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% TikZ-Feynman
% Feynman Diagrams with TikZ
% Copyright (C) 2015 Joshua Ellis
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% This LaTeX file is free: you can redistribute it and/or modify it under the
% terms of the GNU General Public License as published by the Free Software
% Foundation, either version 3 of the License, or (at your option) any later
% version.
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% This is distributed in the hope that it will be useful, but WITHOUT ANY
% WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
% A PARTICULAR PURPOSE. See the GNU General Public License for more details.
%
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\usepackage{tikz} % Powerful drawing language
\usepackage{tikz-feynman}
\makeatletter
\tikzfeynmanset{compat=\tikzfeynman@version@major.\tikzfeynman@version@minor.\tikzfeynman@version@patch}
\makeatother
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%% The following setup works on Linux, and should work on OS X too.
% \usetikzlibrary{external}
% \tikzexternalize[shell escape=-shell-escape, prefix=pgf-img/]
% \immediate\write18{mkdir -p pgf-img}
% \tikzset{
% external/mode=list and make,
% external/system call={
% lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname="\image" "\texsource" || rm "\image.pdf"},
% }
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\usepackage{mathtools} % Various extra maths functions
% \usepackage{cancel} % Show cancellations with \cancel{}
% \usepackage{autonum} % Only number referenced equations (must be loaded after cleverref)
\usepackage{dsfont}
\usepackage[cmintegrals,varg]{newtxmath} % Nice math with Garamond
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\usepackage{listings} % Code listings
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\usepackage{makeidx} % Index creation
\usepackage{xr} % Cross-referencing
\usepackage[orig,UKenglish]{isodate} % Handle dates
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\providecommand{\tikzfeynmanname}{\tikzname-Feynman}
\providecommand{\pgfmanual}{\href{
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\IfFileExists{pgfmanual-en-macros}{
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}{
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This document requires the file pgfmanual-en-macros.tex (distributed
with pgf) to compile. Please place a copy of that file in the current
directory}{}}
\makeindex
\pgfkeys{
/pdflinks/search key prefixes in={/tikzfeynman/}
/pdflinks/internal link prefix=tikzfeynman,
%
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% for debugging:
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}
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Abstract
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\newif\ifarxiv
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%% Acknowledgements go in two different places depending on whether it is the
%% arXiv version or not. Have the common code here.
\def\acknowledgements{
\subsection*{Acknowledgements}
\label{subsec:acknowledgements}
The original proof-of-concept for using \tikzname{} to draw Feynman diagrams
was done by the user `\href{
http://tex.stackexchange.com/users/2552}{Jake}' on
the \TeX{} StackExchange. His original answer can be viewed at:
\url{
http://tex.stackexchange.com/a/87395/26980}.
I must also thank all the people who have used the development versions of
\tikzfeynmanname{} and offered suggestions to improve it and found bugs for me
to fix.
}
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\codeexample@orig
}
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}
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\makeatother
\title{\tikzfeynmanname}
\author{Joshua \textsc{Ellis}}
\institution{
ARC Centre of Excellence for Particle Physics at the Terascale \\
School of Physics, The University of Melbourne \textsc{vic} 3010, Australia
}
\keywords{Feynman diagram, TeX, LaTeX, TikZ, pgf, TikZ-Feynman}
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%% DOCUMENT
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\begin{document}
\pagenumbering{roman}
\begin{titlepage}
\makeatletter
\begin{center}
\vspace*{1em}
\tikz\node[scale=1.5]{%
\color{gray}\Huge\ttfamily \char`\{\textcolor{red!75!black}{\@title}\char`\}};
\vspace{0.5em}
{\huge Feynman diagrams with \tikzname}
\vspace{0.7em}
{Version \texttt{\tikzfeynman@version} \qquad \origdate\printdateTeX{\tikzfeynman@date}}
\vspace{1.3em}
{by \@author} \\[1em]
{\@institution}
\end{center}
\makeatother
\vfill
\begin{codeexample}[graphic=white]
\feynmandiagram [large, vertical=e to f] {
a -- [fermion] b -- [photon, momentum=\(k\)] c -- [fermion] d,
b -- [fermion, momentum'=\(p_{1}\)] e -- [fermion, momentum'=\(p_{2}\)] c,
e -- [gluon] f,
h -- [fermion] f -- [fermion] i;
};
\end{codeexample}
\vfill
\begin{multicols}{2}
\tableofcontents
\end{multicols}
\end{titlepage}
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%% CONTENT
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\clearpage
\pagenumbering{arabic}
\ifarxiv
\begin{abstract}
\tikzfeynmanname{} is a \LaTeX{} package allowing Feynman diagrams to be
easily generated within \LaTeX{} with minimal user instructions and without
the need of external programs. It builds upon the \tikzname{} package and
leverages the graph placement algorithms from \tikzname{} in order to automate
the placement of many vertices. \tikzfeynmanname{} still allows fine-tuned
placement of vertices so that even complex diagrams can be generated with
ease.
\end{abstract}
\fi
\section{Introduction}
\label{sec:introduction}
\tikzfeynmanname{} provides a new way to draw Feynman diagrams in \LaTeX{} that
does not rely on external programs and uses a clear extensible syntax.
\ifarxiv\else
If you use \tikzfeynmanname{} in an academic setting, please cite:
\begin{quote}
\fullcite{tikz-feynman}
\end{quote}
\fi
Feynman diagrams provide a description of interactions of subatomic particles in
a form that is clearer and more succinct than the corresponding mathematical
description. They were introduced by \citeauthor{PhysRev.76.769} and first
appear in his paper \citetitle{PhysRev.76.769} \cite{PhysRev.76.769}. Since
then, \LaTeX{} has become widely used to type-set scientific papers and
currently, two leading methods of drawing Feynman diagrams in \LaTeX{} are
\href{
https://www.ctan.org/pkg/feynmf}{|feynMF|/|feynMP|} \cite{feynmf} and
\href{
https://www.ctan.org/pkg/axodraw}{|AxoDraw|} \cite{axodraw}, with the
latter also featuring a \textsc{gui} front-end called
\href{
http://jaxodraw.sourceforge.net}{|JaxoDraw|} \cite{jaxodrawV1,jaxodrawV2}.
Both |feynMF|/|feynMP| and |AxoDraw| have quite complicated syntax. As an
example, the code to generate an \(\ell\ell \to \ell\ell\) scattering Feynman
diagram in each package is:
\begin{center}
\begin{tabular}{p{0.3\linewidth} p{0.27\linewidth} p{0.34\linewidth}}
|AxoDraw| & |feynMF|/|feynMP| & \tikzfeynmanname{} \\[-2em]
\begin{codeexample}[execute code=false]
\begin{picture}
\ArrowLine(190,270)(160,300)
\ArrowLine(160,240)(190,270)
\ArrowLine(270,300)(240,270)
\ArrowLine(240,270)(270,240)
\Photon(190,270)(240,270){4}{4.5}
\Vertex(190,270){1.5}
\Vertex(240,270){1.5}
\end{picture}
\end{codeexample}
&
\begin{codeexample}[execute code=false]
\begin{fmfchar*}(40,30)
\fmfpen{thick}
\fmfleft{i1,i2}
\fmfright{o1,o2}
\fmf{fermion}{i1,v1,o1}
\fmf{fermion}{i2,v2,o2}
\fmf{photon,label=$q$}{v1,v2}
\fmfdot{v1,v2}
\end{fmfchar*}
\end{codeexample}
&
\begin{codeexample}[execute code=false]
\feynmandiagram [horizontal=a to b] {
i1 -- [fermion] a -- [fermion] i2,
a -- [photon] b,
f1 -- [fermion] b -- [fermion] f2,
};
\end{codeexample} \\[-2em]
\end{tabular}
\end{center}
The learning curves for both |AxoDraw| and |feynMF|/|feynMP| are quite steep,
and although this is partly resolved by using |JaxoDraw|, this requires an
external program. In addition, the creation of Feynman diagrams in
|feynMF|/|feynMP| requires further processing outside of \LaTeX{}.
