Impact parameter of semileptonic B hadron decay in proton collisions, with tau decay to three pions.
% Author: Izaak Neutelings (October 2019)
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{esvect} % \vv
\usepackage{tikz}
\usetikzlibrary{patterns,decorations.pathmorphing}
\tikzset{>=latex}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{angles,quotes} % for pic
\newcommand\Bc{{\mathrm{B}}}
\newcommand\Jpsi{{\mathrm{J}\!/\!\psi}}
\newcommand{\tikzAngleOfLine}{\tikz@AngleOfLine}
\def\tikz@AngleOfLine(#1)(#2)#3{%
\pgfmathanglebetweenpoints{%
\pgfpointanchor{#1}{center}}{%
\pgfpointanchor{#2}{center}}
\pgfmathsetmacro{#3}{\pgfmathresult}%
}
%\tikzstyle{mydashed}=[dash pattern=on 1.5pt off 1.5pt]
\colorlet{beamcol}{orange!40!yellow!95!black}
\colorlet{SVcol}{green!50!blue!80!white}
\colorlet{Bccol}{green!80!blue!90!black}
\colorlet{Jpsicol}{red!90!black}
\colorlet{taucol}{orange!95!black}
\colorlet{mygreen}{green!70!black}
\tikzset{
ext/.style={shorten >=-#1,shorten <=-#1},
ext/.default=1cm,
smallarr/.style={{Latex[length={#1*4},width={#1*2.5}]}-{Latex[length={#1*4},width={#1*2.5}]}},
smallarr/.default=1,
}
\begin{document}
% Bc -> J/psi tau nu
\begin{tikzpicture}
\def\angJpsi{80}
\coordinate (BL) at (-1,0);
\coordinate (BR) at ( 3,0);
\coordinate (PV) at ( 0,0);
\coordinate (SV) at ( 2.0,1.8);
\coordinate (T) at ($(SV)+(20:0.6)$);
\coordinate (Jp1) at ($(SV)+({\angJpsi-180}:2.6)$);
\coordinate (Jp2) at ($(SV)+(\angJpsi:2.8)$);
% DASHES
\draw[beamcol,dashed,name path=beam]
(BL) -- (BR);
\draw[SVcol,dashed]
(PV) -- (SV) -- ($(PV)!1.54!(SV)$);
\draw[->,Jpsicol,dashed,line width=1,name path=mumu]
(Jp1) -- (Jp2) node[right=9,above] {$\vec{p}_{\mu\mu} = \vec{p}_\Jpsi$};
% MUONS
\draw[->,red,line width=1]
(SV) to[out=\angJpsi+5,in=\angJpsi-160] ++(\angJpsi+15:2.5) node[above left=-4] {$\mu^+$};
\draw[->,red,line width=1]
(SV) to[out=\angJpsi-5,in=\angJpsi-220] ++(\angJpsi-20:2.4) node[above right] {$\mu^-$};
% TAU
\draw[thick,taucol] %,mydashed]
(SV) to[out=11,in=-148,looseness=0.6] (T);
\path (SV) -- (T) node[taucol,pos=0.4,below right=-3] {$\tau^\pm$};
% PIONS
\draw[->,taucol,line width=1]
(T) to[out=28,in=-130] ++(38:2.4) node[above right] {$\pi^\pm$};
\draw[->,taucol,line width=1]
(T) to[out=20,in=-150] ++(24:3.0) node[above right] {$\pi^\pm$};
\draw[->,taucol,line width=1]
(T) to[out=16,in=170] ++( 2:2.4) node[right] {$\pi^\mp$};
\fill[taucol!80!black]
(T) circle (0.06);
% BLOBS
\fill[beamcol]
(PV) ellipse (9pt and 4.5pt)
node[beamcol!95!black,above left=3] {$\mathrm{b}\overline{\mathrm{b}}$ PV};
\fill[SVcol]
(SV) circle (4pt) node[above left] {SV};
% LABELS
\draw[smallarr,shorten <=4,Jpsicol,name intersections={of=beam and mumu,name=beam-mumu}]
([yshift=2]PV) -- ([yshift=2]beam-mumu-1) node[scale=0.85,right=6,midway,above=-2] {$\ell_z(\Jpsi)$};
%\draw[smallarr,shorten <=4,Jpsicol] %,dashed
