Some leading-order diagrams of basic QCD processes, inspired by Table 7.1 of Griffith’s Introduction to Elementary Particles (2008).
- Electron-muon scattering
- Electron-electron scattering
- Electron-positron scattering
- Compton scattering
- Inelastic scattering
Click on a diagram to jump to the code & download links below:
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
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}
Full code
The LaTeX code below collects all the diagrams above into one big file that produces a multipage PDF. Please find download links below, or edit and compile here 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.pdfOpen in Overleaf: basic_QED.tex.
See also: Original Source by Izaak Neutelings
Note: The copyright belongs to the blog author and the blog. For the license, please see the linked original source blog.










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