{{latex:tikz:impact_parameters1.png ? 0x1000 }} {{latex:tikz:impact_parameters2.png ? 0x1000 }} {{latex:tikz:impact_parameters3.png ? 0x1000 }} Impact parameters using projections with the ''calc'' package. For more, please visit https://tikz.net/category/physics/particle-physics/. % 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}% } \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} \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} %% Simple projection %\begin{tikzpicture} % \coordinate (A) at (0,0); % \coordinate (B) at (4,3); % \coordinate (C) at (0.5,3); % \draw (A) -- (B); % \draw [blue] (C) -- ($(A)!(C)!(B)$); %\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 (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) -- ($(PV)!1.50!(SV)$); \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=-80] ++(\angJpsi+15:2.5) node[above left=-4] {$\mu^+$}; \draw[->,red,line width=1] (SV) to[out=\angJpsi-5,in=-140] ++(\angJpsi-20:2.4) node[above right] {$\mu^-$}; % 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[above 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] {$\ell_z(\Jpsi)$}; %\draw[smallarr,shorten <=4,Jpsicol] %,dashed % (PV) -- ($(Jp1)!(PV)!(Jp2)$) node[scale=0.85,left=3,midway,below=1] {$\delta(\Jpsi)$}; \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) -- ($(PV)!1.50!(SV)$); % 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[above 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 tau nu \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) -- ($(PV)!1.50!(SV)$); \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=-80] ++(\angJpsi+20:2.1) node[above left=-4] {$\mu^+$}; \draw[->,red,line width=1] (SV) to[out=\angJpsi-5,in=-140] ++(\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 tau nu \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 (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) -- ($(PV)!1.50!(SV)$); \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=-80] ++(\angJpsi+15:2.5) node[above left=-4] {$\mu^+$}; \draw[->,line width=1] (SV) to[out=\angJpsi-5,in=-140] ++(\angJpsi-20:2.4) node[above right] {$\mu^-$}; % TAU \draw[thick,green!70!black] (SV) --++ (23:0.6) coordinate (T) node[midway,below right=-2] {$\tau^+$}; \fill[green!70!black] (T) circle (0.06); % PIONS \draw[->,green!70!black,line width=1] (T) to[out=28,in=-130] ++(38:2.0) node[above right] {$\pi^\pm$}; \draw[->,green!70!black,line width=1] (T) to[out=20,in=-150] ++(24:2.6) node[above right] {$\pi^\pm$}; \draw[->,green!70!black,line width=1] (T) to[out=16,in=170] ++( 2:2.0) node[above right] {$\pi^\mp$}; % 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}