% (PV) -- ($(Jp1)!(PV)!(Jp2)$) node[scale=0.85,left=3,midway,below=1] {$\delta(\Jpsi)$};
\end{tikzpicture}
% Bc -> J/psi tau nu - no J/psi pT
\begin{tikzpicture}
\def\angJpsi{95}
\coordinate (BL) at (-1,0);
\coordinate (BR) at ( 3,0);
\coordinate (PV) at ( 0,0);
\coordinate (SV) at ( 2.0,1.8);
\coordinate (T) at ($(SV)+(20:0.6)$);
\coordinate (Jp1) at ($(SV)+({\angJpsi-180}:2.6)$);
\coordinate (Jp2) at ($(SV)+(\angJpsi:2.8)$);
% DASHES
\draw[beamcol,dashed,name path=beam]
(BL) -- (BR);
\draw[SVcol,dashed]
(PV) -- (SV) -- ($(PV)!1.54!(SV)$);
% MUONS
\draw[->,red,line width=1]
(SV) to[out=\angJpsi+5,in=\angJpsi-160] ++(\angJpsi+15:2.5) node[above left=-4] {$\mu^+$};
\draw[->,red,line width=1]
(SV) to[out=\angJpsi-5,in=\angJpsi-220] ++(\angJpsi-20:2.4) node[above right] {$\mu^-$};
% TAU
\draw[thick,taucol] %,mydashed]
(SV) to[out=11,in=-148,looseness=0.6] (T);
\path (SV) -- (T) node[taucol,pos=0.4,below right=-3] {$\tau^\pm$};
% PIONS
\draw[->,taucol,line width=1]
(T) to[out=28,in=-130] ++(38:2.4) node[above right] {$\pi^\pm$};
\draw[->,taucol,line width=1]
(T) to[out=20,in=-150] ++(24:3.0) node[above right] {$\pi^\pm$};
\draw[->,taucol,line width=1]
(T) to[out=16,in=170] ++( 2:2.4) node[right] {$\pi^\mp$};
\fill[taucol!80!black]
(T) circle (0.06);
% BLOBS
\fill[beamcol]
(PV) ellipse (9pt and 4.5pt)
node[beamcol!95!black,above left=3] {$\mathrm{b}\overline{\mathrm{b}}$ PV};
\fill[SVcol]
(SV) circle (4pt) node[above=2,left=1] {SV};
\end{tikzpicture}
% Bs -> tau(mu) tau(3pi) 2nu
\begin{tikzpicture}
\def\angJpsi{80}
\coordinate (BL) at (-1,0);
\coordinate (BR) at ( 3,0);
\coordinate (PV) at ( 0,0);
\coordinate (SV) at ( 2.0,1.8);
\coordinate (Jp1) at ($(SV)+({\angJpsi-184}:2.6)$);
\coordinate (Jp2) at ($(SV)+(\angJpsi+6:2.6)$);
% DASHES
\draw[beamcol,dashed,name path=beam]
(BL) -- (BR);
\draw[SVcol,dashed]
(PV) -- (SV) -- ($(PV)!1.54!(SV)$);
% MUONS
\draw[Jpsicol,line width=1,dashed,name path=mumu]
(Jp1) to[out=74,in=-100] (SV);
\draw[->,Jpsicol,line width=1]
(SV) to[out=80,in=-86] (Jp2) node[right=9,above] {$\mu^\mp$};
% PIONS
\draw[->,taucol,line width=1]
(SV) to[out=28,in=-130] ++(38:2.0) node[above right] {$\pi^\pm$};
\draw[->,taucol,line width=1]
(SV) to[out=20,in=-150] ++(24:2.6) node[above right] {$\pi^\pm$};
\draw[->,taucol,line width=1]
(SV) to[out=16,in=170] ++( 2:2.0) node[right] {$\pi^\mp$};
% BLOBS
\fill[beamcol]
(PV) ellipse (9pt and 4.5pt)
node[beamcol!95!black,above left=3] {$\mathrm{b}\overline{\mathrm{b}}$ PV};
\fill[SVcol]
(SV) circle (4pt) node[above left] {SV};
% LABELS
\draw[smallarr,shorten <=4,Jpsicol,name intersections={of=beam and mumu,name=beam-mumu}]
([yshift=2]PV) -- ([yshift=2]beam-mumu-1) node[scale=0.85,right=6,midway,above=-2] {$\ell_z(\mu)$};
%\draw[smallarr,shorten <=4,Jpsicol] %,dashed
% (PV) -- ($(Jp1)!(PV)!(SV)$) node[scale=0.85,left=3,midway,below=1] {$\delta(\mu)$};
\end{tikzpicture}
% Bc -> J/psi + 3rd mu
\begin{tikzpicture}
