Some custom piecharts illustrating the branching fraction of the decay of several Standard Model particles like the tau lepton, Z boson, W boson, top, ttbar, Higgs boson, …
Tau lepton decay
Ditau decay
W boson (or top) decay
Same for top quark decay assuming BR(t → Wb) ≈ 100%:
Specifying quark flavors:
Top quark pair (ttbar) decay
Z boson decay
Specifying quark flavors:
Higgs boson decay
Energy composition of the Universe
Energy composition of the Universe according to Planck's high-precision measurements of the cosmic microwave background:
Edit and compile if you like:
% Author: Izaak Neutelings (May 2022)
% https://github.com/IzaakWN/CodeSnippets/blob/master/LaTeX/TikZ/physics/tau_decay_matrix.py
% Inspiration:
% https://texample.net/tikz/examples/pie-chart-color/
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath} % for \text
%\usepackage{mathabx} % for \widebar
\usepackage{bm} % for bold Greek letters via \bm
\usepackage[outline]{contour} % glow around text
\contourlength{0.25pt}
% STYLES
\usetikzlibrary{shapes} % for ellipse node
\usetikzlibrary{shadows.blur}
\colorlet{myred}{red!85!black!65}
\colorlet{mycyan}{blue!40!cyan!85!black!55}
\colorlet{myblue}{blue!70!cyan!85!black!55}
\colorlet{mydarkblue}{myblue!90!black!90}
\colorlet{mydarkerblue}{myblue!80!black!90}
\colorlet{mydarkestblue}{myblue!70!black!90}
\colorlet{mylightblue}{blue!50!cyan!80!black!45}
\colorlet{mypink}{magenta!95!red!100!black!72}
\colorlet{mypurple}{blue!50!red!90!black!70}
\colorlet{mydarkpurple}{blue!50!red!70!black!70}
\colorlet{mygreen}{green!60!black!75}
\colorlet{mylightgreen}{green!80!red!90!black!50}
\colorlet{myorange}{orange!95!black!70}
\colorlet{mybrown}{brown!80!orange!95!black!80}
\colorlet{myyellow}{yellow!80!orange!95!black!80}
\colorlet{mylightyellow}{yellow!80!orange!95!black!45}
\def\R{1} % default pie radius
\tikzstyle{pin}=[very thin,line cap=round]
\tikzset{
slice/.style={fill=#1,draw=#1!80!black,line join=round,line width=0.4,
blur shadow={shadow blur steps=20,shadow xshift=0.5,
shadow yshift=-1,shadow opacity=40}},
slice/.default=myblue,
pics/piechart/.style n args={2}{ % SIMPLE PIECHART 1
code={
\foreach \frac/\name/\col [
count=\i,
remember=\angb as \anga (initially #1), % start angle
evaluate={\angm=\anga-\frac*1.8; % middle angle
\angb=\anga-\frac*3.6; % final angle
\exp=\R*max(0.02,0.2*(1-\frac/100)^8); % explode (radial shift)
\r=\exp+\R*max(0.5,(0.8-\frac/100));} % label radial positon
] in {#2}{ % loop over slices
\coordinate (P\i) at (\angm:\exp+\R);
\draw[slice=\col] % slice / circle sector
(\angm:\exp) --++ (\anga:\R) arc(\anga:\angb:\R) -- cycle;
\node[white,scale=0.9]
at (\angm:\r) {\contour{\col!75!black}{\bm{$\frac\mathbf{\%}$}}};
\node[\col!70!black,anchor=180+\angm,inner sep=4]
at (P\i) {\bf\bm{$\name$}};
}
}
},
pics/piechart2/.style n args={2}{ % SIMPLE PIECHART 2
code={
\foreach \frac/\name/\col [
remember=\angb as \anga (initially #1), % start angle
evaluate={\angm=\anga+\frac*1.8; % middle angle
\angb=\anga+\frac*3.6; % final angle
\exp=\R*max(0.02,0.14*(1-\frac/100)^3); % explode (radial shift)
\r=\exp+\R*max(0.5,(1-\frac/100)^2);} % label radial positon
] in {#2}{ % loop over slices
\message{^^J frac=\frac: anga=\anga -> angb=\angb}
\draw[slice=\col] % slice / circle sector
(\angm:\exp) --++ (\anga:\R) arc(\anga:\angb:\R) -- cycle;
\ifdim \frac pt > 10pt % label inside slice
\node[white,align=center]
at (\angm:\r) {\boldlabel{$\name$}{\frac}};