\tikzfeynmanname{} on the other hand uses a clear syntax and delegates the
positioning of vertices to algorithms originally developed by
\citeauthor{hu2005} \cite{hu2005}, and \citeauthor{eades1991} \cite{eades1991},
both of which were implemented into \tikzname{} by \citeauthor{pohlmann2011}
\cite{pohlmann2011}. Since \tikzfeynmanname{} is built on \tikzname{}, users
can harness the power and extensibilty of \tikzname{} \cite{tikz} making it easy
to extend to accommodate individual needs. In order to produce more complicated
diagrams, relative or absolute positioning of vertices can also be used in
\tikzfeynmanname{} so that any diagram can be generated with relative ease.
\tikzfeynmanname{} is made available through the
\href{
https://ctan.org/pkg/tikz-feynman}{Comprehensive \TeX{} Archive Network
(\textsc{ctan})}\footnote{\url{
https://ctan.org/pkg/tikz-feynman}} and can
also be downloaded from the
\href{
http://www.jpellis.me/projects/tikz-feynman}{project
page}\footnote{\url{
http://www.jpellis.me/projects/tikz-feynman}}. The
project is open source and contributions are welcome. The management of bugs
and feature requests is done at
\href{
https://github.com/JP-Ellis/tikz-feynman}{Github}\footnote{\url{
https://github.com/JP-Ellis/tikz-feynman}}.
\tikzfeynmanname{}'s versioning will approximately follow
\href{
http://semverg.org}{semantic versioning}. This means that changes in the
third number (|1.0.0| to |1.0.1|) will consist of bug fixes and very minor
changes but they should not change the output otherwise\footnote{That is, with
the exception of the bug that they are fixing.}. Changes in the second number
(|1.0.0| to |1.1.0|) will consist of new features but everything should be
backwards compatible. Finally, changes in the first number (|1.0.0| to |2.0.0|)
indicates a major change in the package and code written for |1.0.0| is not
guaranteed to work on |2.0.0|. The intended version of this package to use
should be indicated when the package is loaded with
|\usepackage[compat=x.y.z]{tikz-feynman}| so the user may be informed of any
discrepancyx. If needed, earlier versions may be downloaded from the
\href{
http://www.jpellis.me/projects/tikz-feynman}{project
page}\footnote{\url{
http://www.jpellis.me/projects/tikz-feynman}}.
\subsection*{Licence}
\label{subsec:licence}
This \emph{documentation} may be redistributed and/or modified under the terms
of the \textsc{gnu} General Public License as published by the Free Software
Foundation, either version 3 of the License, or (at your option) any later
version.
The \emph{code of this package} may be distributed and/or modified under the
conditions of the \LaTeX{} Project Public License, either version 1.3 of this
license or (at your option) any later version.
This work has the LPPL maintenance status `maintained'.
The Current Maintainer of this work is Joshua Ellis.
This package is distributed in the hope that it will be useful, but
\textsc{without any warranty}; without even the implied warranty of
\textsc{merchantability} or \textsc{fitness for a particular purpose}.
\ifarxiv\else
\acknowledgements
\fi
\clearpage
\section{Tutorial}
\label{sec:tutorial}
\subsection{Loading the Package}
\label{sibsec:loading_the_package}
After installing the package, the \tikzfeynmanname{} package can be loaded with
|\usepackage{tikz-feynman}| in the preamble. It is recommend that you also
specify the version of \tikzfeynmanname{} to use with the optional package
argument |compat|: |\usepackage[compat=1.1.0]{tikz-feynman}|. This ensures that
any new versions of \tikzfeynmanname{} do not produce any undesirable changes
without warning.
\subsection{A First Diagram}
\label{subsec:a_first_diagram}
Feynman diagrams can be declared with the |\feynmandiagram| command. It is
analogous to the |\tikz| command from \tikzname~and requires a final semi-colon
(|;|) to finish the environment. For example, a simple \(s\)-channel diagram
is:
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
i1 -- [fermion] a -- [fermion] i2,
a -- [photon] b,
f1 -- [fermion] b -- [fermion] f2,
};
\end{codeexample}
Let's go through this example line by line:
\begin{description}
\item[Line 1] |\feynmandiagram| introduces the Feynman diagram and allows for
optional arguments to be given in the brackets \texttt{[\meta{options}]}. In
this instance, |horizontal=a to b| orients the algorithm outputs such that the
line through vertices |a| and |b| is horizontal.
\item[Line 2] The left fermion line is drawn by declaring three vertices (|i1|,
|a| and |i2|) and connecting them with edges |--|. Just like the
|\feynmandiagram| command above, each edge also take optional arguments
specified in brackets \texttt{[\meta{options}]}. In this instance, we want
these edges to have arrows to indicate that they are fermion lines, so we add
the |fermion| style to them.
As you will see later on, optional arguments can also be given to the vertices
in exactly the same way.
\item[Line 3] This edge connects vertices |a| and |b| with an edge styled as a
photon. Since there is already a vertex labelled |a|, the algorithm will
connect it to a new vertex labeled |b|.
\item[Line 4] This line is analogous to line 2 and introduces two new vertices,
|f1| and |f2|. It re-uses the previously labelled |b| vertex.
\item[Line 5] Finish the declaration of the Feynman diagram. The final
semi-colon (|;|) is important.
\end{description}
The name given to each vertex in the graph does not matter. So in this example,
|i1|, |i2| denote the initial particles; |f1|, |f2| denotes the final particles;
and |a|, |b| are the end points of the propagator. The only important aspect is
that what we called |a| in line 2 is also |a| in line 3 so that the underlying
algorithm treats them as the same vertex.
The order in which vertices are declared does not matter as the default
algorithm re-arranges everything\footnote{It is possible for the algorithm to
get a litte confused in some circumstances, but these cases should be rather
rare. For some algorithms (such as the |layered~layout|), the order in which
vertices are introduces \emph{does} matter. This is documented in
\cref{subsubsec:diagram_keys}.}. For example, one might prefer to draw the
fermion lines all at once, as with the following example (note also that the way
we named vertices is completely different):
\begin{codeexample}[]
\feynmandiagram [horizontal=f2 to f3] {
f1 -- [fermion] f2 -- [fermion] f3 -- [fermion] f4,
f2 -- [photon] p1,
f3 -- [photon] p2,
};
\end{codeexample}
As a final remark, the calculation of where vertices should be placed is usually
done through an algorithm written in Lua. As a result, \LuaTeX{} is required in
order to make use of these algorithms. If \LuaTeX{} is not used,
\tikzfeynmanname{} will default to a more rudimentary algorithm and will warn
the user instead.