\def\angJpsi{70}
\coordinate (BL) at (-1,0);
\coordinate (BR) at ( 3,0);
\coordinate (PV) at ( 0,0);
\coordinate (SV) at ( 2.2,1.8);
\coordinate (Jp1) at ($(SV)+({\angJpsi-180}:2.6)$);
\coordinate (Jp2) at ($(SV)+(\angJpsi:2.4)$);
% DASHES
\draw[beamcol,dashed,name path=beam]
(BL) -- (BR);
\draw[SVcol,dashed]
(PV) -- (SV) -- ($(PV)!1.54!(SV)$);
\draw[->,Jpsicol,dashed,line width=1,name path=mumu]
(Jp1) -- (Jp2) node[right=9,above] {$\vec{p}_{\mu\mu} = \vec{p}_\Jpsi$};
\draw[Jpsicol,dashed]
(PV) -- ($(Jp1)!(PV)!(Jp2)$);
% MUONS
\draw[->,red,line width=1]
(SV) to[out=\angJpsi+5,in=\angJpsi-150] ++(\angJpsi+20:2.1) node[above left=-4] {$\mu^+$};
\draw[->,red,line width=1]
(SV) to[out=\angJpsi-5,in=\angJpsi-220] ++(\angJpsi-20:2) node[above right] {$\mu^-$};
\draw[->,taucol,line width=1]
(SV) to[out=30,in=-170] ++(20:2.4) node[above left] {$\mu^\text{3rd}$};
% BLOBS
\fill[beamcol]
(PV) ellipse (9pt and 4.5pt)
node[beamcol!95!black,above left=3] {$\mathrm{b}\overline{\mathrm{b}}$ PV};
\fill[SVcol]
(SV) circle (4pt) node[above left] {SV};
% LABELS
\draw[smallarr,shorten <=4,Jpsicol,name intersections={of=beam and mumu,name=beam-mumu}]
(PV) -- (beam-mumu-1) node[scale=0.85,right=6,midway,above=-2] {$\ell_z(\Jpsi)$};
\draw[smallarr,shorten <=4,Jpsicol] %,dashed
(PV) -- ($(Jp1)!(PV)!(Jp2)$) node[scale=0.85,left=3,midway,below=1] {$\delta(\Jpsi)$};
\end{tikzpicture}
% Bc -> J/psi + 3rd mu
\begin{tikzpicture}
\def\angJpsi{78}
\def\angBc{48}
\def\qlab{0.79}
\coordinate (BL) at (-1,0);
\coordinate (BR) at ( 4.5,0);
\coordinate (PV) at ( 0,0);
\coordinate (SV) at ( 3.4,1.6);
\coordinate (Jp1) at ($(SV)+({\angJpsi-180}:3.2)$);
\coordinate (Jp2) at ($(SV)+(\angJpsi:2.4)$);
\coordinate (Bc1) at ($(SV)+({\angBc-180}:4.1)$);
\coordinate (Bc2) at ($(SV)+(\angBc:3.3)$);
\coordinate (SV2) at ($(PV)!1.50!(SV)$);
% DASHES
\draw[beamcol,dashed,name path=beam]
(BL) -- (BR);
\draw[SVcol,dashed]
(PV) -- (SV) -- (SV2);
\draw[->,Jpsicol,dashed,line width=1,name path=Jpsi]
(Jp1) -- (Jp2) node[right=9,above] {$\vec{p}_{\mu\mu} = \vec{p}_\Jpsi$};
\draw[->,Bccol,dashed,line width=1,name path=Bc]
(Bc1) -- (Bc2) node[left=10,above right] {$\vec{p}_{\mu\mu\mu} = \vec{p}_\mathrm{B}$};
% MUONS
\draw[->,red,line width=1]
(SV) to[out={\angJpsi+5},in={\angJpsi-150}] ++({\angJpsi+18}:2.1) node[above left=-4] {$\mu^+$};
\draw[->,red,line width=1]
(SV) to[out={\angJpsi-8},in={\angJpsi-210}] ++({\angJpsi-20}:2) node[right=2,above] {$\mu^-$};
\draw[->,taucol,line width=1]
(SV) to[out=38,in=-160] ++(29:3.1) node[above=2,above right] {$\mu^\text{3rd}$}; %{3^\text{rd}}
% BLOBS
\fill[beamcol]
(PV) ellipse (9pt and 4.5pt)
node[beamcol!95!black,above left=3] {$\mathrm{b}\overline{\mathrm{b}}$ PV};
\fill[SVcol]
(SV) circle (4pt) node[above left] {SV};
% LABELS
\draw[smallarr,shorten <=6,Bccol!90!black,
name intersections={of=beam and Bc,name=beam-Bc}]
