Different modes of tau decay to hadron, their intermediate resonances and the interaction with high-energy physics detectors (tracker, ECAL, HCAL), such as CMS. For the four-pion (“3-prong plus pi0”) decay mode, an intermediated resonance of ρ’ was assumed, see this CLEO paper. For more related figures, please see the “decay” tag or Particle Physics category.
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% Author: Izaak Neutelings (July 2017) \documentclass[border=3pt,tikz]{standalone} %\documentclass{article} \usepackage{amsmath} % for \text \usepackage{tikz} \tikzset{>=latex} % for LaTeX arrow head \colorlet{myblue}{blue!40!black} %\definecolor{mylightblue}{RGB}{172,188,63} %\definecolor{mylightgreen}{RGB}{150,220,150} % split figures into pages %\usepackage[active,tightpage]{preview} %\PreviewEnvironment{tikzpicture} %\setlength\PreviewBorder{1pt}% % vertical custom shading %https://tex.stackexchange.com/questions/191735/is-it-possible-to-define-the-position-of-top-bottom-and-middle-color-in-fill \makeatletter \tikzset{vertical custom shading/.code={% \pgfmathsetmacro\tikz@vcs@middle{#1} \pgfmathsetmacro\tikz@vcs@bottom{\tikz@vcs@middle/2} \pgfmathsetmacro\tikz@vcs@top{(100-\tikz@vcs@middle)/2+\tikz@vcs@middle} \pgfdeclareverticalshading[tikz@axis@top,tikz@axis@middle,tikz@axis@bottom]{newaxis}{100bp}{% color(0bp)=(tikz@axis@bottom); color(\tikz@vcs@bottom bp)=(tikz@axis@bottom); color(\tikz@vcs@middle bp)=(tikz@axis@middle); color(\tikz@vcs@top bp)=(tikz@axis@top); color(100bp)=(tikz@axis@top)} \pgfkeysalso{/tikz/shading=newaxis} } } \makeatother \begin{document} % arrow style \usetikzlibrary{decorations.markings} \tikzset{->-/.style={decoration={markings, mark=at position .7 with {\arrow{>}}}, postaction={decorate}}} % photon \usetikzlibrary{decorations.pathmorphing} \tikzset{photon/.style={decorate, decoration={snake,segment length=5,amplitude=1.1}}} % cone style \usetikzlibrary{shadows.blur} \tikzset{mycone/.pic={ \shadedraw[top color=white, bottom color=black!50,shading angle=50,vertical custom shading=10] (-0.4,0.99) -- (0,0) -- (0.4,0.99); \shadedraw[top color=white, bottom color=black!20,shading angle=90] (0,1) ellipse (0.4 and 0.12);}} % TAU DECAY MODES 0, 1, 10, 11 \begin{tikzpicture}[scale=0.9] \large \def\R{120} % inner radius \def\hca{5} % half central angle \def\hcl{\R*sin(\hca)} % half chord length c = 2Rsin(theta/2) \def\tracker{3} % tracker \def\ECAL{4.8} % ECAL \def\HCAL{7.2} % HCAL \def\hclmax{(\R+\HCAL)*sin(\hca)} % mac % detectors \foreach \r in {\tracker,\ECAL,\HCAL}{ \draw[thick] (0,\r) arc (90:90-\hca:\R+\r) (0,\r) arc (90:90+\hca:\R+\r); } \node[left=0,above left] at ({1.08*\hclmax},{0.10*\tracker}) {tracker}; \node[left=0,above left] at ({1.08*\hclmax},\tracker) {ECAL}; \node[left=0,above left] at ({1.08*\hclmax},\ECAL) {HCAL}; % DM 0 \begin{scope}[shift={({-0.79*\hcl},0)}, rotate=6] \node[below] at (0,0) {$\tau^\pm$}; \node[left=5,below=18] at (0,0) {$\tau^\pm\to\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-30] % neutrinos (tau) --+ (0,1.3) node[right=6pt,above] {$\nu_\tau$}; \draw[->-, thick,rotate=12] % pion (tau) --+ (0,3.9) node[left=10,above=38] {$\pi^\pm$} pic[rotate=20,scale=1.2] {mycone}; \end{scope} % DM 1 \begin{scope}[shift={({-0.46*\hcl},0)}, rotate=1] \node[below] at (0,0) {$\tau^\pm$}; \node[right=14,below=18] at (0,0) {$\tau^\pm\to\rho^\pm\nu_\tau\to\pi^\pm\pi^0\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick] % neutrinos (tau) --+ (45:1.5) node[above right] {$\nu_\tau$}; \draw[->-,thick] % rho (tau) --+ (115:0.7) coordinate (rho) node[midway,left] {$\rho^\pm$}; \draw[->-,thick] % pion (rho) --+ (114:3.5) node[left=15,above=38] {$\pi^\pm$} pic[rotate=22,scale=1.2] {mycone}; \draw[->-,densely dashed,thick] % pion0 (rho) --+ (72:0.7) coordinate (pion0) node[midway,right] {$\pi^0$}; \draw[photon] % photon 1 (pion0) --+ (100:0.9) node[left=8,above=32] {$\gamma$} pic[rotate=11.5,xscale=0.8] {mycone}; \draw[photon] % photon 2 (pion0) --+ (60:1.0) node[right=15,above=30] {$\gamma$} pic[rotate=-24,xscale=0.8] {mycone}; \end{scope} % DM 10 \begin{scope}[shift={({0.01*\hcl},0)}, rotate=-3] \node[below] (0,0) {$\tau^\pm$}; \node[right=30,below=18] at (0,0) {$\tau^\pm\to\text{a}_1^\pm\nu_\tau\to\pi^\pm\pi^\mp\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick] % neutrinos (tau) --+ (40:1.5) node[above right] {$\nu_\tau$}; \draw[->-,thick] % a1 (tau) --+ (110:0.5) coordinate (a1) node[midway,left] {$\text{a}_1^\pm$}; \draw[->-,thick] % rho (a1) --+ (124:0.8) coordinate (rho) node[midway,left] {$\rho^0$}; \draw[->-,thick] % pion 1 (rho) --+ (126:3.4) node[left=10,above=38] {$\pi^\pm$} pic[rotate=20,scale=1.2] {mycone}; \draw[->-,thick] % pion 2 (rho) --+ (85:2.8) node[right=15,above=38] {$\pi^\mp$} pic[rotate=-12,scale=1.2] {mycone}; \draw[->-,thick] % pion 3 (a1) --+ (66:4.0) node[right=18,above=38] {$\pi^\pm$} pic[rotate=-22,scale=1.2] {mycone}; \end{scope} % DM 11 \begin{scope}[shift={({0.64*\hcl},0)}, rotate=-6] \node[below] (0,0) {$\tau^\pm$}; \node[right=18,below=18] at (0,0) {$\tau^\pm\to\rho'^\pm\nu_\tau\to\pi^\pm\pi^\mp\pi^\pm\pi^0\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (88:0.5) coordinate (tau); \draw[->-,dotted,thick] % neutrinos (tau) --+ (18:1.4) node[right] {$\nu_\tau$}; \draw[->-,thick] % rho' (tau) --+ (110:0.5) coordinate (rho') node[midway,below=4,left=-1] {$\rho'^\pm$}; \draw[->-,thick] % a1 (rho') --+ (130:0.6) coordinate (a1) node[midway,below=2,left] {$\text{a}_1^\pm$}; \draw[->-,thick] % rho (a1) --+ (149:0.6) coordinate (rho) node[midway,below=3,left] {$\rho^0$}; \draw[->-,thick] % pion 1 (rho) --+ (119:3.0) node[left=10,above=38] {$\pi^\pm$} pic[rotate=16,scale=1.2] {mycone}; \draw[->-, thick] % pion 2 (rho) --+ (86:2.8) node[right=6,above=40] {$\pi^\mp$} pic[rotate=0,scale=1.2] {mycone}; \draw[->-,thick] % pion 3 (a1) --+ (72:3.3) node[right=20,above=37] {$\pi^\pm$} pic[rotate=-22,scale=1.2] {mycone}; \draw[->-,densely dashed,thick] % pion0 (rho') --+ (40:1.2) coordinate (pion0) node[midway,above=0,right=4] {$\pi^0$}; \draw[photon] % photon 1 (pion0) --+ (68:1.2) node[right=10,above=30] {$\gamma$} pic[rotate=-19,xscale=0.8] {mycone}; \draw[photon] % photon 2 (pion0) --+ (40:1.8) node[right=21,above=25] {$\gamma$} pic[rotate=-36,xscale=0.8] {mycone}; \end{scope} \end{tikzpicture} % TAU DECAY MODES 0, 1, 2, 10 \begin{tikzpicture}[scale=0.9] \large \def\R{120} % inner radius \def\hca{5} % half central angle \def\hcl{\R*sin(\hca)} % half chord length c = 2Rsin(theta/2) \def\tracker{3} % tracker \def\ECAL{4.8} % ECAL \def\HCAL{7.2} % HCAL \def\hclmax{(\R+\HCAL)*sin(\hca)} % mac % detectors \foreach \r in {\tracker,\ECAL,\HCAL}{ \draw[thick] (0,\r) arc (90:90-\hca:\R+\r) (0,\r) arc (90:90+\hca:\R+\r); } \node[left=0,above left] at ({1.08*\hclmax},{0.10*\tracker}) {tracker}; \node[left=0,above left] at ({1.08*\hclmax},\tracker) {ECAL}; \node[left=0,above left] at ({1.08*\hclmax},\ECAL) {HCAL}; % DM 0 \begin{scope}[shift={({-0.79*\hcl},0)}, rotate=6] \node[below] at (0,0) {$\tau^\pm$}; \node[below=18] at (0,0) {$\tau^\pm\to\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-30] % neutrinos (tau) --+ (0,1.3) node[right=6pt,above] {$\nu_\tau$}; \draw[->-, thick,rotate=12] % pion (tau) --+ (0,3.9) node[left=10,above=38] {$\pi^\pm$} pic[rotate=20,scale=1.2] {mycone}; \end{scope} % DM 1 \begin{scope}[shift={({-0.44*\hcl},0)}, rotate=1] \node[below] at (0,0) {$\tau^\pm$}; \node[right=8pt,below=18] at (0,0) {$\tau^\pm\to\rho^\pm\nu_\tau\to\pi^\pm\pi^0\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-45] % neutrinos (tau) --+ (0,1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick,rotate= 15] % rho (tau) --+ (0,0.7) coordinate (rho) node[midway,left] {$\rho^\pm$}; \draw[->-, thick,rotate= 24] % pion (rho) --+ (0,3.4) node[left=15,above=38] {$\pi^\pm$} pic[rotate=22,scale=1.2] {mycone}; \draw[->-,densely dashed,thick,rotate=-18] % pion0 (rho) --+ (0,0.7) coordinate (pion0) node[midway,right] {$\pi^0$}; \draw[photon,rotate=10] % photon 1 (pion0) --+ (0,0.9) node[left=8,above=32] {$\gamma$} pic[rotate=11.5,xscale=0.8] {mycone}; \draw[photon,rotate=-30] % photon 2 (pion0) --+ (0,1.0) node[right=15,above=30] {$\gamma$} pic[rotate=-24,xscale=0.8] {mycone}; \end{scope} % DM 2 \begin{scope}[shift={({0.09*\hcl},0)}, rotate=-3] \node[below] (0,0) {$\tau^\pm$}; \node[right=14pt,below=18] at (0,0) {$\tau^\pm\to\text{a}_1^\pm\nu_\tau\to\pi^\pm\pi^0\pi^0\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-50] % neutrinos (tau) --+ (0,1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick,rotate= 20] % a1 (tau) --+ (0,0.5) coordinate (a1) node[midway,left] {$\text{a}_1^\pm$}; \draw[->-, thick,rotate= 