\else % label outside slice
\node[\col!5!black,align=center,anchor=180+\angm,inner sep=3]
at (\angm:\exp+\R) {\boldlabel{$\name$}{\frac}};
\fi
}
}
},
}
% MACROS
%\renewcommand\bar{\overline}
\newcommand\WW{\mathrm{WW}} %W^+W^-
\newcommand\ZZ{\mathrm{ZZ}}
\newcommand\TT{\tau\tau}
\newcommand\qbar{\bar{q}}
\newcommand\ttbar{\mathrm{t}\bar{\mathrm{t}}}
\newcommand\bbbar{\mathrm{b}\bar{\mathrm{b}}}
\newcommand\ccbar{\mathrm{c}\bar{\mathrm{c}}}
\newcommand\udbar{\mathrm{u}\bar{\mathrm{d}}}
\newcommand\csbar{\mathrm{c}\bar{\mathrm{s}}}
\newcommand\e{\mathrm{e}}
\newcommand\hp{\mathrm{h}^\pm}
\newcommand\hM{\mathrm{h}^\mp}
\newcommand\pz{\pi^0}
\newcommand\tauh{\tau_\mathrm{h}}
\newcommand\jets{\mathrm{jets}}
\newcommand\boldlabel[2]{\bf\bm{#1}\\[-1]\small\bm{$#2\mathbf{\%}$}}
\newcommand\boldlabeltiny[2]{\bf\bm{$#1$}\\[-2.5]\footnotesize\bm{$#2\mathbf{\%}$}}
\begin{document}
% TAU BRANCHING FRACTION - PIE CHART (SIMPLE)
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-leptons.pdf
% https://arxiv.org/abs/2201.08458 (Table 1)
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JDitau pie chart}
\draw pic[scale=1.5] {piechart={-126}{
64.8/\text{hadrons}\qquad/myblue,
17.4/\!\!\mu^\pm/myred,
17.8/\e^\pm /mygreen%
}};
%\node[above,scale=1.2] at (0,1.8) {\bf\bm{$\tau$} lepton decay modes};
\end{tikzpicture}
% TAU BRANCHING FRACTION - PIE CHART (HADRONIC DECAY MODES)
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-leptons.pdf
% https://arxiv.org/abs/2201.08458 (Table 1)
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JTau pie chart}
\draw pic[scale=1.6] {piechart={-126}{
11.5/\hp /myblue,
25.9/\hp\pz /myblue!90!black,
9.5/\hp\pz\pz /myblue!80!black,
9.8/\qquad\hp\hM\hp /mycyan,
4.8/\quad\hp\hM\hp\pz/mycyan!95!black,
3.3/\text{other} /mylightblue,
17.4/\!\!\mu^\pm /myred,
17.8/\e^\pm /mygreen%
}};
%\node[mycyan!70!black,anchor=-160] at (P4) {\bm{$\hp\hM\hp$}};
%\node[mycyan!65!black,anchor=-160] at (P5) {\bm{$\hp\hM\hp\pz$}};
%\node[above,scale=1.2] at (0,2.2) {\bf\bm{$\tau$} lepton decay modes};
\end{tikzpicture}
% DITAU BRANCHING FRACTION - PIE CHART
\begin{tikzpicture} %[scale=1,transform shape]
\message{^^JDitau pie chart}
\draw pic[scale=1.4] {piechart2={-90}{
23/\e\tauh /mygreen,
23/\mu\tauh /myred,
42/\tauh\tauh/myblue,
3/\;\e\e /mylightgreen,
6/\;\e\mu /myorange,
3/\;\;\mu\mu/mypink%
}};
%\node[above,scale=1.2] at (0,1.5) {\bf\bm{$\TT$} decay modes};
\end{tikzpicture}
% DITAU BRANCHING FRACTION - PIE CHART ALTERNATIVE
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JDitau pie chart}
\draw pic[scale=1.4] {piechart2={-90}{
23/\mu\tauh /mypurple,
42/\tauh\tauh/myblue,
23/\e\tauh /mygreen,
3/\;\e\e /myyellow,
6/\;\e\mu /myorange,
3/\;\;\mu\mu/myred%
}};
%\node[above,scale=1.2] at (0,1.5) {\bf \bf\bm{$\TT$} decay modes};
\end{tikzpicture}
% W BOSON / TOP QUARK MAIN BRANCHING FRACTION - PIE CHART
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-quarks.pdf
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-gauge-higgs-bosons.pdf
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JW boson / top pie chart}
\draw pic[scale=1.6] {piechart={-60}{
67.4/q\qbar/mycyan,
11.4/\tau /myblue,
10.6/\mu /myred,
10.7/\e /mygreen%
}};
%\node[above,scale=1.2] at (0,1.6) {\bf Top decay modes};
\end{tikzpicture}
% W BOSON / TOP QUARK MAIN BRANCHING FRACTION - PIE CHART (SPLIT)
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-quarks.pdf
