Decay of the Z boson to leptons.
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% Author: Izaak Neutelings (Februari 2023)
% Description: Decay of the Z boson to leptons.
\documentclass[border=3pt,tikz]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{math} % for \tikzmath
\usetikzlibrary{arrows.meta} % for arrow size
\usetikzlibrary{decorations.pathmorphing} % for snakes
\tikzset{>=latex} % for LaTeX arrow head
\colorlet{myred}{red!75!black}
\colorlet{myblue}{blue!70!black}
%\colorlet{mydarkblue}{blue!50!black}
\colorlet{mygreen}{green!60!black}
\colorlet{myorange}{orange!75!yellow!90!black}
\colorlet{isocol}{blue!70!black} % color isolation cone
\colorlet{sigcol}{red!90!black} % color isolation cone
\tikzstyle{track}=[->,line width=0.6,myred]
\tikzstyle{dashed track}=[->,mygreen,line width=0.6,line cap=round,
dash pattern=on 2.3 off 2.0]
\tikzstyle{part}=[circle,ball color=#1,text=#1!30!black,
postaction={fill=#1!77,fill opacity=0.8,
draw=#1!60!black!90,thin}]
\tikzstyle{mysmallarrow}=[-{Latex[length=4.2,width=3.5]},mygreen,thick]
% JET CONE
\newcommand\jetcone[6][sigcol]{{
\pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}
\pgfmathsetmacro\oang{#4/2} % half-opening angle
\edef\e{#5} % ratio a/b ("eccentricity") of cone top
\def\tmpL{tmpL-#2-#3} % unique coordinate name
\edef\vang{\pgfmathresult} % angle of vector OV
\tikzmath{
coordinate \C;
\C = (#2)-(#3); % vector OV
\x = veclen(\Cx,\Cy)*\e*sin(\oang)^2; % x coordinate P
\y = tan(\oang)*(veclen(\Cx,\Cy)-\x); % y coordinate P
\a = veclen(\Cx,\Cy)*sqrt(\e)*sin(\oang); % vertical radius
\b = veclen(\Cx,\Cy)*tan(\oang)*sqrt(1-\e*sin(\oang)^2); % horizontal radius
\angb = acos(sqrt(\e)*sin(\oang)); % angle of P in ellipse
}
\coordinate (\tmpL) at ($(#3)-(\vang:\x pt)+(\vang+90:\y pt)$); % tangency
\draw[thin,#1!50!black,fill=#1!80!black!50,line cap=round,rotate=\vang] % cone back
(#2) -- (\tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt}) -- (#2); %-- cycle;
\draw[thin,#1!50!black,rotate=\vang, % cone inside
top color=#1!60!black!60,bottom color=#1!50!black!75,shading angle=\vang]
(#3) ellipse({\a pt} and {\b pt});
#6 % extra tracks
\draw[thin,#1!50!black,rotate=\vang,fill opacity=0.80, % cone front
top color=#1!90!black!20,bottom color=#1!50!black!50,line cap=round,shading angle=\vang]
(#2) -- (\tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt}) -- (#2); %-- cycle;
}}
\begin{document}
% Z -> mumu
\begin{tikzpicture}[
scale=2.4, % set scale for all figures
]
% Z BOSON
\node[circle,part=myorange,inner sep=1.8pt,scale=1.1]
(Z) at (0,0) {\textbf{Z}};
% MUONS
\draw[track] (Z) to[bend right=12] (70:1.0)
node[anchor=-80,inner sep=0pt] {$\mu$}; %^-
\draw[track] (Z) to[bend left=12] (30:1.1)
node[anchor=-160,inner sep=1pt] {$\mu$}; %^+
\end{tikzpicture}
% TAU JET - THREE PRONG, PI ZERO\small
\def\angiso{45} % opening angle of isolation cone (CMS: DR = 0.4 => 0.8*180/pi = 45.8)
\def\angsig{12} % opening angle of signal cone (CMS: 0.05 <= DR <= 0.1 => 0.1*180/pi = 11.4)
\def\e{0.11} % a/b ratio of ellipse minor and major radii
\begin{tikzpicture}[
scale=2.4, % set scale for all figures
every node/.style={inner sep=1,circle} %,draw=black!9,very thin}
]
% Z BOSON
\node[part=myorange,inner sep=1.8pt,scale=1.1]
(Z) at (0,0) {\textbf{Z}};
% TAUS
\node[part=mygreen,minimum size=8pt,scale=0.7]
(T1) at (50:0.3) {};
\node[part=mygreen,minimum size=8pt,scale=0.7]
(T2) at (-20:0.3) {};
\node[mygreen!80!black,anchor=-50,inner sep=1pt,scale=0.9]
at (T1) {$\tau^+$};
\node[mygreen!80!black,anchor=60,inner sep=1pt,scale=0.9]
at (T2) {$\tau^-$};
\draw[mysmallarrow] (Z) -- (T1);
\draw[mysmallarrow] (Z) -- (T2);
% MUONS
\draw[track] (T1) to[out=20,in=-138] ++(32:1.22)
node[anchor=-160,inner sep=0pt] {$\mu^+$};
% NEUTRINOS
\begin{scope}[dashed track,opacity=0.4,thin]
\draw
(T1) --++ (80:0.64)
node[anchor=-110,inner sep=0pt,scale=0.8] {$\overline{\nu}_\tau$};
\draw
(T1) --++ (50:0.84)
node[anchor=-150,inner sep=0pt,scale=0.8] {$\nu_\mu$};
\draw
(T2) --++ (-29:0.84)
node[anchor=160,inner sep=1pt,scale=0.8] {$\nu_\tau$};
\end{scope}
% TAUH
\begin{scope}[rotate around={-85:(T2)}]
\coordinate (T2') at ($(T2)+(0,1pt)$); % isolation cone
\coordinate (I) at ($(T2)+(0,0.92)$); % isolation cone
\coordinate (S) at ($(T2)+(0,1.00)$); % signal cone
\coordinate (T) at ($(T2')+(0,0.02)$); % tau vertex
%\jetcone[isocol]{T2'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{T2'}{S}{\angsig}{\e}{ % signal cone
\draw[dashed track] (T) --++ (92:1.18);
%node[anchor=-85+\anang,inner sep=0.5] {$\pi^0$};
\draw[track] (T) to[out=90,in=-55] ++(100:1.18);
%node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\pi^-$};
\draw[track] (T) to[out=93,in=-110] ++(85:1.26);
%node[anchor=-110+\anang,inner sep={0.6*sin(\ang)^2}] {$\pi^+$};
\draw[track] (T) to[out=88,in=-117] ++(83:1.11);
%node[anchor=-145+\anang,inner sep={0.6*sin(\ang)^2}] {$\pi^+$};
}
%}
\node[myblue!80!black,anchor=-140,inner sep=0pt]
at ($(T2)+(0,1.3)$) {$\tau_\mathrm{h}$};
\end{scope}
\end{tikzpicture}
\end{document}Click to download: SM_Z_decay.tex • SM_Z_decay.pdf
Open in Overleaf: SM_Z_decay.tex.