\subsection{Adding Styles}
\label{subsec:adding_styles}
So far, the examples have only used the |photon| and |fermion| styles. The
\tikzfeynmanname{} package comes with quite a few extra styles for edges and
vertices which are all documented over in \cref{sec:documentation}. As an
example, it is possible to add momentum arrows with |momentum=|\meta{text}, and
in the case of end vertices, the particle can be labelled with
|particle=|\meta{text}. As an example, we take the generic \(s\)-channel
diagram from \cref{subsec:a_first_diagram} and make it a \(e^{+}e^{-} \to
\mu^{+}\mu^{-}\) diagram:
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
i1 [particle=\(e^{-}\)] -- [fermion] a -- [fermion] i2 [particle=\(e^{+}\)],
a -- [photon, edge label=\(\gamma\), momentum'=\(k\)] b,
f1 [particle=\(\mu^{+}\)] -- [fermion] b -- [fermion] f2 [particle=\(\mu^{-}\)],
};
\end{codeexample}
In addition to the style keys documented below, style keys from \tikzname{} can
be used as well:
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
i1 [particle=\(e^{-}\)] -- [fermion, very thick] a -- [fermion, opacity=0.2] i2 [particle=\(e^{+}\)],
a -- [red, photon, edge label=\(\gamma\), momentum'={[arrow style=red]\(k\)}] b,
f1 [particle=\(\mu^{+}\)] -- [fermion, opacity=0.2] b -- [fermion, very thick] f2 [particle=\(\mu^{-}\)],
};
\end{codeexample}
For a list of all the various styles that \tikzname{} provides, have a look at
the \pgfmanual; it is extremely thorough and provides many usage examples.
\tikzfeynmanname{} also supports combining styles together which can be useful
in certain new models such as supersymmetry:
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
i1 [particle=\(\tilde W\)] -- [plain, boson] a -- [anti fermion] i2 [particle=\(q\)],
a -- [charged scalar, edge label=\(\tilde q\)] b,
f1 [particle=\(\tilde g\)] -- [plain, gluon] b -- [fermion] [particle=\(q\)],
};
\end{codeexample}
\subsection{When the Algorithm Isn't Enough}
\label{subsec:when_the_algorithm_isnt_enough}
By default, the |\feynmandiagram| and |\diagram| commands use the
|spring layout| algorithm to place all the edges\footnote{For more details on
this layout and any other graph layouts available, see
\cref{subsubsec:diagram_keys}}. The |spring layout| algorithm attempts to
`spread out' the diagram as much as possible which---for most simpler
diagrams---gives a satisfactory result; however in some cases, this does not
produce the best diagram and this section will look at alternatives. There are
three main alternatives:
\begin{description}
\item[Add invisible edges] While still using the default algorithm, it is
possible to force certain vertices to be closer together by adding extra edges
and making them invisible through |draw=none|. The algorithm will treat these
extra edges in the same way, but they are simply not drawn at the end;
\item[Use a different algorithm] In some circumstances, other algorithms may be
better suited. Some of the other graph layout algorithms are listed in
\cref{subsubsec:diagram_keys}, and an exhaustive list of all algorithms and
their parameters is given in the \pgfmanual;
\item[Manual placement] As a last resort, very complicated or unusual diagrams
will require each vertex to be manually placed.
\end{description}
\subsubsection{Invisible Edges}
\label{subsubsec:invisible_edges}
The underlying algorithm treats all edges in exactly the same way when
calculating where to place all the vertices, and the actual drawing of the
diagram (after the placements have been calculated) is done separately.
Consequently, it is possible to add edges to the algorithm, but prevent them
from being drawn by adding |draw=none| to the edge style.
This is particularly useful if you want to ensure that the initial or final
states remain closer together than they would have otherwise as illustrated in
the following example (note that |opacity=0.2| is used instead of |draw=none| to
illustrate where exactly the edge is located).
\begin{codeexample}[]
% No invisible to keep the two photons together
\feynmandiagram [small, horizontal=a to t1] {
a [particle=\(\pi^{0}\)] -- [scalar] t1 -- t2 -- t3 -- t1,
t2 -- [photon] p1 [particle=\(\gamma\)],
t3 -- [photon] p2 [particle=\(\gamma\)],
};
\end{codeexample}
\begin{codeexample}[]
% Invisible edge ensures photons are parallel
\feynmandiagram [small, horizontal=a to t1] {
a [particle=\(\pi^{0}\)] -- [scalar] t1 -- t2 -- t3 -- t1,
t2 -- [photon] p1 [particle=\(\gamma\)],
t3 -- [photon] p2 [particle=\(\gamma\)],
p1 -- [opacity=0.2] p2,
};
\end{codeexample}
\subsubsection{Alternative Algorithms}
\label{subsubsec:alternative_algorithms}
The graph drawing library from \tikzname{} has several different algorithms to
position the vertices\footnote{See \cref{subsubsec:diagram_keys} for some
alternative algorithms.} By default, |\diagram| and |\feynmandiagram| use the
|spring layout| algorithm to place the vertices. The |spring layout| attempts
to spread everything out as much as possible which, in most cases, gives a nice
diagram; however, there are certain cases where this does not work. A good
example where the |spring layout| doesn't work are decays where we have the
decaying particle on the left and all the daughter particles on the right.
\begin{codeexample}[]
% Using the default spring layout
\feynmandiagram [horizontal=a to b] {
a [particle=\(\mu^{-}\)] -- [fermion] b -- [fermion] f1 [particle=\(\nu_{\mu}\)],
b -- [boson, edge label=\(W^{-}\)] c,
f2 [particle=\(\overline \nu_{e}\)] -- [fermion] c -- [fermion] f3 [particle=\(e^{-}\)],
};
\end{codeexample}
\begin{codeexample}[]
% Using the layered layout
\feynmandiagram [layered layout, horizontal=a to b] {
a [particle=\(\mu^{-}\)] -- [fermion] b -- [fermion] f1 [particle=\(\nu_{\mu}\)],
b -- [boson, edge label'=\(W^{-}\)] c,
c -- [anti fermion] f2 [particle=\(\overline \nu_{e}\)],
c -- [fermion] f3 [particle=\(e^{-}\)],
};
\end{codeexample}
You may notice that in addition to adding the |layered layout| style to
|\feynmandiagram|, we also changed the order in which we specify the vertices.
This is because the |layered layout| algorithm does pay attention to the order
in which vertices are declared (unlike the default |spring layout|); as a
result, |c--f2, c--f3| has a different meaning to |f2--c--f3|. In the former
case, |f2| and |f3| are both on the layer below |c| as desired; whilst the
latter case places |f2| on the layer above |c| (that, the same layer as where
the \(W^{-}\) originates).
\subsubsection{Manual Placement}
\label{subsubsec:manual_placement}
In more complicated diagrams, it is quite likely that none of the algorithms
work, no matter how many invisible edges are added. In such cases, the vertices
have to be placed manually. \tikzfeynmanname{} allows for vertices to be
manually placed by using the |\vertex| command.
The |\vertex| command is available only within the |feynman| environment (which
itself is only available inside a |tikzpicture|). The |feynman| environment
loads all the relevant styles from \tikzfeynmanname{} and declares additional
\tikzfeynmanname-specific commands such as |\vertex| and |\diagram|. This is
inspired from PGFPlots and its use of the |axis| environment.
The |\vertex| command is very much analogous to the |\node| command from
\tikzname{}, with the notable exception that the vertex contents are optional;
that is, you need not have |{|\meta{text}|}| at the end. In the case where |{}|
is specified, the vertex automatically is given the |particle| style, and
otherwise it is a usual (zero-sized) vertex.
To specify where the vertices go, it is possible to give explicit coordinates
though it is probably easiest to use the |positioning| library from \tikzname{}
which allows vertices to be placed relative to existing vertices\footnote{The
\pgfmanual{} has some extensive documentation explaining how to use the
|positioning| library.}. By using relative placements, it is possible to
easily tweak one part of the graph and everything will adjust accordingly---the
alternative being to manually adjust the coordinates of every affected vertex.
