\\ 
\multicolumn{2}{l}{Indices: Lorentz.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: S(1) = $ H $, &  Fieldtype: Real Scalar Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: S(2) = $ \phi  $, &  Fieldtype: Real Scalar Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: S(3) = $ \text{phi2} $, &  Fieldtype: Complex Scalar Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\item 
\begin{tabular}{ll}
Class: S(4) = $ \text{Sk} $, &  Fieldtype: Real Scalar Field.\\ 
\multicolumn{2}{l}{Indices: SGen.}\\ 
\multicolumn{2}{l}{Class Members: \text{S1}, S2, S3, S4.}
\end{tabular}
\end{enumerate}


%%
%% The Lagrangian
%%

\section{The lagrangian}


%
% NewSector
%

The lagrangian corresponding to \verb+NewSector+.

\begin{respr}
-\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}

%%
%% The Vertices
%%
\section{Vertices}

\subsection{ 3-point vertices}

\begin{itemize}
\item
Vertex $\{H,1\} $, $\{\text{Sk},2\} $, $\{\text{Sk},3\} $
\begin{respr}
-\frac{1}{4} i v \omega  \delta _{k_2,k_3}\end{respr}
\end{itemize}

\subsection{ 4-point vertices}

\begin{itemize}
\item
Vertex $\{H,1\} $, $\{H,2\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $
\begin{respr}
-\frac{1}{4} i \omega  \delta _{k_3,k_4}\end{respr}
\item
Vertex $\{\phi ,1\} $, $\{\phi ,2\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $
\begin{respr}
-\frac{1}{4} i \omega  \delta _{k_3,k_4}\end{respr}
\item
Vertex $\{\text{phi2},1\} $, $\big\{\text{phi2}^{\dagger },2\big\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $
\begin{respr}
-\frac{1}{4} i \omega  \delta _{k_3,k_4}\end{respr}
\item
Vertex $\{\text{Sk},1\} $, $\{\text{Sk},2\} $, $\{\text{Sk},3\} $, $\{\text{Sk},4\} $
\begin{respr}
-\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}
\end{itemize}


\end{document}