HiggsEffectiveTheory: HiggsEffective.tex

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\begin{document}


\section{Model description}
This file contains the Feynman rules for the model \verb+Higgs_Effective_Couplings+.
The Feynman rules have been generated automatically by FeynRules1.2.2.

\subsection{Model information}

Author(s) of the model file: \\
\indent N. Christensen\\
\indent C. Duhr\\
Date: {04. 03. 2008}\\

\subsection{Index description}

\begin{center}\begin{tabular}{|c|c|c|}
\hline
Index & Index range & Symbol\\ 
\hline
Generation & 1 \ldots 3 & $ f $\\ 
\hline
Colour & 1 \ldots 3 & $ i $\\ 
\hline
Gluon & 1 \ldots 8 & $ a $\\ 
\hline
SU2W & 1 \ldots 3 & N/A
\\ \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{h1} $, &  Fieldtype: Real Scalar Field.\\ 
\multicolumn{2}{l}{Indices: N/A.}\\ 
\end{tabular}
\end{enumerate}


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

\subsection{ 3-point vertices}

\begin{itemize}
\item
Vertex $\{H,1\} $, $\{A,2\} $, $\{A,3\} $
\begin{respr}
-i A_H \big(p_2^{\mu _3} p_3^{\mu _2}-\eta _{\mu _2,\mu _3} p_2.p_3\big)\end{respr}
\item
Vertex $\{H,1\} $, $\{G,2\} $, $\{G,3\} $
\begin{respr}
-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}
\item
Vertex $\{\text{h1},1\} $, $\{G,2\} $, $\{G,3\} $
\begin{respr}
\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}
\item
Vertex $\{\text{h1},1\} $, $\{A,2\} $, $\{A,3\} $
\begin{respr}
\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}
\end{itemize}

\subsection{ 4-point vertices}

\begin{itemize}
\item
Vertex $\{H,1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $
\begin{respr}
G_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}
\item
Vertex $\{\text{h1},1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $
\begin{respr}
\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}
\end{itemize}

\subsection{ 5-point vertices}

\begin{itemize}
\item
Vertex $\{H,1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $, $\{G,5\} $
\begin{respr}
i 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}
\item
Vertex $\{\text{h1},1\} $, $\{G,2\} $, $\{G,3\} $, $\{G,4\} $, $\{G,5\} $
\begin{respr}
-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}
\end{itemize}


\end{document}