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-gauge-higgs-bosons.pdf
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JW boson / top pie chart (split quarks)}
\draw pic[scale=1.6] {piechart={-60}{
33.3/\udbar/mycyan, %mylightblue,
34.0/\csbar/mydarkerblue, %mycyan
11.4/\tau /myblue,
10.6/\mu /myred,
10.7/\e /mygreen%
}};
%\node[above,scale=1.2] at (0,1.7) {\bf Top decay modes};
\end{tikzpicture}
% TOP PAIR BRANCHING FRACTION - PIE CHART
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-quarks.pdf
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-gauge-higgs-bosons.pdf
\begin{tikzpicture}[scale=2.0]
\message{^^JWW or ttbar boson pie chart}
%\node[above,scale=1.2] at (0,1.2) {\bf\bm{$\ttbar\to\bbbar\WW$} decay modes};
% PIE CHART
\def\angA{180} % initial angle
\foreach \subgroup in { % loop over subgroup
{ 1/\e\e /mylightgreen, % dileptonic decays
2/\e\mu /myorange,
2/\mu\mu /mypink,
1/\e\tau /mydarkestblue,
2/\mu\tau /mydarkerblue,
1/\tau\tau /mydarkblue},%
{15/\e+\jets /mygreen, % semileptonic decays
15/\mu+\jets /myred,
15/\tau+\jets/myblue},%
{46/\text{all jets}/mylightblue}% % fully hadronic decays
}{%
\message{^^JSubgroup at angA=\angA}
\def\ftot{0}
\foreach \frac/\d/\d in \subgroup{
\pgfmathparse{\ftot+\frac} \xdef\ftot{\pgfmathresult}
}
% MAKE SLICE FOR SUBGROUP
\begin{scope}[shift={(\angA+\ftot*1.8:0.03*\R)}]
\foreach \frac/\name/\col [
remember=\angb as \anga (initially \angA), % start angle
evaluate={\angm=\anga+\frac*1.8; % middle angle
\angb=\anga+\frac*3.6; % final angle
\exp=\R*0.2*(1-\frac/100)^15; % explode (radial shift)
\r=\exp+\R*max(0.5,(1-\frac/100)^2.5);} % label radial positon
] in \subgroup{ % loop over subgroup
\message{^^J Slice at anga=\anga -> angb=\angb}
\draw[slice=\col,shadow opacity=15] % slice / circle sector
(\angm:\exp) --++ (\anga:\R) arc(\anga:\angb:\R) -- cycle;
\ifdim \frac pt > 10pt % fraction inside slice
\node[white]
at (\angm:\r) {\bm{$\frac\mathbf{\%}$}};
\node[\col!90!black,anchor=180+\angm,inner sep=5]
at (\angm:\exp+\R) {\bf\bm{$\name$}};
\else % fraction and label outside slice
\node[black,align=center,anchor=0,rotate=180+\angm,inner sep=3,scale=0.8]
at (\angm:\exp+\R) {\bf\bm{$\name$}, \small\bm{$\frac\mathbf{\%}$}};
\fi
\xdef\angA{\angb} % globally redefine \angA to last angle \angb
}
\end{scope}
}
\end{tikzpicture}
% Z BOSON BRANCHING FRACTION - PIE CHART
% https://en.wikipedia.org/wiki/W_and_Z_bosons#Z0_boson
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-gauge-higgs-bosons.pdf
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JZ boson pie chart}
\draw pic[scale=1.6] {piechart={-18}{
69.9/q\qbar /mycyan,
20.0/\qquad\text{invisible}/mylightyellow, %myorange
3.4/\tau^+\tau^-/myblue,
3.4/\mu^+\mu^- /myred,
3.4/\e^+\e^- /mygreen%
}};
%\node[above,scale=1.2] at (0,1.7) {\bf Z boson decay modes};
\end{tikzpicture}
% Z BOSON BRANCHING FRACTION - PIE CHART (SPLIT)
% https://en.wikipedia.org/wiki/W_and_Z_bosons#Z0_boson
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-gauge-higgs-bosons.pdf
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JZ boson pie chart}
\draw pic[scale=1.6] {piechart={-18}{
15.6/\bbbar/mydarkestblue, %mylightgreen
11.6/\ccbar/mydarkerblue, %myorange,
15.6/\mathrm{s\bar{s}}/mydarkblue,
11.6/\mathrm{u\bar{u}}/mycyan,
15.6/\mathrm{d\bar{d}}/mylightblue,
20.0/\qquad\text{invisible}/mylightyellow, %myorange
%6.7/\qquad\nu_\tau\nu_\tau/mylightyellow,