Finally, once all the vertices have been specified, the |\diagram*| command is
used to specify all the edges. This works in much the same way as |\diagram|
(and also |\feynmandiagram|), except that it uses an very basic algorithm
to place new nodes and allows existing (named) nodes to be included. In order
to refer to an existing node, the node must be given in parentheses.
This whole process of specifying the nodes and then drawing the edges between
them is shown below for the muon decay:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{feynman}
\vertex (a) {\(\mu^{-}\)};
\vertex [right=of a] (b);
\vertex [above right=of b] (f1) {\(\nu_{\mu}\)};
\vertex [below right=of b] (c);
\vertex [above right=of c] (f2) {\(\overline \nu_{e}\)};
\vertex [below right=of c] (f3) {\(e^{-}\)};
\diagram* {
(a) -- [fermion] (b) -- [fermion] (f1),
(b) -- [boson, edge label'=\(W^{-}\)] (c),
(c) -- [anti fermion] (f2),
(c) -- [fermion] (f3),
};
\end{feynman}
\end{tikzpicture}
\end{codeexample}
\clearpage
\section{Documentation}
\label{sec:documentation}
\subsection{Commands \emph{\&} Environments}
\label{subsec:commands}
\begin{command}{\tikzfeynmanset\marg{options}}
This command will process \meta{options} using |\pgfkeys| with the default
path set to |/tikzfeynman|. Typically, \meta{options} will be a
comma-separated list of the form \meta{key}|=|\meta{value}, though the full
power of the mechanism behind |\pgfkeys| can be used (see the \pgfmanual{} for
a complete description).
Typically, this is used in the preamble of the document to add or change
certain keys for the whole document.
\end{command}
\begin{command}{\feynmandiagram\opt{\oarg{TikZ options}\oarg{diagram options}}\marg{diagram instructions}}
This commands creates a |{tikzpicture}| and |{feynman}| environment, and
places a |\diagram| inside with the provided \meta{diagram instruction}.
Please refer to the documentation for |\diagram| for the \meta{diagram
instruction} syntax.
The optional arguments specified in \meta{tikz options} are passed on to the
|{tikzpicture}|, and the \meta{diagram options} are passed on to |\diagram|.
If only one optional argument is given, then the optional arguments are given
to both. A single optional argument will usually suffice as most keys are
recognized by both commands; however, in the event that a key is not
recognized, both options are provided.
\end{command}
\begin{environment}{{feynman}\opt{\oarg{options}}}
The |{feynman}| environment is where all the drawing of Feynman diagrams takes
place. It makes all the \tikzfeynmanname{} styles available and defines
commands such as |\vertex| and |\diagram| which are otherwise unavailable
outside of this environment. The |{feynman}| environment is only accessible
within the |{tikzpicture}| environment.
Options which are passed in \meta{options} apply for the whole environment in
the same way that the |{scope}| environment work in \tikzname.
\begin{command}{\vertex\opt{\oarg{options}} (\meta{name}) \opt{at (\meta{coordinate})} \opt{\marg{contents}};}
Defines a new vertex with the provided \meta{name}. If \meta{contents} is
not provided, the resulting vertex will have zero size. On the other hand,
if \meta{contents} is provided, the |particle=|\meta{contents} style is
applied. Additional styles can be applied to the vertex through
\meta{options}.
The final semicolon (|;|) is vital for this command since without it, the
\LaTeX{} engine will not know when the |\vertex| command ends.
Additionally, this command \emph{cannot} be chained like one can do with the
inbuilt \tikzname{} commands.
This command is only available with the |{feynman}| environment.
\end{command}
\begin{command}{\diagram\opt{\oarg{options}}\marg{diagram instructions}}
Begins a new diagram using the |spring layout|. Keys passed through
\meta{options} can include general \tikzname{} keys, graph-specific keys and
any applicable \tikzfeynmanname{} keys too. Other algorithms (such as |tree
layout|) can be passed through \meta{options} and that will override the
|spring layout|.
The syntax for the \meta{diagram instructions} is thoroughly described in
the \pgfmanual, but in the context of this package, it will usually suffice
to know the following:
\begin{itemize}
\item Vertices within the graph are specified with no delimiters (i.e.~no
parenthesis, no brackets) and only require spaces around either side. In
order to refer to a vertex defined outside of the |\diagram| command, its
name must be given in parenthesis: |(|\meta{name}|)|. Note that in order
to refer to external vertices, one must use |\diagram*| as most algorithms
(including the default |spring layout|) are incompatible with vertices
defined outside of the algorithm.
When a vertex name is used multiple times, the underlying algorithm will
consider them to be the same vertex and introduces additional edges.
Options can be given to the vertex in brackets after the name: \meta{name}
|[|\meta{options}|]|. For vertices defined outside of the |\diagram|
command, these options should be specified when the vertex is first
declared.
\item The edges between each pair of vertices is specified with |--|, and
these can be chained together: \verb|a -- b -- c|. In order to pass a
style to the edge, it is specified in brackets after the dashed:
|-- | \oarg{options}. For example, to make on edge red, one would use
|-- [red]|.
\item A comma (|,|)---or equivalently a semicolon (|;|)---specifies the end
of a sequence of edges and vertices and allows for another sequence to be
started. So \verb|a -- b, c -- d| will create two disconnected edges.
\item Subgroups (aking to scopes in \tikzname) are specified with braces:
|{|\oarg{options}\meta{diagram instructions}|}|. This can be quite
useful when a lot of edges or nodes share a common style. For example,
one could use |{[edges={fermion}]|\verb| a -- b -- c, x -- y -- z}| and
every edge will have the |fermion| style applied automatically.
Another useful feature of subgroups is that an edge to a group will create
an edge to each vertex in that subgroup as shown below. The example also
shows how they can be nested which in some cases (such as with a
|layered layout|) can be extremely useful.
\begin{codeexample}[]
\feynmandiagram [nodes=circle, horizontal=a1 to b3] {
a1 -- {b1, b2, b3 -- {c1, c2 -- d1}}
};
\end{codeexample}
\end{itemize}
\end{command}
\begin{command}{\diagram*\opt{\oarg{options}}\marg{diagram instructions}}
Same as |\diagram|, but instead of using the |spring layout| algorithm to
place the vertices, this uses the most basic algorithm. This basic
algorithm in most cases will not produce a satisfactory diagram, but is
intended to be used with vertices are declared and positioned outside of the
|\diagram*| command. Essentially, |\diagram*| should be used only to
connect existing vertices.
\end{command}
\end{environment}
\subsection{Keys \emph{\&} Styles}
\label{subsec:Keys}
The various styles and options that allow the Feynman diagrams to be customized
are defined in what \tikzname{} calls \emph{keys}. The documentation includes
all keys which are defined within \tikzfeynmanname{} which all begin with the
prefix |/tikzfeynman|. In addition, a few of the keys from \tikzname{} itself
which are particularly useful to \tikzfeynmanname{} are documented and these are
prefixed with |/tikz| or |/graph drawing|. Please refer to the \pgfmanual{} for
a more in thorough documentation of the \tikzname{} keys.
\tikzfeynmanname{} provides many |every |\meta{key} which allow every instance
of \meta{key} to be modified. For example, to make every diagram red except for
small diagrams which should be blue, then one would add to the preamble:
\begin{codeexample}[execute code=false]
\tikzfeynmanset{
every diagram={red},
every small={blue},
}
\end{codeexample}
If you are completely unhappy with a particular inbuilt style, you can define
your own style with with \meta{key}|/.style={...}| as shown in the
following example:
\begin{codeexample}[execute code=false]
\tikzfeynmanset{
myblob/.style={
shape=circle,
draw=blue,
fill=red,
}
}
\end{codeexample}
All the keys defined here are made available inside the |{feynman}| environment
and inside |\feynmandiagram|; but if you wish to access them outside of this
(say, in a regular |{tikzpicture}| environment), you will need to specify the
full path with the leading |/tikzfeynman|.
