Basic QED processes (LO)

by Posted on

Some leading-order diagrams of basic QCD processes, inspired by Table 7.1 of Griffith’s Introduction to Elementary Particles (2008).

Click on a diagram to jump to the code & download links below:
basic_QED-001.png basic_QED-002.png basic_QED-003.png basic_QED-004.png basic_QED-005.png basic_QED-006.png basic_QED-007.png basic_QED-008.png basic_QED-009.png basic_QED-010.png basic_QED-011.png

Electron-muon scattering

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{fermion}{i2,v2,o2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{$\mu^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{$\mu^-$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Electron-electron scattering

Electron-electron scattering, also known as Møller scattering. The t-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{fermion}{i2,v2,o2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^-$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

The u-channel, using the style option “rubout” to create a white border around the crossing line:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{phantom}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{phantom}{i2,v2,o2}
    \fmffreeze
    % main - outgoing lines
    \fmf{fermion,rubout}{i1,v1,o2}
    \fmf{fermion}{i2,v2,o1}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^-$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Electron-positron scattering

Electron-positron scattering, also known as Bhabba scattering. The t-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{fermion}{o2,v2,i2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^+$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

The u-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,i2}
    \fmf{boson,label.side=left,label=$\gamma$}{v1,v2} % s-channel
    \fmf{fermion}{o2,v2,o1}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^+$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Compton scattering

Compton scattering between an electron and photon. The t-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,13)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{boson}{i1,v1}
    \fmf{fermion}{o1,v1}
    \fmf{fermion,tension=0.7}{v2,v1} % t-channel
    \fmf{boson}{o2,v2}
    \fmf{fermion}{v2,i2}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{$\gamma$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

The s-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,13)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{boson}{i1,v1}
    \fmf{fermion}{i2,v1}
    \fmf{fermion}{v1,v2} % s-channel
    \fmf{fermion}{v2,o2}
    \fmf{boson}{v2,o1}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{$\gamma$}{o1}
    \fmflabel{e$^-$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Inelastic scattering

Pair annihilation in the t-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,13)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1}
    \fmf{fermion}{v2,i2}
    \fmf{fermion,tension=0.7}{v1,v2} % t-channel
    \fmf{boson}{v1,o1}
    \fmf{boson}{v2,o2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{$\gamma$}{o1}
    \fmflabel{$\gamma$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Pair annihilation in the u-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % skeleton
    \fmf{phantom}{i1,v1,o1}
    \fmf{fermion,tension=0.7}{v1,v2} % t-channel
    \fmf{phantom}{i2,v2,o2}
    \fmffreeze
    % main incoming/outgoing lines
    \fmf{fermion}{i1,v1}
    \fmf{fermion}{v2,i2}
    \fmf{boson,rubout}{v1,o2}
    \fmf{boson}{v2,o1}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{$\gamma$}{o1}
    \fmflabel{$\gamma$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Pair creation in the t-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,13)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{boson}{i1,v1}
    \fmf{boson}{v2,i2}
    \fmf{fermion,tension=0.7}{v2,v1} % t-channel
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{o2,v2}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{$\gamma$}{i2}
    \fmflabel{e$^-$}{o1}
    %\fmflabel{e$^+$}{o2}
    \fmfv{l.d=4,l.a=-25,l=e$^+$}{o2} % more control
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Pair creation in the u-channel:

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-2,12)(0,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % skeleton
    \fmf{phantom}{i1,v1,o1}
    \fmf{fermion,tension=0.7}{v1,v2} % t-channel
    \fmf{phantom}{i2,v2,o2}
    \fmffreeze
    % main incoming/outgoing lines
    \fmf{boson}{i1,v1}
    \fmf{boson}{i2,v2}
    \fmf{fermion}{v2,o1}
    \fmf{fermion,rubout}{o2,v1}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{$\gamma$}{i2}
    \fmflabel{e$^-$}{o1}
    %\fmflabel{e$^+$}{o2}
    \fmfv{l.d=4,l.a=-25,l=e$^+$}{o2} % more control
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

Full code

Edit and compile if you like:

% !TEX program = pdflatexmk
% !TEX parameter = -shell-escape
% Author: Izaak Neutelings (August 2024)
% Description: Basic LO QED processes
% Instructions: To compile via command line, run the following twice
%   pdflatex -shell-escape basic_QED.tex
\documentclass[11pt,border=4pt,multi=page,crop]{standalone}
\usepackage{feynmp-auto}

