ttbar plus W/Z boson production in pp

by Posted on

This posts shows code examples of Feynman diagrams of ttbar quark plus W or Z boson production in proton-proton collisions. For a nice overview from the experimental point of view, have a look at this review article by the CMS collaboration published in Physics Reports.

Click on a diagram to jump to the code & download links below:
ttbarV-001.png ttbarV-002.png ttbarV-003.png ttbarV-004.png ttbarV-005.png ttbarV-006.png ttbarV-007.png 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-10,14)(7,16){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(120,75) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,oV,o1}
    \fmfshift{2 up}{oV}
    % main
    \fmf{fermion}{i1,v1,i2}
    \fmf{gluon,label=$g$,l.s=right,l.d=10}{v2,v1}
    \fmf{phantom,t=1.1}{o2,v2,o1}
    \fmffreeze
    \fmf{fermion}{o2,v2,vV,o1}
    \fmf{boson,t=0}{vV,oV}
    % labels
    \fmflabel{$q$}{i1}
    \fmflabel{$\overline{q}$}{i2}
    \fmflabel{$\overline{\mathrm{t}}$}{o2}
    \fmflabel{t}{o1}
    \fmfv{l.a=-15,l.d=4,l=Z}{oV}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-9,14)(6,16){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(120,75) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,oV,o1}
    \fmfshift{2 left}{i1}
    \fmfshift{2 up}{oV}
    % main
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{v1,i2}
    \fmf{gluon,t=1.2,l.s=left,label=$g$}{v1,v2}
    \fmf{phantom}{o2,v2,o1}
    \fmffreeze
    \fmf{fermion}{o2,v2,vV,o1}
    \fmf{boson,t=0}{vV,oV}
    % labels
    \fmfv{l.d=4,l=$g$}{i1}
    \fmfv{l.d=6,l=$g$}{i2}
    \fmflabel{$\overline{\mathrm{t}}$}{o2}
    \fmflabel{t}{o1}
    \fmfv{l.a=-15,l.d=4,l=Z}{oV}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(3,14)(9,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o2,oV,o1}
    \fmfshift{2 up}{oV}
    \fmfshift{3 right}{oV}
    % main
    \fmf{gluon}{v1,i1}
    \fmf{fermion,label=t,l.s=left}{v2,v1} % t-channel
    \fmf{gluon}{i2,v2}
    \fmf{phantom}{v1,o1}
    \fmf{fermion}{o2,v2}
    \fmffreeze
    \fmf{fermion}{v1,vV,o1}
    \fmf{boson,t=0}{vV,oV}
    % labels
    \fmflabel{$g$}{i2}
    \fmflabel{$g$}{i1}
    \fmfv{l.d=7,l.a=22,l=t}{o1}
    \fmfv{l.d=7,l.a=-20,l=$\overline{\mathrm{t}}$}{o2}
    \fmfv{l.a=-15,l.d=4,l=Z}{oV}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(1,12)(6,15){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{20 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.33w,.75h)}{v1} % exact placement
    \fmfforce{(.33w,.25h)}{v2} % exact placement
    \fmfforce{(.72w,.75h)}{g} % exact placement
    % main
    \fmf{fermion}{i1,v1,v2,i2}
    \fmf{gluon}{g,v1}
    \fmf{fermion}{o2,g,o1}
    \fmf{boson}{v2,o3}
    % labels
    \fmfv{l.d=5,l.a=155,l=$q$}{i1}
    \fmfv{l.d=4,l.a=-150,l=$\overline{q}$}{i2}
    \fmfv{l.d=6,l.a=22,l=t}{o1}
    \fmfv{l.d=6,l.a=-20,l=$\overline{\mathrm{t}}$}{o2}
    \fmfv{l.d=5,l.a=-20,l=Z}{o3}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(3,12)(6,16){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{20 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.33w,.75h)}{v1} % exact placement
    \fmfforce{(.33w,.25h)}{v2} % exact placement
    \fmfforce{(.72w,.75h)}{g} % exact placement
    % main
    \fmf{fermion}{i1,v1,v2,i2}
    \fmf{gluon}{g,v1}
    \fmf{fermion}{o2,g,o1}
    \fmf{boson}{v2,o3}
    % labels
    \fmfv{l.d=5,l.a=155,l=$q$}{i1}
    \fmfv{l.d=4,l.a=-150,l=$\overline{q}'$}{i2}
    \fmfv{l.d=6,l.a=22,l=t}{o1}
    \fmfv{l.d=6,l.a=-20,l=$\overline{\mathrm{t}}$}{o2}
    \fmfv{l.d=5,l.a=-20,l=W}{o3}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-9,9)(6,9){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(110,70) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfleft{i2,m,i1}
    \fmfright{o2,z,o1}
    % skeleton
    \fmf{gluon,t=1.9}{v1,i1}
    \fmf{gluon,t=1.9}{i2,v2}
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{o2,v2}
    % Z boson
    \fmf{fermion,t=1.0}{v2,v,v1}
    \fmf{dashes}{z,v} % Z boson
    % labels
    \fmfv{l.a=158,l.d=5,l=$g$}{i1}
    \fmfv{l.a=-158,l.d=5,l=$g$}{i2}
    \fmfv{l.a=22,l.d=5,l=\strut t}{o1}
    \fmfv{l.a=0,l.d=4,l=Z}{z}
    \fmfv{l.a=-22,l.d=5,l=\strut$\overline{\mathrm{t}}$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-9,10)(6,10){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(110,65) % dimensions (WH)
    % line style
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    % external vertices
    \fmfleft{i2,m,i1}
    \fmfright{o2,z,o1}
    % skeleton
    \fmf{gluon,t=1.2}{v1,i1}
    \fmf{gluon,t=1.2}{i2,v2}
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{o2,v2}
    \fmffreeze
    % Z boson
    \fmf{fermion,t=1}{v2,v,v1}
    \fmf{dashes}{z,v} % Z boson
    % labels
    \fmfv{l.a=158,l.d=5,l=$g$}{i1}
    \fmfv{l.a=-158,l.d=5,l=$g$}{i2}
    \fmfv{l.a=22,l.d=5,l=\strut t}{o1}
    \fmfv{l.a=0,l.d=4,l=Z}{z}
    \fmfv{l.a=-22,l.d=5,l=\strut$\overline{\mathrm{t}}$}{o2}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

