Top jet

Different boosted jet regimes of the hadronic top decay.
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 (May 2021)
% Description: hadronic top quark jet
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{physics}
\usepackage{xcolor}
\usetikzlibrary{calc}
\usetikzlibrary{math} % for \tikzmath
\tikzset{>=latex} % for LaTeX arrow head
\usetikzlibrary{decorations.pathreplacing} % for curly braces

\colorlet{myblue}{blue!70!black}
\colorlet{mydarkblue}{blue!40!black}
\colorlet{mygreen}{green!40!black}
\colorlet{myred}{red!65!black}
\tikzstyle{vector}=[->,very thick,myblue,line cap=round]
\tikzstyle{ptmiss}=[->,dashed,thick,myred,line cap=round]
\tikzstyle{cone}=[thin,blue!50!black,fill=blue!50!black!30] %,fill opacity=0.8
\tikzstyle{conebase}=[cone,fill=blue!50!black!50] %,fill opacity=0.8

\newcommand\jetcone[5][blue]{{
  \pgfmathanglebetweenpoints{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}
  \edef\ang{#4/2}
  \edef\e{#5}
  \edef\vang{\pgfmathresult} % angle of vector OV
  \tikzmath{
    coordinate \C;
    \C = (#2)-(#3);
    \x = veclen(\Cx,\Cy)*\e*sin(\ang)^2; % x coordinate P
    \y = tan(\ang)*(veclen(\Cx,\Cy)-\x); % y coordinate P
    \a = veclen(\Cx,\Cy)*sqrt(\e)*sin(\ang); % vertical radius
    \b = veclen(\Cx,\Cy)*tan(\ang)*sqrt(1-\e*sin(\ang)^2); % horizontal radius
    \angb = acos(sqrt(\e)*sin(\ang)); % angle of P in ellipse
  }
  \coordinate (tmpL) at ($(#3)-(\vang:\x pt)+(\vang+90:\y pt)$); % tangency
  \draw[thin,#1!40!black,rotate=\vang, %,fill=#1!50!black!80
    top color=#1!50!black!80,bottom color=#1!40!black!80,shading angle=\vang]
    (#3) ellipse({\a pt} and {\b pt});
  \draw[thin,#1!40!black,rotate=\vang,%fill=#1!80!black!40,
  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})
    -- ($(#2)+(\vang:0.018)$) -- cycle;
}}


\begin{document}


% RESOLVED TOP JETS
\def\R{2.3}
\begin{tikzpicture}
  \coordinate (O) at (0,0);
  \coordinate (BJ) at ( 65:1.1*\R); % b jet 1
  \coordinate (J1) at ( 15:1.0*\R); % q jet 1
  \coordinate (J2) at (-20:1.0*\R); % q jet 2
  \jetcone[green!80!black]{O}{BJ}{14}{0.10}
  \jetcone{O}{J1}{16}{0.08}
  \jetcone{O}{J2}{16}{0.10}
  \node[green!50!black] at (65:1.26*\R) {b};
  \node[blue!80!black,right] at (-5:1.00*\R) {$\mathrm{W} \to qq$};
\end{tikzpicture}


% BOOSTED TOP JETS, partially merged
\begin{tikzpicture}
  \edef\ang{28}
  \edef\e{0.05}
  \coordinate (O) at (0,0);
  \coordinate (BJ) at ( 56:1.1*\R); % b jet 1
  \coordinate (J1) at ( 12:1.0*\R); % q jet 1
  \coordinate (J2) at (-12:1.0*\R); % q jet 2
  \coordinate (M) at (0:0.85*\R); % merged
  \edef\vang{\pgfmathresult} % angle of vector OV
  \tikzmath{
    coordinate \C;
    \C = (O)-(M);
    \x = veclen(\Cx,\Cy)*\e*sin(\ang)^2; % x coordinate P
    \y = tan(\ang)*(veclen(\Cx,\Cy)-\x); % y coordinate P
    \a = veclen(\Cx,\Cy)*sqrt(\e)*sin(\ang); % vertical radius
    \b = veclen(\Cx,\Cy)*tan(\ang)*sqrt(1-\e*sin(\ang)^2); % horizontal radius
    \angb = acos(sqrt(\e)*sin(\ang)); % angle of P in ellipse
  }
  \coordinate (ML) at ($(M)+(\vang-180:\x pt)+(\vang+90:\y pt)$); % tangency
  
  % JETS
  \draw[thin,red!40!black,rotate=\vang, %,fill=red!70!black!60
        top color=red!70!black!60,bottom color=red!50!black!70,shading angle=\vang] % base
    (M) ellipse({\a pt} and {\b pt});
  \jetcone[green!80!black]{O}{BJ}{14}{0.10}
  \jetcone{O}{J1}{16}{0.08}
  \jetcone{O}{J2}{16}{0.10}
  \draw[thin,red!40!black,fill opacity=0.9,rotate=\vang, %,fill=red!90!black!40
        top color=red!90!black!40,bottom color=red!80!black!50,shading angle=\vang]
    (ML) arc(180-\angb:180+\angb:{\a pt} and {\b pt})
    -- ($(O)-(\vang:0.03)$) -- cycle;
  
  \node[green!50!black] at (56:1.26*\R) {b};
  \node[blue!80!black,right] at (0:1.05*\R) {${\color{red!80!black}\mathrm{W} \to}\; qq$};
\end{tikzpicture}


% BOOSTED TOP JETS, fully merged
\begin{tikzpicture}
  \edef\ang{35}
  \edef\e{0.05}
  \coordinate (O) at (0,0);
  \coordinate (BJ) at ( 31:1.15*\R); % b jet 1
  \coordinate (J1) at (  9:1.00*\R); % q jet 1
  \coordinate (J2) at (-11:1.00*\R); % q jet 2
  \coordinate (M) at (13:0.80*\R); % merged
  \edef\vang{\pgfmathresult} % angle of vector OV
  \tikzmath{
    coordinate \C;
    \C = (O)-(M);
    \x = veclen(\Cx,\Cy)*\e*sin(\ang)^2; % x coordinate P
    \y = tan(\ang)*(veclen(\Cx,\Cy)-\x); % y coordinate P
    \a = veclen(\Cx,\Cy)*sqrt(\e)*sin(\ang); % vertical radius
    \b = veclen(\Cx,\Cy)*tan(\ang)*sqrt(1-\e*sin(\ang)^2); % horizontal radius
    \angb = acos(sqrt(\e)*sin(\ang)); % angle of P in ellipse
  }
  \coordinate (ML) at ($(M)+(\vang-180:\x pt)+(\vang+90:\y pt)$); % tangency
  
  % JETS
  \draw[thin,red!40!black,rotate=\vang, %,fill=red!70!black!60
        top color=red!70!black!60,bottom color=red!50!black!70,shading angle=\vang] % base
    (M) ellipse({\a pt} and {\b pt});
  \jetcone[green!80!black]{O}{BJ}{12}{0.10}
  \jetcone{O}{J1}{16}{0.08}
  \jetcone{O}{J2}{16}{0.10}
  \draw[thin,red!40!black,fill opacity=0.9,rotate=\vang, %,fill=red!90!black!40
        top color=red!90!black!40,bottom color=red!80!black!50,shading angle=\vang]
    (ML) arc(180-\angb:180+\angb:{\a pt} and {\b pt})
    -- ($(O)-(\vang:0.03)$) -- cycle;
  
  \node[green!50!black] at (31:1.3*\R) {b};
  \node[blue!80!black,right] at (0:1.05*\R) {$\mathrm{W} \to qq$};
\end{tikzpicture}


\end{document}