\subsubsection{Feynman Keys}
\label{subsubsec:feynman_keys}
\begin{keylist}{%
/tikzfeynman/execute at begin feynman=\marg{\TeX{} code},
/tikzfeynman/execute at end feynman=\marg{\TeX{} code}}
Allows for custom code to be executed at the start or end of each |{feynman}|
environment.
\end{keylist}
\begin{key}{/tikzfeynman/every feynman=\meta{styles}}
Set of styles which are applied to every |{feynman}| environments (and
consequently, every apply inside all |\feynmandiagram| too). The style also
applies to regular \tikzname{} commands used inside the |{feynman}|
environment.
\begin{codeexample}[]
\tikzfeynmanset{every feynman={red}}
\begin{tikzpicture}
\node at (0, 0.5) {This is not red};
\begin{feynman}
\node at (0, -0.5) {This is red};
\end{feynman}
\end{tikzpicture}
\end{codeexample}
\end{key}
\begin{stylekey}{/tikzfeynman/inline=\meta{node}}
A style used to display a Feynman diagram inline (typically in an equation),
and aligning such that its vertical placement is at the node specified. The
node specification must enclosed in parentheses. For nodes which contain text
(such as when the |particle| style is applied), it is possible to use the
baseline of the text inside the node to line up with the baseline of the
equation by using |(|\meta{node}|.base)| as demonstrated in the following
example. Note that this key applies additional styles to make the diagram fit
in an equation more nicely; if you do not wish to have these additional
styles, use the |baseline| key.
\begin{equation}
\feynmandiagram [inline=(d.base), horizontal=d to b] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d [particle=\(\gamma\)],
};
= i g_{e} \gamma^{\mu}
\end{equation}
\begin{codeexample}[execute code=false]
\begin{equation}
\feynmandiagram [inline=(d.base), horizontal=d to b] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d [particle=\(\gamma\)],
};
= i g_{e} \gamma^{\mu}
\end{equation}
\end{codeexample}
\end{stylekey}
\begin{key}{/tikz/baseline=\meta{node}}
Changes the vertical alignment of the Feynman diagram such that it diagram's
baseline is at the node specified. This works in the same was as
|inline=|\meta{node}, but it does not apply any additional styles (notice how
the following example is larger than the one above).
\begin{equation}
\feynmandiagram [baseline=(d.base), horizontal=d to b] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d [particle=\(\gamma\)],
};
= i g_{e} \gamma^{\mu}
\end{equation}
\begin{codeexample}[execute code=false]
\begin{equation}
\feynmandiagram [baseline=(d.base), horizontal=d to b] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d [particle=\(\gamma\)],
};
= i g_{e} \gamma^{\mu}
\end{equation}
\end{codeexample}
\end{key}
\begin{keylist}{%
/graph drawing/horizontal=\meta{node} to \meta{node},
/graph drawing/horizontal'=\meta{node} to \meta{node},
/graph drawing/vertical=\meta{node} to \meta{node},
/graph drawing/vertical'=\meta{node} to \meta{node}}
The underlying algorithm will arrange all the nodes relative to each other,
but beyond that it has no idea how the overall graph should be oriented.
By using one of the above keys, the final output of the algorithm is oriented
and/or mirrored such that the two nodes specified are on the same horizontal
(or vertical) line. The two nodes need not actually be connected by an edge
for this to work.
The two \meta{node} specifications should \emph{not} be enclosed in
parentheses, unlike the |inline| and |baseline| keys.
The |horizontal'| and |vertical'| keys work in the same was as |horizontal|
and |vertical|, but with a flip.
\begin{codeexample}[]
\feynmandiagram [inline=(b), horizontal=a to b, red] {
a -- b -- {c [particle=\(c\)], d [particle=\(d\)]}
};
\feynmandiagram [inline=(b), horizontal'=a to b, blue] {
a -- b -- {c [particle=\(c\)], d [particle=\(d\)]}
};
\feynmandiagram [inline=(b), vertical=a to b, green!40!black] {
a -- b -- {c [particle=\(c\)], d [particle=\(d\)]}
};
\feynmandiagram [inline=(b), vertical=b to a, black] {
a -- b -- {c [particle=\(c\)], d [particle=\(d\)]}
};
\end{codeexample}
\end{keylist}
\subsubsection{Diagram Keys}
\label{subsubsec:diagram_keys}
\begin{key}{/tikzfeynman/every diagram=\meta{styles}}
Set of styles which are applied to every diagram; that is, to everything
inside the |\feynmandiagram|, |\diagram| and |\diagram*| commands but not the
general |{feynman}| environment (see \cref{subsubsec:feynman_keys} for that).
\begin{codeexample}[]
\tikzfeynmanset{every diagram={red}}
\feynmandiagram [small, horizontal=d to b] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d,
};
\end{codeexample}
\end{key}
\begin{keylist}{%
/tikzfeynman/small,
/tikzfeynman/medium,
/tikzfeynman/large}
Changes the default separation between the vertices and changes the size of
arrows, blobs, and other shapes to fit different context. The |small| size is
best used with when the diagram is quite simple and doesn't have too many
annotations (such as momentum arrows and particle labels). The |medium| size
is the default and is usually large enough that even diagrams with many labels
and momentum arrows do not become too cluttered. Finally the |large| key is
best for large illustrations as used on the title page of this document.
\begin{codeexample}[]
\feynmandiagram [baseline=(b), small, horizontal=d to b, red] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d,
};
\feynmandiagram [baseline=(b), medium, horizontal=d to b, green!40!black] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d,
};
\feynmandiagram [baseline=(b), large, horizontal=d to b, blue] {
a -- [fermion] b -- [fermion] c,
b -- [boson] d,
};
\end{codeexample}
\end{keylist}
There are several algorithms which are available to place the vertices which are
all provided within the |graph drawing| library from \tikzname. Below are
listed a few of these layouts which are more relevant for drawing Feynman
diagrams. For a more complete description of how these algorithm work, please
refer to the \pgfmanual{}. Please note that most graph drawing algorithms are
implemented in Lua and thus require \LuaTeX{} in order to work. If \LuaTeX{} is
not used, \tikzfeynmanname{} will default to a more rudimentary algorithm and
will warn the user instead.
\begin{key}{/graph drawing/spring layout=\opt{\meta{string}}}
Uses Hu's spring layout \cite{hu2005} as implemented by Pohlmann
\cite{pohlmann2011}. This models each edge as springs and attempts to spread
everything out as much as possible. This is the default layout.
\begin{codeexample}[]
\feynmandiagram [nodes=circle, small, horizontal=c to d] {
{a, b} -- c -- d -- {e, f},
};
\end{codeexample}
\end{key}
\begin{key}{/graph drawing/spring electrical layout=\opt{\meta{string}}}
Uses Hu's spring electrical layout \cite{hu2005} as implemented by Pohlmann
\cite{pohlmann2011}. This models each edge as springs and gives each vertex a
charge. This algorithm allows for the charge of a particular vertex to be
adjusted using the |electric charge| key (the default is |1|).
\begin{codeexample}[]
\feynmandiagram [nodes=circle,
small, horizontal=c to d,
spring electrical layout
] {
{a, b [electric charge=2]} -- c -- d -- {e, f [electric charge=0.1]},
};
\end{codeexample}
\end{key}
\begin{key}{/graph drawing/layered layout=\opt{\meta{string}}}
Uses the Sugiyama layout algorithm \cite{eades1991} as implemented by Pohlmann
\cite{pohlmann2011} in order to place the node.