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 (February 2023)
% Instructions: To compile via command line, run the following twice
%   pdflatex -shell-escape ttbar.tex
\documentclass[11pt,border=2pt,multi=page,crop]{standalone}
\usepackage{amsmath}
\usepackage{feynmp-auto}

% DEFINE fmfpicture ENVIRONMENT
\usepackage{environ} % for \NewEnviron
\NewEnviron{fmfpicture}[3]{%
  \begin{page} % to create standalone page
  \fmfframe(#1)(#2){ % padding (LT)(RB)
  \begin{fmffile}{feynmp-#3} % auxiliary files (use unique name!)
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    \BODY % main code
  \end{fmffile}
  }
  \end{page}
}

\begin{document}

% TTBAR + Z PRODUCTION - Quark-antiquark annihilation, s-channel
\begin{fmfpicture}{-10,14}{7,16}{ttbarV_qq-ttbarZ_schan} % padding (LTRB)
  \begin{fmfgraph*}(120,75) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,oV,o1}
    \fmfshift{2 up}{oV}
    % main
    \fmf{fermion}{i1,v1,i2}
    \fmf{gluon,label=$g$,l.s=right,l.d=10}{v2,v1}
    \fmf{phantom,t=1.1}{o2,v2,o1}
    \fmffreeze
    \fmf{fermion}{o2,v2,vV,o1}
    \fmf{boson,t=0}{vV,oV}
    % labels
    \fmflabel{$q$}{i1}
    \fmflabel{$\overline{q}$}{i2}
    \fmflabel{$\overline{\mathrm{t}}$}{o2}
    \fmflabel{t}{o1}
    \fmfv{l.a=-15,l.d=4,l=Z}{oV}
  \end{fmfgraph*}
\end{fmfpicture}

% TTBAR + Z PRODUCTION - Gluon fusion, s-channel
\begin{fmfpicture}{-9,14}{6,16}{ttbarV_gg-ttbarZ_schan} % padding (LTRB)
  \begin{fmfgraph*}(120,75) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,oV,o1}
    \fmfshift{2 left}{i1}
    \fmfshift{2 up}{oV}
    % main
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{v1,i2}
    \fmf{gluon,t=1.2,l.s=left,label=$g$}{v1,v2}
    \fmf{phantom}{o2,v2,o1}
    \fmffreeze
    \fmf{fermion}{o2,v2,vV,o1}
    \fmf{boson,t=0}{vV,oV}
    % labels
    \fmfv{l.d=4,l=$g$}{i1}
    \fmfv{l.d=6,l=$g$}{i2}
    \fmflabel{$\overline{\mathrm{t}}$}{o2}
    \fmflabel{t}{o1}
    \fmfv{l.a=-15,l.d=4,l=Z}{oV}
  \end{fmfgraph*}
\end{fmfpicture}

% TTBAR + Z PRODUCTION - Gluon fusion, t-channel
\begin{fmfpicture}{3,14}{9,14}{ttbarV_gg-ttbarZ_tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o2,oV,o1}
    \fmfshift{2 up}{oV}
    \fmfshift{3 right}{oV}
    % main
    \fmf{gluon}{v1,i1}
    \fmf{fermion,label=t,l.s=left}{v2,v1} % t-channel
    \fmf{gluon}{i2,v2}
    \fmf{phantom}{v1,o1}
    \fmf{fermion}{o2,v2}
    \fmffreeze
    \fmf{fermion}{v1,vV,o1}
    \fmf{boson,t=0}{vV,oV}
    % labels
    \fmflabel{$g$}{i2}
    \fmflabel{$g$}{i1}
    \fmfv{l.d=7,l.a=22,l=t}{o1}
    \fmfv{l.d=7,l.a=-20,l=$\overline{\mathrm{t}}$}{o2}
    \fmfv{l.a=-15,l.d=4,l=Z}{oV}
  \end{fmfgraph*}
\end{fmfpicture}

