Isolation (blue) and signal cone (red) of a hadronically decayed tau, and for comparison an electron, muon and quark/gluon-initiated jet. For more related figures, please see the “jet” tag or the Particle Physics category. The cones are constructed with the tangent methods presented here.
Edit and compile if you like:
% Author: Izaak Neutelings (November 2021)
% Description: jet cones for taus & others
\documentclass[border=3pt,tikz]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{math} % for \tikzmath
\tikzset{>=latex} % for LaTeX arrow head
\colorlet{myblue}{blue!70!black}
%\colorlet{mydarkblue}{blue!50!black}
\colorlet{mygreen}{green!60!black}
\colorlet{myred}{red!75!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]
\newcommand\jetcone[6][sigcol]{{
\pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}
\pgfmathsetmacro\oang{#4/2} % half-opening angle
\edef\e{#5} % ratio a/b
\def\tmpL{tmpL-#2-#3} % unique coordinate name
\edef\vang{\pgfmathresult} % angle of vector OV
\tikzmath{
coordinate \C;
\C = (#2)-(#3);
\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,rotate=\vang] % cone back
(\tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt})
-- ($(#2)+(0.01,0)$) -- 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,shading angle=\vang]
(\tmpL) arc(180-\angb:180+\angb:{\a pt} and {\b pt})
-- ($(#2)+(0.01,0)$) -- cycle;
}}
\begin{document}
% COMMON SETTINGS
\small
\def\angiso{44} % opening angle of isolation cone
\def\angsig{22} % opening angle of isolation cone
\def\e{0.11} % a/b ratio of ellipse minor and major radii
\foreach \ang [evaluate={\ang; \anang=\ang-90;}] in {90,\angiso/2,0,180}{ % rotate each cone
\tikzset{
every picture/.append style={scale=2.4,rotate=\ang-90}, % set scale for all figures
every node/.style={inner sep=1,circle} %,draw=black!9,very thin}
}
% TAU JET - ONE PRONG
\begin{tikzpicture}
\coordinate (O) at (0,0);
\coordinate (O') at (0,-0.01); % shifted
\coordinate (I) at (0,0.92); % isolation cone
\coordinate (S) at (0,1.00); % signal cone
\coordinate (T) at (0,0.02); % tau vertex
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone
\draw[track] (T) to[out=88,in=-70] (93:1.33)
node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\pi^-$};
}
}
\end{tikzpicture}
% TAU JET - ONE PRONG, 2 PI ZEROS
\begin{tikzpicture}
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone
\draw[dashed track] (T) -- (97:1.18)
node[anchor=-40+\anang,inner sep={2*cos(\ang)^2-1.0}] {$\pi^0$};
\draw[dashed track] (T) -- (82:1.20)
node[anchor=-110+\anang,inner sep=0.0] {$\pi^0$};
\draw[track] (T) to[out=88,in=-70] (94:1.33)
node[anchor=-100+\anang,inner sep={-sin(\ang)^2}] {$\pi^-$};
}
}
\end{tikzpicture}
% TAU JET - THREE PRONG
\begin{tikzpicture}
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone
\draw[track] (T) to[out=90,in=-55] (103:1.33)
node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\pi^-$};
\draw[track] (T) to[out=90,in=-112] (87:1.29)
node[anchor=-110+\anang,inner sep={0.6*sin(\ang)^2}] {$\pi^+$};
\draw[track] (T) to[out=88,in=-117] (82:1.16)
node[anchor=-145+\anang,inner sep={0.6*sin(\ang)^2}] {$\pi^+$};
}
}
\end{tikzpicture}
% TAU JET - THREE PRONG, PI ZERO
\begin{tikzpicture}
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{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] (103:1.33)
node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\pi^-$};
\draw[track] (T) to[out=93,in=-110] (84:1.29)
node[anchor=-110+\anang,inner sep={0.6*sin(\ang)^2}] {$\pi^+$};
\draw[track] (T) to[out=88,in=-117] (80:1.16)
node[anchor=-145+\anang,inner sep={0.6*sin(\ang)^2}] {$\pi^+$};
}
}
\end{tikzpicture}
% ELECTRON JET
\begin{tikzpicture}
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone
%\draw[dashed track] (T) to[out=88,in=-70] (96:1.26)
% node[right=0,above=-2] {$\mathrm{e}^-$};
\draw[dashed track] (T) to[out=88,in=-70] (96:1.26)
node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\mathrm{e}^-$};
}
}
\end{tikzpicture}
% MUON JET
\begin{tikzpicture}
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone
\draw[track] (T) to[out=88,in=-70] (93:1.33)
node[anchor=-70+\anang,inner sep={2.5*cos(\ang)^2-1.5}] {$\mu^-$};
}
}
\end{tikzpicture}
% QUARK/GLUON JET
\begin{tikzpicture}
\jetcone[isocol]{O'}{I}{\angiso}{\e}{ % isolation cone
\jetcone[sigcol]{O}{S}{\angsig}{\e}{ % signal cone
\draw[dashed track] (T) -- (105:1.18);
\draw[dashed track] (T) -- (94:1.22);
\draw[dashed track] (T) -- (84:1.22);
\draw[track] (T) to[out=105,in=-50] (113:1.18);
\draw[track] (T) to[out=90,in=-55] (103:1.33);
\draw[track] (T) to[out=98,in=-105] (87:1.29);
\draw[track] (T) to[out=68,in=-92] (79:1.20);
}
}
\end{tikzpicture}
} % end \foreach
\end{document}
Click to download: jet_tau.tex • jet_tau.pdf
Open in Overleaf: jet_tau.tex