When an edge is specified, the first vertex is always located on the layer
above the second vertex. This creates a hierarchy of vertices which is
particularly useful for decays.
Two vertices can be forced to be on the same layer with the
|/graph drawing/same layer| key.
\begin{codeexample}[]
\feynmandiagram [nodes=circle, small, horizontal=a to b, layered layout] {
a -- b -- {c, d -- {e, f}},
};
\end{codeexample}
\begin{codeexample}[]
\feynmandiagram [nodes=circle, small, horizontal=a to b, layered layout] {
a -- b -- {c -- {c1, c2}, d -- {d1, d2}},
{[same layer] c1, d},
};
\end{codeexample}
\end{key}
\begin{key}{/graph drawing/tree layout=\opt{\meta{string}}}
Uses the Reingold--Tilform algorithm in order to place the node. This works
in a similar way to the layered layout, but has quite a lot of additional
options to handle missing children in the tree. Please refer to the
\pgfmanual{} for a thorough description of these additional features.
When an edge is specified, the first vertex is always located on the layer
above the second vertex. This creates a hierarchy of vertices which is
particularly useful for decays.
\begin{codeexample}[]
\feynmandiagram [nodes=circle, small, horizontal=a to b, tree layout] {
a -- b -- {c, d -- {e, f}},
};
\end{codeexample}
\begin{codeexample}[]
\feynmandiagram [nodes=circle, small, horizontal=a to b, tree layout] {
a -- b -- {c -- {c1, c2}, d -- {d1, d2}},
};
\end{codeexample}
\end{key}
\begin{keylist}{%
/tikz/graphs/edges=\meta{options},
/tikz/graphs/nodes=\meta{options}}
Just like it is possible to change the shape of every vertex or edge in the
whole document, it is also possible to change the shape of every vertex or
edge in a single diagram by modifying these keys and adding the desired
styles.
\end{keylist}
\subsubsection{Vertex Keys}
\label{subsubsec:vertex_keys}
\begin{key}{/tikzfeynman/vertex}
The default, base style applied to every vertex initially. Other styles
are subsequently added. This sets the vertex |shape| to be a |coordinate|,
that is, a null shape with no size or width.
\end{key}
\begin{key}{/tikzfeynman/every \meta{vertex shape}=\meta{styles}}
The style of specific vertices can be modified by changing the appropriate
|every |\meta{vertex shape} key. For example, in order to change the style of
every |dot|-styled vertex, you can modify the |every dot| key, or to modify
every vertex globally, the |every vertex| key can be modified.
\begin{codeexample}[]
\tikzfeynmanset{
every vertex={red, dot},
every particle={blue},
every blob={draw=green!40!black, pattern color=green!40!black},
}
\feynmandiagram [horizontal=a to b] {
a [particle={\(\gamma, Z\)}] -- [boson] b [blob],
c -- [fermion] b -- [fermion] d,
};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/dot}
Modifies the vertex so that it has a small filled circle.
\begin{codeexample}[]
\feynmandiagram [small] {
a -- b [dot] -- {c, d}
};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/square dot}
Modifies the vertex so that it has a small filled square.
\begin{codeexample}[]
\feynmandiagram [small] {
a -- b [square dot] -- {c, d}
};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/empty dot}
Modifies the vertex so that it has a small empty circle.
\begin{codeexample}[]
\feynmandiagram [small] {
a -- b [empty dot] -- {c, d}
};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/crossed dot}
Modifies the vertex so that it has a small circle with a cross inside.
\begin{codeexample}[]
\feynmandiagram [small] {
a -- b [crossed dot] -- {c, d}
};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/blob}
Modifies the vertex so that it is a large blob, usually used to denote an
effective operator.
\begin{codeexample}[]
\feynmandiagram [small] {
a -- b [blob] -- {c, d}
};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/particle=\meta{name}}
Modifies the vertex so that it shows \meta{name}. This is intended to label
initial and final particles, but it should not be used on internal vertices as
it will result in the lines at the vertex having a gap. For propagators (the
|edge label| key is much more appropriate).
Note that if \meta{name} contains characters such as brackets (|[]|) or
commas (|,|), the whole \meta{name} has to be enclosed in braces (|{}|);
otherwise, the parser will interpret the comma as the end of the \meta{name}
and the start of the next key, or the closing bracket as the end of all
optional arguments.
\begin{codeexample}[]
\feynmandiagram [small, horizontal=a to b] {
a [particle={\(\gamma, Z\)}] -- [boson] b -- {c, d},
};
\end{codeexample}
\end{key}
\subsubsection{Edge Keys}
\label{subsubsec:edge_keys}
Just like with the various vertex keys, each edge type has a corresponding
|every |\meta{edge type}; however, due to the existence of very similar keys
such as |scalar|, |charged scalar| and |anti charged scalar|, more specific keys
inherit styles from less specific ones. For example, styles in |every scalar|
will apply to |charged scalar| and |anti charged scalar|.
The edge styles do not override each other and instead stack. This means that
an edge styled with both |boson| and |fermion| will consist of a straight line
with a wavy line on top and an error. If not styles are provided, then a simple
solid line is drawn.
\begin{key}{/tikzfeynman/every edge=\meta{styles}}
A style to apply to every edge initially.
\end{key}
\begin{stylekey}{/tikzfeynman/every \meta{edge style}=\meta{styles}}
The style of specific edges can be modified by changing the appropriate
|every |\meta{edge style} key. For example, in order to make a global change
to every |boson|, you can modify the |every boson| key.
\begin{codeexample}[]
\tikzfeynmanset{
every edge={green},
every boson={red},
every photon={blue},
}
\feynmandiagram [small] {
a [particle=\(a\)] -- [boson] o -- [photon] b [particle=\(b\)],
f1 [particle=\(c\)] -- [fermion] o -- [scalar] f2 [particle=\(d\)],
};
\end{codeexample}
\end{stylekey}
\begin{key}{/tikzfeynman/plain}
Draws a simple solid line. This style is identical to the default style
applied if no other style is used, but is provided so that it can be combined
with other styles.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [plain] b};
\feynmandiagram [horizontal=a to b] {a -- [plain, gluon] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/boson}
Draws a sinusoidal line to denote a boson.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [boson] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/charged boson}
Draws a sinusoidal line with an arrow to denote a charged boson.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [charged boson] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/anti charged boson}
Draws a sinusoidal line with an arrow pointing the other way to to denote a
anti charged boson.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [anti charged boson] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/photon}
Draws a sinusoidal line to denote a photon.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [photon] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/scalar}
Draws a dashed line to denote a scalar.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [scalar] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/charged scalar}
Draws a dashed line with an arrow to denote a charged scalar.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [charged scalar] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/anti charged scalar}
Draws a dashed line with an arrow pointing the other way to denote a charged
scalar antiparticle.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [anti charged scalar] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/ghost}
Draws a dotted line to denote a ghost.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [ghost] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/fermion}
Draws a solid line with an arrow to denote a fermion.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [fermion] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/anti fermion}
Draws a solid line with an arrow pointing the other way to denote an antifermion.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [anti fermion] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/majorana}
Draws a solid line with two arrows pointing to the center to denote an
Majorana particle.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [majorana] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/anti majorana}
Draws a solid line with two arrows pointing to the ends to denote a Majorana
particle.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [anti majorana] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/gluon}
Draws a coiled line to denote a gluon.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [gluon] b};
\end{codeexample}
\end{key}
\begin{keylist}{%
/tikz/edge label=\meta{text},
/tikz/edge label'=\meta{text}}
Places a label halfway along the edge with the given text. The primed key
switches which side of the edge the label is placed.