% TTBAR + Z PRODUCTION - Quark-antiquark annihilation, t-channel
\begin{fmfpicture}{1,12}{6,15}{ttbarV_qq-ttbarZ_tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{20 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.33w,.75h)}{v1} % exact placement
    \fmfforce{(.33w,.25h)}{v2} % exact placement
    \fmfforce{(.72w,.75h)}{g} % exact placement
    % main
    \fmf{fermion}{i1,v1,v2,i2}
    \fmf{gluon}{g,v1}
    \fmf{fermion}{o2,g,o1}
    \fmf{boson}{v2,o3}
    % labels
    \fmfv{l.d=5,l.a=155,l=$q$}{i1}
    \fmfv{l.d=4,l.a=-150,l=$\overline{q}$}{i2}
    \fmfv{l.d=6,l.a=22,l=t}{o1}
    \fmfv{l.d=6,l.a=-20,l=$\overline{\mathrm{t}}$}{o2}
    \fmfv{l.d=5,l.a=-20,l=Z}{o3}
  \end{fmfgraph*}
\end{fmfpicture}

% TTBAR + W PRODUCTION - Quark-antiquark annihilation, t-channel
\begin{fmfpicture}{3,12}{6,16}{ttbarV_qq-ttbarW_tchan} % padding (LTRB)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{20 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.33w,.75h)}{v1} % exact placement
    \fmfforce{(.33w,.25h)}{v2} % exact placement
    \fmfforce{(.72w,.75h)}{g} % exact placement
    % main
    \fmf{fermion}{i1,v1,v2,i2}
    \fmf{gluon}{g,v1}
    \fmf{fermion}{o2,g,o1}
    \fmf{boson}{v2,o3}
    % labels
    \fmfv{l.d=5,l.a=155,l=$q$}{i1}
    \fmfv{l.d=4,l.a=-150,l=$\overline{q}'$}{i2}
    \fmfv{l.d=6,l.a=22,l=t}{o1}
    \fmfv{l.d=6,l.a=-20,l=$\overline{\mathrm{t}}$}{o2}
    \fmfv{l.d=5,l.a=-20,l=W}{o3}
  \end{fmfgraph*}
\end{fmfpicture}

% TTBAR PRODUCTION + W - Gluon fusion, t-channel
\begin{fmfpicture}{-9,9}{6,9}{ttbarV_gg-ttbarW_tchan} % padding (LTRB)
  \begin{fmfgraph*}(110,70) % dimensions (WH)
    % external vertices
    \fmfleft{i2,m,i1}
    \fmfright{o2,z,o1}
    % skeleton
    \fmf{gluon,t=1.9}{v1,i1}
    \fmf{gluon,t=1.9}{i2,v2}
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{o2,v2}
    % Z boson
    \fmf{fermion,t=1.0}{v2,v,v1}
    \fmf{dashes}{z,v} % Z boson
    % labels
    \fmfv{l.a=158,l.d=5,l=$g$}{i1}
    \fmfv{l.a=-158,l.d=5,l=$g$}{i2}
    \fmfv{l.a=22,l.d=5,l=\strut t}{o1}
    \fmfv{l.a=0,l.d=4,l=Z}{z}
    \fmfv{l.a=-22,l.d=5,l=\strut$\overline{\mathrm{t}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% TTBAR PRODUCTION + W - Gluon fusion, t-channel, straight
\begin{fmfpicture}{-9,10}{6,10}{ttbarV_gg-ttbarW_tchan_straight} % padding (LTRB)
  \begin{fmfgraph*}(110,65) % dimensions (WH)
    % external vertices
    \fmfleft{i2,m,i1}
    \fmfright{o2,z,o1}
    % skeleton
    \fmf{gluon,t=1.2}{v1,i1}
    \fmf{gluon,t=1.2}{i2,v2}
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{o2,v2}
    \fmffreeze
    % Z boson
    \fmf{fermion,t=1}{v2,v,v1}
    \fmf{dashes}{z,v} % Z boson
    % labels
    \fmfv{l.a=158,l.d=5,l=$g$}{i1}
    \fmfv{l.a=-158,l.d=5,l=$g$}{i2}
    \fmfv{l.a=22,l.d=5,l=\strut t}{o1}
    \fmfv{l.a=0,l.d=4,l=Z}{z}
    \fmfv{l.a=-22,l.d=5,l=\strut$\overline{\mathrm{t}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

\end{document}

Click to download: ttbarV.tex • ttbarV.pdf
Open in Overleaf: ttbarV.tex.


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