34] % rho (a1) --+ (0,0.8) coordinate (rho) node[midway,left] {$\rho^\pm$}; \draw[->-, thick,rotate= 38] % pion (rho) --+ (0,3.5) node[left=15,above=38] {$\pi^\pm$} pic[rotate=22,scale=1.2] {mycone}; \draw[->-,densely dashed,thick,rotate=-35] % pion0 (a1) --+ (0,0.8) coordinate (pion01) node[midway,right] {$\pi^0$}; \draw[->-,densely dashed,thick,rotate=-14] % pion0 (rho) --+ (0,0.6) coordinate (pion02) node[midway,right] {$\pi^0$}; \draw[photon,rotate= 26] % photon 1 (pion02) --+ (0,0.6) node[left=8,above=32] {$\gamma$} pic[rotate=11.5,xscale=0.8] {mycone}; \draw[photon,rotate=-20] % photon 2 (pion02) --+ (0,0.6) node[right=12,above=32] {$\gamma$} pic[rotate=-22,xscale=0.8] {mycone}; \draw[photon,rotate=-24] % photon 3 (pion01) --+ (0,1.3) node[right=10,above=32] {$\gamma$} pic[rotate=-20,xscale=0.8] {mycone}; \draw[photon,rotate=-46] % photon 4 (pion01) --+ (0,1.8) node[right=25,above=26] {$\gamma$} pic[rotate=-36,xscale=0.8] {mycone}; \end{scope} % DM 10 \begin{scope}[shift={({0.64*\hcl},0)}, rotate=-10] \node[below] (0,0) {$\tau^\pm$}; \node[right=14pt,below=18] at (0,0) {$\tau^\pm\to\text{a}_1^\pm\nu_\tau\to\pi^\pm\pi^\mp\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-50] % neutrinos (tau) --+ (0,1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick,rotate= 20] % a1 (tau) --+ (0,0.5) coordinate (a1) node[midway,left] {$\text{a}_1^\pm$}; \draw[->-, thick,rotate= 34] % rho (a1) --+ (0,0.8) coordinate (rho) node[midway,left] {$\rho^0$}; \draw[->-, thick,rotate= 36] % pion 1 (rho) --+ (0,3.0) node[left=10,above=38] {$\pi^\pm$} pic[rotate=20,scale=1.2] {mycone}; \draw[->-, thick,rotate= -5] % pion 2 (rho) --+ (0,2.7) node[right=15,above=38] {$\pi^\mp$} pic[rotate=-15,scale=1.2] {mycone}; \draw[->-, thick,rotate=-24] % pion 3 (a1) --+ (0,3.9) node[right=29,above=33] {$\pi^\pm$} pic[rotate=-38,scale=1.2] {mycone}; \end{scope} \end{tikzpicture} % TAU DECAY MODES 0, 1, 10 \begin{tikzpicture}[scale=0.9] \large \def\R{70} % inner radius \def\hca{7} % half central angle \def\hcl{\R*sin(\hca)} % half chord length c = 2Rsin(theta/2) \def\tracker{3} % tracker \def\ECAL{4.75} % ECAL \def\HCAL{7.2} % HCAL \def\hclmax{(\R+\HCAL)*sin(\hca)} % mac % detectors \foreach \r in {\tracker,\ECAL,\HCAL}{ \draw[thick] (0,\r) arc (90:90-\hca:\R+\r) (0,\r) arc (90:90+\hca:\R+\r); } \node[left=0,above left] at ({1.08*\hclmax},{0.10*\tracker}) {tracker}; \node[left=0,above left] at ({1.08*\hclmax},\tracker) {ECAL}; \node[left=0,above left] at ({1.08*\hclmax},\ECAL) {HCAL}; % DM 0 \begin{scope}[shift={({-0.64*\hcl},0)}, rotate=8] \node[below] at (0,0) {$\tau^\pm$}; \node[below=18] at (0,0) {$\tau^\pm\to\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-30] % neutrinos (tau) --+ (0,1.3) node[right=6pt,above] {$\nu_\tau$}; \draw[->-, thick,rotate=12] % pion (tau) --+ (0,3.9) node[left=10,above=38] {$\pi^\pm$} pic[rotate=20,scale=1.2] {mycone}; \end{scope} % DM 