% DEFINE fmfpicture ENVIRONMENT
\usepackage{environ} % for \NewEnviron
\DeclareGraphicsRule{*}{mps}{*}{}
\NewEnviron{fmfpicture}[3]{%
  \begin{page} % to create standalone page
    \fmfframe(#1)(#2){ % padding (L,T)(R,B)
    \begin{fmffile}{feynmp-#3} % auxiliary files (use unique name!)
      \BODY % main code
    \end{fmffile}
    }
  \end{page}
}

\begin{document}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% ELECTRON-MUON SCATTERING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ELECTRON-MUON SCATTERING (Mott/Rutherford) - t-channel
\begin{fmfpicture}{-2,12}{0,14}{em-em-tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{fermion}{i2,v2,o2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{$\mu^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{$\mu^-$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% ELECTRON-ELECTRON SCATTERING %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ELECTRON-ELECTRON SCATTERING (Moller) - t-channel
\begin{fmfpicture}{-2,12}{0,14}{ee-ee-tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{fermion}{i2,v2,o2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^-$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% ELECTRON-ELECTRON SCATTERING (Moller) - u-channel
\begin{fmfpicture}{-2,12}{0,14}{ee-ee-uchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{phantom}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{phantom}{i2,v2,o2}
    \fmffreeze
    % main - outgoing lines
    \fmf{fermion,rubout}{i1,v1,o2}
    \fmf{fermion}{i2,v2,o1}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^-$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% ELECTRON-POSITRON SCATTERING %%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ELECTRON-POSITRON SCATTERING (Bhabba) - t-channel
\begin{fmfpicture}{-2,12}{0,14}{ep-ep-tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,o1}
    \fmf{boson,tension=0.7,label.side=right,label=$\gamma$}{v1,v2} % t-channel
    \fmf{fermion}{o2,v2,i2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^+$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% ELECTRON-POSITRON SCATTERING - s-channel
\begin{fmfpicture}{-2,12}{0,14}{ep-ep-schan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1,i2}
    \fmf{boson,label.side=left,label=$\gamma$}{v1,v2} % s-channel
    \fmf{fermion}{o2,v2,o1}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{e$^+$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% COMPTON SCATTERING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% COMPTON SCATTERING - t-channel
\begin{fmfpicture}{-2,13}{0,14}{eg-eg-tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{boson}{i1,v1}
    \fmf{fermion}{o1,v1}
    \fmf{fermion,tension=0.7}{v2,v1} % t-channel
    \fmf{boson}{o2,v2}
    \fmf{fermion}{v2,i2}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{e$^-$}{o1}
    \fmflabel{$\gamma$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% COMPTON SCATTERING - s-channel
\begin{fmfpicture}{-2,13}{0,14}{eg-eg-schan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{boson}{i1,v1}
    \fmf{fermion}{i2,v1}
    \fmf{fermion}{v1,v2} % s-channel
    \fmf{fermion}{v2,o2}
    \fmf{boson}{v2,o1}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{e$^-$}{i2}
    \fmflabel{$\gamma$}{o1}
    \fmflabel{e$^-$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% INELASTIC SCATTERING %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% PAIR ANNIHILATION - t-channel
\begin{fmfpicture}{-2,13}{0,14}{ep-gg-tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{fermion}{i1,v1}
    \fmf{fermion}{v2,i2}
    \fmf{fermion,tension=0.7}{v1,v2} % t-channel
    \fmf{boson}{v1,o1}
    \fmf{boson}{v2,o2}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{$\gamma$}{o1}
    \fmflabel{$\gamma$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% PAIR ANNIHILATION - u-channel
\begin{fmfpicture}{-2,12}{0,14}{ep-gg-uchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % skeleton
    \fmf{phantom}{i1,v1,o1}
    \fmf{fermion,tension=0.7}{v1,v2} % t-channel
    \fmf{phantom}{i2,v2,o2}
    \fmffreeze
    % main incoming/outgoing lines
    \fmf{fermion}{i1,v1}
    \fmf{fermion}{v2,i2}
    \fmf{boson,rubout}{v1,o2}
    \fmf{boson}{v2,o1}
    % labels
    \fmflabel{e$^-$}{i1}
    \fmflabel{e$^+$}{i2}
    \fmflabel{$\gamma$}{o1}
    \fmflabel{$\gamma$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% PAIR CREATION - t-channel
\begin{fmfpicture}{-2,13}{0,14}{gg-ep-tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main
    \fmf{boson}{i1,v1}
    \fmf{boson}{v2,i2}
    \fmf{fermion,tension=0.7}{v2,v1} % t-channel
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{o2,v2}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{$\gamma$}{i2}
    \fmflabel{e$^-$}{o1}
    %\fmflabel{e$^+$}{o2}
    \fmfv{l.d=4,l.a=-25,l=e$^+$}{o2} % more control
  \end{fmfgraph*}
\end{fmfpicture}

% PAIR CREATION - u-channel
\begin{fmfpicture}{-2,12}{0,14}{gg-ep-uchan} % padding (LTRB)
  \begin{fmfgraph*}(100,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % skeleton
    \fmf{phantom}{i1,v1,o1}
    \fmf{fermion,tension=0.7}{v1,v2} % t-channel
    \fmf{phantom}{i2,v2,o2}
    \fmffreeze
    % main incoming/outgoing lines
    \fmf{boson}{i1,v1}
    \fmf{boson}{i2,v2}
    \fmf{fermion}{v2,o1}
    \fmf{fermion,rubout}{o2,v1}
    % labels
    \fmflabel{$\gamma$}{i1}
    \fmflabel{$\gamma$}{i2}
    \fmflabel{e$^-$}{o1}
    %\fmflabel{e$^+$}{o2}
    \fmfv{l.d=4,l.a=-25,l=e$^+$}{o2} % more control
  \end{fmfgraph*}
\end{fmfpicture}


\end{document}

Click to download: basic_QED.tex • basic_QED.pdf
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