\end{keylist}
\begin{key}{/tikzfeynman/insertion=\opt{\oarg{options}}\meta{distance}}
Places an insertion (for mass or momentum insertion) along an edge. The
distance specifies how far along the edge the insertion should be placed such
that |0| and |1| respectively correspond to the start and the end of the edge.
Multiple insertions can be placed along a single edge by repeating the style
key.
Through the \meta{options} argument, the insertion size and style can be
changed.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [insertion=0.33, insertion=0.67] b};
\end{codeexample}
\begin{key}{/tikzfeynman/insertion/size=\meta{distance} (initially 3pt)}
Specifies how big the insertion should be. The length of each edge starting
from the center will be \(\sqrt{2} \times \meta{distance}\).
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [insertion={[size=10pt]0.4}] b};
\end{codeexample}
\end{key}
\begin{key}{/tikzfeynman/insertion/style=\meta{distance} (initially \normalfont empty)}
Specifies additional styles to applying to the lines of the insertion.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {a -- [insertion={[style=red]0.4}] b};
\end{codeexample}
\end{key}
\end{key}
\subsubsection{Momentum Keys}
\label{subsubsec:momentum_keys}
\begin{keylist}{%
/tikzfeynman/momentum=\opt{\oarg{options}}\meta{text},
/tikzfeynman/momentum'=\opt{\oarg{options}}\meta{text},
/tikzfeynman/reversed momentum=\opt{\oarg{options}}\meta{text},
/tikzfeynman/reversed momentum'=\opt{\oarg{options}}\meta{text},
/tikzfeynman/rmomentum=\opt{\oarg{options}}\meta{text},
/tikzfeynman/rmomentum'=\opt{\oarg{options}}\meta{text}}
Places a momentum arrow on the specified edge with label given by \meta{text}.
The primed (|'|) version place the momentum arrow on the other side of the
edge; that is, if the momentum arrow was on the right, it will be placed on
the left of the edge. The |reversed momentum| and |reversed momentum'| keys
are analogous to |momentum| and |momentum'| except that the momentum arrow
points in the opposite direction. Finally, the |rmomentum| and |rmomentum'|
are aliases of |reversed momentum| and |reversed momentum'|.
Note that due to the way the arrow is drawn, it doesn't inherit styles of the
edge. As a result, they have to be re-specified through \meta{options}.
\begin{codeexample}[]
\feynmandiagram [layered layout, horizontal=a to b] {
a -- [red, fermion, edge label'=\(ab\), momentum={[arrow style=red]\(p_{ab}\)}] b
-- [blue, photon, edge label'=\(bc\)] c
-- [green!40!black, scalar, momentum=\(p_{cd}\)] d,
};
\end{codeexample}
\begin{codeexample}[]
\feynmandiagram [layered layout, horizontal=b to c] {
a -- [photon, momentum=\(p\)] b
-- [fermion, half left, looseness=1.5, momentum=\(k\)] c
-- [fermion, half left, looseness=1.5, momentum=\(k-p\)] b,
c -- [photon, momentum=\(p\)] d,
};
\end{codeexample}
The \meta{options} allows for the following options to customize the appearance
of the momentum arrows. These can be either set globally with the usual
|\tikzfeynmanset|, or can be set on a individual basis through the
\meta{options} argument of the |momentum| key. In the latter case, only the
\meta{key} in |/tikzfeynman/momentum/|\meta{key} is required.
\begin{key}{/tikzfeynman/momentum/label distance=\meta{distance} (initially 0pt)}
Set the separation between the text and the arrow. Note that the text is
still surrounded by an |inner sep=0.3333em| by default so the default
distance of |0pt| will not result in the momentum label touching the arrow.
\end{key}
\begin{key}{/tikzfeynman/momentum/arrow distance=\meta{distance} (initially 3mm)}
Set the separation between the edge and the arrow.
\end{key}
\begin{key}{/tikzfeynman/momentum/arrow shorten=\meta{distance} (initially 0.15)}
Specify the fraction of the total edge length by which the momentum arrow is
shortened at each end.
\end{key}
\begin{key}{/tikzfeynman/momentum/label style=\meta{style} (initially \normalfont empty)}
Define styles to apply to the momentum label node.
\end{key}
\begin{key}{/tikzfeynman/momentum/arrow style=\meta{style} (initially \normalfont empty)}
Define style to apply to the momentum arrow.
\end{key}
\end{keylist}
\subsubsection{Modifier Keys}
\label{subsubsec:modifier_keys}
Modifier keys serve only to slightly modify a small feature of the edge.
\begin{keylist}{%
/tikzfeynman/half left,
/tikzfeynman/half right,
/tikzfeynman/quarter left,
/tikzfeynman/quarter right}
Modifies the edge so that it bends left or right in such a way that it
completes half a circle, or a quarter of a circle.
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
a -- [red, fermion, half left] b -- [blue, fermion, half left] a,
};
\end{codeexample}
\begin{codeexample}[]
\feynmandiagram [horizontal=a to c] {
a -- [red!0!blue, fermion, quarter left] b
-- [red!33!blue, fermion, quarter left] c
-- [red!66!blue, fermion, quarter left] d
-- [red!100!blue, fermion, quarter left] a,
};
\end{codeexample}
\end{keylist}
\begin{keylist}{%
/tikz/out=\meta{angle},
/tikz/in=\meta{angle}}
Specifies the angle at which the edge leaves the first vertex in an edge and
the angle at which it enters the second vertex in an edge.
\end{keylist}
\begin{key}{/tikz/relative=\opt{\meta{true or false}} (default true)}
If |relative| is set to |false|, the angle is relative to the paper whilst when
|relative| is set to |true|, the angle is relative to the straight line
joining the two vertices.
\end{key}
\begin{key}{/tikz/looseness=\meta{number} (initially 1)}
As the name suggests, this specifies how `loose' or `tight' a curve is
connecting two vertices.
\end{key}
\clearpage
\section{Examples}
\label{sec:examples}
Below are a few diagrams which demonstrate how the package can be used in some
more practical examples..