%6.7/\qquad\nu_\mu\nu_\mu/mylightyellow,
%6.7/\qquad\nu_\e\nu_\e/mylightyellow,
3.4/\tau^+\tau^-/myblue,
3.4/\mu^+\mu^- /myred,
3.4/\e^+\e^- /mygreen%
}};
%\node[above,scale=1.2] at (0,1.9) {\bf Z boson decay modes};
\end{tikzpicture}
% HIGGS BRANCHING FRACTION - PIE CHART (MH = 125.1)
% https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHWG#Higgs_cross_sections_and_decay_b
% https://pdg.lbl.gov/2021/tables/rpp2021-sum-gauge-higgs-bosons.pdf
% other = 0.00202 = 1-(0.5807+0.2154+0.08179+0.06256+0.02883+0.02643+0.00227)
\begin{tikzpicture}[scale=1.7]
\message{^^JHigss pie chart}
\foreach \frac/\name/\col [
count=\i,
remember=\angb as \anga (initially -10), % start angle
evaluate={\angm=\anga-\frac*1.8; % middle angle
\angb=\anga-\frac*3.6; % final angle
\exp=\R*max(0.02,0.4*(1-\frac/100)^15); % explode (radial shift)
\r=\exp+\R*max(0.5,(0.83-\frac/100));} % label radial positon
] in { % loop over slices
0.2/\gamma\gamma/myyellow, % 0.00227
0.2/other /mydarkerblue, % 0.00202
%0.02/\mu\mu /myblue!80!black, % 0.000217
%0.02/Z\gamma /myblue!80!black% % 0.001541
58.1/\bbbar /mygreen, % 0.5807
21.5/\WW /myred, % 0.2154
8.2/gg /mycyan, % 0.08179
6.3/\tau\tau /myblue, % 0.06256
2.9/\ccbar /myorange, % 0.02883
2.6/\ZZ /mypurple% % 0.02643
}{
\message{^^J frac=\frac: anga=\anga -> angb=\angb}
\coordinate (P\i) at (\angm:\exp+\R);
\draw[slice=\col,line width={\frac>2?0.6:0.2},shadow opacity=20] % slice / circle sector
(\angm:\exp) --++ (\anga:\R) arc(\anga:\angb:\R) -- cycle;
\ifdim \frac pt > 9pt % label inside slice
\node[white,align=center]
at (\angm:\r) {\boldlabel{$\name$}{\frac}};
\else \ifdim \frac pt > 2pt % label inside slice, frac inside
\node[white,scale={\frac>4?0.9:0.8}]
at (\angm:\r) {\contour{\col!70!black!90}{\bm{$\frac\mathbf{\%}$}}};
\node[\col!80!black,anchor=190+\angm,inner sep=4]
at (P\i) {\bf\bm{$\name$}};
%\else \ifdim \frac pt > 2pt % label & frac outside slice
% \node[\col!80!black,align=center,anchor=180+\angm,inner sep=3]
% at (P\i) {\bm{$\name$} \small$\mathbf{\frac\%}$}; %{\boldlabel{$\name$}{\frac}};
%\else % pinned label
% \node[\col!80!black,align=center,pin={\angm-20:$\name$},inner sep=3]
% at (\angm:\exp+\R) {};
\fi \fi %\fi
}
% MANUALLY PLACED LABELS
\draw[pin,myyellow!85!black]
(P1)++(-30:0.01) --++ (-28:0.2)
node[anchor=178,inner sep=2]
{\bm{$\gamma\gamma$} \footnotesize$\mathbf{0.2\%}$};
\draw[pin,mydarkerblue!80!black]
(P2)++(-40:0.01) --++ (-80:0.2)
node[anchor=100,align=center,inner sep=2]
{\bf other\\[-2.5]\footnotesize$\mathbf{0.2\%}$};
%{\bm{$\mu\mu$}, \bf{$\mathrm{Z}\gamma$}, ...\\[-2.5]\footnotesize$\mathbf{0.2\%}$};
%% TITLE
%\node[above,scale=1.2] at (0,1.1) {\bf Higgs decay channels};
\end{tikzpicture}
% ENERGY DENSITY (Planck)
% https://doi.org/10.1051%2F0004-6361%2F201525830
% https://sci.esa.int/web/planck/-/51557-planck-new-cosmic-recipe
\begin{tikzpicture} %[scale=1.0,transform shape=false]
\message{^^JEnergy density}
\draw pic[scale=1.5] {piechart={-2}{
68.3//mydarkpurple,
26.8//mydarkestblue,
4.9//mygreen%
}};
\node[anchor=5,inner sep=3,align=left,mydarkpurple!70!black]
at (P1) {\bf Dark\\[-2]\bf energy};
\node[anchor=-170,inner sep=4,mydarkestblue!70!black]
at (P2) {\bf Dark matter};
\node[anchor=185,inner sep=3,align=center,mygreen!70!black]
at (P3) {\bf Ordinary\\[-2]\bf matter};
\end{tikzpicture}
\end{document}Click to download: SM_decay_piechart.tex • SM_decay_piechart.pdf
Open in Overleaf: SM_decay_piechart.tex.