([yshift=2]PV) -- ([yshift=2]beam-Bc-1)
node[scale=\qlab,right=14,midway,above=-1] {$\ell_z(\Bc)$};
\draw[smallarr,shorten <=6,Jpsicol!90!black,
name intersections={of=beam and Jpsi,name=beam-Jpsi}]
([yshift=-0.3]PV) -- ([yshift=-0.3]beam-Jpsi-1)
node[scale=\qlab,left=15,above=-1] {$\ell_z(\Jpsi)$};
\draw[smallarr,shorten <=4,Bccol] %,dashed
(PV) -- ($(Bc1)!(PV)!(Bc2)$)
node[scale=\qlab,left=3,midway,below=2] {$\delta(\Bc)$};
\draw[smallarr,shorten <=6,Jpsicol] %,dashed
(PV) -- ($(Jp1)!(PV)!(Jp2)$)
node[scale=\qlab,below=4,left=10] {$\delta(\Jpsi)$};
\draw[smallarr,shorten <=5,shorten >=2,SVcol!70!black] %,dashed
([shift={(120:0.01)}]PV) -- ([shift={(120:0.01)}]SV)
node[scale=\qlab,midway,above=1] {$\ell$};
% ANGLES
\tikzAngleOfLine(SV)(Jp2){\angJp}
\tikzAngleOfLine(SV)(Jp1){\angJpb}
\tikzAngleOfLine(SV)(Bc2){\angBc}
\tikzAngleOfLine(SV)(Bc1){\angBcb}
\tikzAngleOfLine(SV)(SV2){\angSV}
\draw[smallarr=0.9,blue] (SV)+(\angSV:0.8)
node[scale=\qlab,right=2,below=0] {$\alpha(\Jpsi)$} arc (\angSV:\angJp:0.8);
\draw[smallarr=0.9,blue] (SV)+(\angSV:1.4)
node[scale=\qlab,right=7,below=-2] {$\alpha(\Bc)$} arc (\angSV:\angBc:1.4);
\draw[smallarr=0.9,blue] (SV)+(\angJpb:0.9)
node[scale=\qlab,right] {$\alpha(\Jpsi,\Bc)$} arc (\angJpb:\angBcb:0.9);
\end{tikzpicture}
% Bc -> J/psi tau nu
\begin{tikzpicture}
\def\angJpsi{80}
\coordinate (BL) at (-1,0);
\coordinate (BR) at ( 3,0);
\coordinate (PV) at ( 0,0);
\coordinate (SV) at ( 2.0,1.8);
\coordinate (T) at ($(SV)+(20:0.6)$);
\coordinate (Jp1) at ($(SV)+({\angJpsi-180}:1.2)$);
\coordinate (Jp2) at ($(SV)+(\angJpsi:2.8)$);
% DASHES
\draw[dashed,name path=beam]
(BL) -- (BR);
\draw[dashed]
(PV) -- (SV) -- ($(PV)!1.54!(SV)$);
\draw[->,dashed,line width=1,name path=mumu]
(Jp1) -- (Jp2) node[right=9,above] {$\vec{p}_{\mu\mu} = \vec{p}_\Jpsi$};
% MUONS
\draw[->,line width=1]
(SV) to[out=\angJpsi+5,in=\angJpsi-160] ++(\angJpsi+15:2.5) node[above left=-4] {$\mu^+$};
\draw[->,line width=1]
(SV) to[out=\angJpsi-5,in=\angJpsi-220] ++(\angJpsi-20:2.4) node[above right] {$\mu^-$};
% TAU
\draw[thick,mygreen] %,mydashed]
(SV) to[out=11,in=-148,looseness=0.6] (T);
\path (SV) -- (T) node[mygreen,pos=0.4,below right=-3] {$\tau^\pm$};
% PIONS
\draw[->,mygreen,line width=1]
(T) to[out=28,in=-130] ++(38:2.4) node[above right] {$\pi^\pm$};
\draw[->,mygreen,line width=1]
(T) to[out=20,in=-150] ++(24:3.0) node[above right] {$\pi^\pm$};
\draw[->,mygreen,line width=1]
(T) to[out=16,in=170] ++( 2:2.4) node[above right] {$\pi^\mp$};
\fill[mygreen]
(T) circle (0.06);
% BLOBS
\fill[]
(PV) ellipse (9pt and 4.5pt)
node[above left=3] {$\mathrm{b}\overline{\mathrm{b}}$ PV};
\fill[]
(SV) circle (4pt) node[above left] {B SV};
%\draw[smallarr,shorten <=4,Jpsicol] %,dashed
% (PV) -- ($(Jp1)!(PV)!(Jp2)$) node[scale=0.85,left=3,midway,below=1] {$\delta(\Jpsi)$};
\end{tikzpicture}
\end{document}
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