\begin{description}
\item[Vertex Rule] \hspace*{0pt} \newline
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
a [particle=\(Z\)] -- [photon, momentum=\(p_{1}\)] b,
f1 [particle=\(\overline f\)]
-- [fermion, rmomentum'=\(p_{3}\)] b
-- [fermion, momentum=\(p_{2}\)] f2 [particle=\(f\)],
};
\end{codeexample}
\item[Tree Level Diagrams] \hspace*{0pt} \newline
\begin{codeexample}[]
\feynmandiagram [horizontal=a to b] {
i1 [particle=\(e^{-}\)] -- [fermion] a -- [fermion] i2 [particle=\(e^{+}\)],
a -- [photon, edge label=\(\gamma\)] b,
f1 [particle=\(\mu^{-}\)] -- [fermion] b -- [fermion] f2 [particle=\(\mu^{+}\)],
};
\end{codeexample}
\begin{codeexample}[]
\feynmandiagram [vertical'=a to b] {
i1 [particle=\(e^{-}\)]
-- [fermion] a
-- [fermion] f1 [particle=\(e^{-}\)],
a -- [photon, edge label=\(\gamma\)] b,
i2 [particle=\(e^{+}\)]
-- [anti fermion] b
-- [anti fermion] f2 [particle=\(e^{+}\)],
};
\end{codeexample}
\begin{codeexample}[]
\begin{tikzpicture}
\begin{feynman}
\diagram [vertical'=a to b] {
i1 [particle=\(e^{-}\)]
-- [fermion] a
-- [draw=none] f1 [particle=\(e^{+}\)],
a -- [photon, edge label'=\(p\)] b,
i2 [particle=\(e^{+}\)]
-- [anti fermion] b
-- [draw=none] f2 [particle=\(e^{-}\)],
};
\diagram* {
(a) -- [fermion] (f2),
(b) -- [anti fermion] (f1),
};
\end{feynman}
\end{tikzpicture}
\end{codeexample}
\item[Loops] \hspace*{0pt} \newline
\begin{codeexample}[]
\feynmandiagram [layered layout, horizontal=b to c] {
a -- [photon, momentum=\(p\)] b
-- [fermion, half left, momentum=\(k\)] c
-- [fermion, half left, momentum=\(k-p\)] b,
c -- [photon, momentum=\(p\)] d,
};
\end{codeexample}
\begin{codeexample}[]
\feynmandiagram [layered layout, horizontal=a to b] [edges=gluon] {
{i1, i2} -- a -- [half left] b -- [half left] a,
b -- {f1, f2},
};
\end{codeexample}
\newpage
\item[Box Diagrams] \hspace*{0pt} \newline
\begin{codeexample}[]
\feynmandiagram [layered layout, horizontal=a to b] {
% Draw the top and bottom lines
i1 [particle=\(d\)]
-- [fermion] a
-- [photon, edge label=\(W^{-}\)] b
-- [fermion] f1 [particle=\(\mu^{-}\)],
i2 [particle=\(\overline s\)]
-- [anti fermion] c
-- [photon, edge label'=\(W^{+}\)] d
-- [anti fermion] f2 [particle=\(\mu^{+}\)],
% Draw the two internal fermion lines
{ [same layer] a -- [fermion, edge label'=\(q\)] c },
{ [same layer] b -- [anti fermion, edge label=\(\nu_{\mu}\)] d},
};
\end{codeexample}
\newpage
\item[Meson decay and mixing] \hspace*{0pt} \newline
\begin{codeexample}[]
\begin{tikzpicture}
\begin{feynman}
\vertex (a1) {\(\overline b\)};
\vertex[right=1.5cm of a1] (a2);
\vertex[right=1cm of a2] (a3);
\vertex[right=1.5cm of a3] (a4) {\(\overline u\)};
\vertex[below=2em of a1] (b1) {\(d\)};
\vertex[below=2em of a4] (b2) {\(d\)};
%% See section 13.5 of PGF/TikZ manual
\vertex at ($(a2)!0.5!(a3)!0.5cm!90:(a3)$) (d);
%% Equivalent way to obtain (d):
% \vertex at ($(b2)!0.5!(b3) + (0, -0.5cm)$) (d);
\vertex[above=of a4] (c1) {\(u\)};
\vertex[above=2em of c1] (c3) {\(\overline d\)};
\vertex at ($(c1)!0.5!(c3) - (1cm, 0)$) (c2);
\diagram* {
(a4) -- [fermion] (a3) -- [fermion] (a2) -- [fermion] (a1),
(b1) -- [fermion] (b2),
(c3) -- [fermion, out=180, in=45] (c2) -- [fermion, out=-45, in=180] (c1),
(a2) -- [boson, quarter left] (d) -- [boson, quarter left] (a3),
(d) -- [boson, bend left, edge label=\(W^{+}\)] (c2),
};
\draw [decoration={brace}, decorate] (b1.south west) -- (a1.north west)
node [pos=0.5, left] {\(B^{0}\)};
\draw [decoration={brace}, decorate] (c3.north east) -- (c1.south east)
node [pos=0.5, right] {\(\pi^{+}\)};
\draw [decoration={brace}, decorate] (a4.north east) -- (b2.south east)
node [pos=0.5, right] {\(\pi^{-}\)};
\end{feynman}
\end{tikzpicture}
\end{codeexample}
\newpage
\begin{codeexample}[]
\begin{tikzpicture}
\begin{feynman}
\vertex (a1) {\(\overline b\)};
\vertex[right=1cm of a1] (a2);
\vertex[right=1cm of a2] (a3);
\vertex[right=1cm of a3] (a4) {\(b\)};
\vertex[right=1cm of a4] (a5);
\vertex[right=2cm of a5] (a6) {\(u\)};
\vertex[below=2em of a1] (b1) {\(d\)};
\vertex[right=1cm of b1] (b2);
\vertex[right=1cm of b2] (b3);
\vertex[right=1cm of b3] (b4) {\(\overline d\)};
\vertex[below=2em of a6] (b5) {\(\overline d\)};
\vertex[above=of a6] (c1) {\(\overline u\)};
\vertex[above=2em of c1] (c3) {\(d\)};
\vertex at ($(c1)!0.5!(c3) - (1cm, 0)$) (c2);
\diagram* {
{[edges=fermion]
(b1) -- (b2) -- (a2) -- (a1),
(b5) -- (b4) -- (b3) -- (a3) -- (a4) -- (a5) -- (a6),
},
(a2) -- [boson, edge label=\(W\)] (a3),
(b2) -- [boson, edge label'=\(W\)] (b3),
(c1) -- [fermion, out=180, in=-45] (c2) -- [fermion, out=45, in=180] (c3),
(a5) -- [boson, bend left, edge label=\(W^{-}\)] (c2),
};
\draw [decoration={brace}, decorate] (b1.south west) -- (a1.north west)
node [pos=0.5, left] {\(B^{0}\)};
\draw [decoration={brace}, decorate] (c3.north east) -- (c1.south east)
node [pos=0.5, right] {\(\pi^{-}\)};
\draw [decoration={brace}, decorate] (a6.north east) -- (b5.south east)
node [pos=0.5, right] {\(\pi^{+}\)};
\end{feynman}
\end{tikzpicture}
\end{codeexample}
\newpage
\begin{codeexample}[]
\begin{tikzpicture}
\begin{feynman}
\vertex (a1) {\(\overline b\)};
\vertex[right=2cm of a1] (a2);
\vertex[right=0.5cm of a2] (a3);
\vertex[right=0.5cm of a3] (a4);
\vertex[right=2cm of a4] (a5) {\(\overline s\)};
\vertex[below=2cm of a1] (b1) {\(d\)};
\vertex[below=2cm of a5] (b2) {\(d\)};
\vertex[below=1.5em of a5] (c1) {\(s\)};
\vertex[above=1.5em of b2] (c3) {\(\overline s\)};
\vertex at ($(c1)!0.5!(c3) - (1cm, 0)$) (c2);
\diagram* {
{[edges=fermion]
(a5) -- (a4) -- (a3) -- (a2) -- (a1),
},
(b1) -- [fermion] (b2),
(c3) -- [fermion, out=180, in=-60] (c2) -- [fermion, out=60, in=180] (c1),
(a3) -- [gluon, bend right] (c2),
(a4) -- [boson, out=90, in=90, looseness=2.0, edge label'=\(W^{+}\)] (a2)
};
\draw [decoration={brace}, decorate] (b1.south west) -- (a1.north west)
node [pos=0.5, left] {\(B^{0}\)};
\draw [decoration={brace}, decorate] (a5.north east) -- (c1.south east)
node [pos=0.5, right] {\(\phi\)};
\draw [decoration={brace}, decorate] (c3.north east) -- (b2.south east)
node [pos=0.5, right] {\(K^{0}\)};
\end{feynman}
\end{tikzpicture}
\end{codeexample}
\end{description}
%% Index
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
\printindex
%% Bibliography (and acknowledgements)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
\pagestyle{plain}
\ifarxiv
\acknowledgements
\fi
\printbibliography
\end{document}
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