1 \begin{scope}[shift={({-0.18*\hcl},0)}, rotate=0] \node[below] at (0,0) {$\tau^\pm$}; \node[right=8pt,below=18] at (0,0) {$\tau^\pm\to\pi^\pm\pi^0\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-45] % neutrinos (tau) --+ (0,1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick,rotate= 15] % rho (tau) --+ (0,0.7) coordinate (rho) node[midway,left] {$\rho^\pm$}; \draw[->-, thick,rotate= 24] % pion (rho) --+ (0,3.4) node[left=15,above=38] {$\pi^\pm$} pic[rotate=22,scale=1.2] {mycone}; \draw[->-,densely dashed,thick,rotate=-18] % pion0 (rho) --+ (0,0.7) coordinate (pion0) node[midway,right] {$\pi^0$}; \draw[photon,rotate=10] % photon 1 (pion0) --+ (0,0.9) node[left=8,above=32] {$\gamma$} pic[rotate=11.5,xscale=0.8] {mycone}; \draw[photon,rotate=-30] % photon 2 (pion0) --+ (0,1.0) node[right=15,above=30] {$\gamma$} pic[rotate=-24,xscale=0.8] {mycone}; \end{scope} % DM 10 \begin{scope}[shift={({0.42*\hcl},0)}, rotate=-10] \node[below] (0,0) {$\tau^\pm$}; \node[right=14pt,below=18] at (0,0) {$\tau^\pm\to\pi^\pm\pi^\mp\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick,rotate=-50] % neutrinos (tau) --+ (0,1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick,rotate= 20] % a1 (tau) --+ (0,0.5) coordinate (a1) node[midway,left] {$\text{a}_1^\pm$}; \draw[->-, thick,rotate= 34] % rho (a1) --+ (0,0.8) coordinate (rho) node[midway,left] {$\rho^0$}; \draw[->-, thick,rotate= 36] % pion 1 (rho) --+ (0,3.0) node[left=10,above=38] {$\pi^\pm$} pic[rotate=20,scale=1.2] {mycone}; \draw[->-, thick,rotate= -5] % pion 2 (rho) --+ (0,2.7) node[right=15,above=38] {$\pi^\mp$} pic[rotate=-15,scale=1.2] {mycone}; \draw[->-, thick,rotate=-24] % pion 3 (a1) --+ (0,3.9) node[right=29,above=33] {$\pi^\pm$} pic[rotate=-38,scale=1.2] {mycone}; \end{scope} \end{tikzpicture} % TAU DECAY MODE 1 only \begin{tikzpicture}[scale=0.9] \large % photon \usetikzlibrary{decorations.pathmorphing} \tikzset{photon/.style={decorate, decoration={snake,segment length=5,amplitude=1.1}}} % cone style \usetikzlibrary{shadows.blur} \tikzset{mycone/.pic={ \shadedraw[top color=white, bottom color=black!50,shading angle=50,vertical custom shading=10] (-0.4,0.99) -- (0,0) -- (0.4,0.99); \shadedraw[top color=white, bottom color=black!20,shading angle=90] (0,1) ellipse (0.4 and 0.12);}}; \def\R{10} % inner radius \def\hca{12} % half central angle \def\hcl{\R*sin(\hca)} % half chord length c = 2Rsin(theta/2) \def\tracker{3} % tracker \def\ECAL{4.8} % ECAL \def\HCAL{7.2} % HCAL \def\hclmax{(\R+\HCAL)*sin(\hca)} % mac % detectors \foreach \r in {\tracker,\ECAL,\HCAL}{ \draw[thick] (0,\r) arc (90:90-\hca:\R+\r) (0,\r) arc (90:90+\hca:\R+\r); } \node[left=0,above left] at ({1.1*\hclmax},{0.10*\tracker}) {tracker}; \node[left=0,above left] at ({1.1*\hclmax},\tracker) {ECAL}; \node[left=0,above left] at ({1.1*\hclmax},\ECAL) {HCAL}; % DM 1 \begin{scope}[shift={(0,0)}, rotate=0] \node[below] at (0,0) {$\tau^\pm$}; \node[right=8pt,below=18] at (0,0) {$\tau^\pm\to\rho^\pm\nu_\tau\to\pi^\pm\pi^0\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick] % neutrinos (tau) --+ (45:1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick] % rho (tau) --+ (105:0.7) coordinate (rho) node[midway,left] {$\rho^\pm$}; \draw[->-, thick] % pion (rho) --+ (114:3.4) node[left=15,above=38] {$\pi^\pm$} pic[rotate=22,scale=1.2] {mycone}; \draw[->-,densely dashed,thick] % pion0 (rho) --+ (72:0.7) coordinate (pion0) node[midway,right] {$\pi^0$}; \draw[photon] % photon 1 (pion0) --+ (100:0.9) node[left=8,above=32] {$\gamma$} pic[rotate=11.5,xscale=0.8] {mycone}; \draw[photon] % photon 2 (pion0) --+ (60:1.0) node[right=15,above=30] {$\gamma$} pic[rotate=-24,xscale=0.8] {mycone}; \end{scope} \end{tikzpicture} % TAU DECAY MODE 10 only \begin{tikzpicture}[scale=0.9] \large % photon \usetikzlibrary{decorations.pathmorphing} \tikzset{photon/.style={decorate, decoration={snake,segment length=5,amplitude=1.1}}} % cone style \usetikzlibrary{shadows.blur} \tikzset{mycone/.pic={ \shadedraw[top color=white, bottom color=black!50,shading angle=50,vertical custom shading=10] (-0.4,0.99) -- (0,0) -- (0.4,0.99); \shadedraw[top color=white, bottom color=black!20,shading angle=90] (0,1) ellipse (0.4 and 0.12);}}; \def\R{10} % inner radius \def\hca{14} % half central angle \def\hcl{\R*sin(\hca)} % half chord length c = 2Rsin(theta/2) \def\tracker{3} % tracker \def\ECAL{4.8} % ECAL \def\HCAL{7.2} % HCAL \def\hclmax{(\R+\HCAL)*sin(\hca)} % mac % detectors \foreach \r in {\tracker,\ECAL,\HCAL}{ \draw[thick] (0,\r) arc (90:90-\hca:\R+\r) (0,\r) arc (90:90+\hca:\R+\r); } \node[left=0,above left] at ({1.1*\hclmax},{0.10*\tracker}) {tracker}; \node[left=0,above left] at ({1.1*\hclmax},\tracker) {ECAL}; \node[left=0,above left] at ({1.1*\hclmax},\ECAL) {HCAL}; % DM 10 \begin{scope}[shift={(0,0)}, rotate=-3] \node[below] (0,0) {$\tau^\pm$}; \node[right=14pt,below=18] at (0,0) {$\tau^\pm\to\text{a}_1^\pm\nu_\tau\to\pi^\pm\pi^\mp\pi^\pm\nu_\tau$}; \draw[->-,thick] % tau (0,0) -- (0,0.7) coordinate (tau); \draw[->-,dotted,thick] % neutrinos (tau) --+ (40:1.5) node[above right] {$\nu_\tau$}; \draw[->-, thick] % a1 (tau) --+ (110:0.5) coordinate (a1) node[midway,left] {$\text{a}_1^\pm$}; \draw[->-, thick] % rho (a1) --+ (124:0.8) coordinate (rho) node[midway,left] {$\rho^0$}; \draw[->-, thick,rotate= 36] % pion 1 (rho) --+ (0,3.0) node[left=10,above=38] {$\pi^\pm$} pic[rotate=30,scale=1.2] {mycone}; \draw[->-, thick] % pion 2 (rho) --+ (85:2.7) node[right=15,above=38] {$\pi^\mp$} pic[rotate=-5,scale=1.2] {mycone}; \draw[->-, thick] % pion 3 (a1) --+ (66:3.9) node[right=29,above=33] {$\pi^\pm$} pic[rotate=-28,scale=1.2] {mycone}; \end{scope} \end{tikzpicture} \end{document}
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