This posts shows code examples of Feynman diagrams of the production and decay of vector-like quarks (VLQs) and vector-like leptons (VLLs) 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:
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(3,16)(8,18){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{quark}{i1,v1,i2} % incoming particles
\fmf{fermion,f=(.5,,0,,.7)}{o2,v2,o1} % outgoing particles
\fmf{gluon,t=1.1}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=q}{i1}
\fmfv{l.d=3,l.a=-156,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=5,l.a=25,l=\color{colVLQ} Q}{o1}
\fmfv{l.d=5,l.a=-25,l=\color{colVLQ}$\overline{\mathrm{Q}}$}{o2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(1,16)(8,18){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{gluon}{i2,v1,i1} % incoming particles
\fmf{fermion,f=(.5,,0,,.7)}{o2,v2,o1} % outgoing particles
\fmf{gluon,t=1.1}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=g}{i1}
\fmfv{l.d=5,l.a=-156,l=g}{i2}
\fmfv{l.d=5,l.a=25,l=\color{colVLQ} Q}{o1}
\fmfv{l.d=5,l.a=-25,l=\color{colVLQ}$\overline{\mathrm{Q}}$}{o2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(1,-4)(46,-5){ % padding (L,T)(R,B)
\begin{fmfgraph*}(130,120) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d}
\fmfright{o4,o3,o2,o1}
\fmftop{t}
\fmfbottom{b}
% gluons
\fmf{gluon,t=1.6}{i2,v1,i1}
\fmf{gluon,t=1.8}{v1,v2}
\fmf{fermion,t=1.3,f=(.5,,0,,.7),label=\color{colVLQ} T,l.s=left}{v2,d1}
\fmf{fermion,t=1.3,f=(.5,,0,,.7),label=\color{colVLQ}$\overline{\mathrm{T}}$,l.s=left}{d2,v2}
% decay products
\fmfshift{16 down}{o1}
\fmfshift{ 8 down}{o2}
\fmfshift{ 8 up}{o3}
\fmfshift{16 up}{o4}
\fmf{fermion,t=1.8}{o1,d1} % decay on top
\fmf{dashes,t=1.8}{d1,o2} % decay on top
\fmf{boson,t=1.8}{d2,o3} % decay on bottom
\fmf{fermion,t=1.8}{o4,d2} % decay on bottom
\fmf{phantom,t=0.8}{t,d1} % pull decay vertex
\fmf{phantom,t=0.8}{d2,b} % pull decay vertex
% labels
\fmfv{l.d=4,l.a=156,l=g}{i1}
\fmfv{l.d=4,l.a=-156,l=g}{i2}
\fmfv{l.d=5,l.a=24,l=t}{o1}
\fmfv{l.d=4,l.a=-20,l=H}{o2}
\fmfv{l.d=4,l.a=20,l=W$^-$/H/Z}{o3}
\fmfv{l.d=5,l.a=-20,l=$\overline{\mathrm{b}}$/$\overline{\mathrm{t}}$/$\overline{\mathrm{t}}$}{o4}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(-10,12)(23,11){ % padding (L,T)(R,B)
\begin{fmfgraph*}(130,85) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
\fmfleft{i2,i1}
\fmfright{o3,o2,o1}
% main
\fmf{fermion}{i1,v1}
\fmf{fermion}{v1,o1}
\fmf{gluon}{i2,v2}
\fmf{fermion}{o3,v2}
\fmf{fermion,t=1}{v2,v} % t-channel
\fmf{boson,t=1,l.s=left,l.d=5,label=W/Z}{v,v1} % t-channel
\fmffreeze
\fmf{fermion,f=(.5,,0,,.7)}{v,o2} % top out
% labels
\fmfv{l.d=6,l.a=160,l=q}{i1}
\fmfv{l.d=6,l.a=-160,l=g}{i2}
\fmfv{l.d=6,l.a=22,l=q$'$/q}{o1}
\fmfv{l.d=6,l.a=0,l=\color{colVLQ} T/B}{o2}
\fmfv{l.d=6,l.a=-20,l=$\overline{\mathrm{b}}$}{o3}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colBSM}{rgb}{.96,.3,0} % BSM mediator (orange)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(2,14)(8,16){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{gluon}{i2,v1,i1} % incoming particles
\fmf{fermion,f=(.5,,0,,.7)}{v2,o1} % outgoing particles
\fmf{fermion}{o2,v2} % outgoing particles
\fmf{boson,t=1.1,f=(.96,,.3,,0),label=\color{colBSM} W$'$,l.s=left,l.d=4}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=g}{i1}
\fmfv{l.d=5,l.a=-156,l=g}{i2}
\fmfv{l.d=5,l.a=25,l=\color{colVLQ} T}{o1}
\fmfv{l.d=5,l.a=-25,l=$\overline{\mathrm{b}}$}{o2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(2,14)(7,16){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{fermion}{i1,v1,i2} % incoming particles
\fmf{fermion,f=(0,,0,,1)}{o2,v2,o1} % outgoing particles
\fmf{boson,t=1.1,label=Z/$\gamma^*$,l.s=left,l.d=5}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=q}{i1}
\fmfv{l.d=5,l.a=-156,l=$\overline{\mathrm{q}}$}{i2}
\fmfv{l.d=5,l.a=25,l=\color{colVLL} L}{o1}
\fmfv{l.d=5,l.a=-25,l=\color{colVLL}$\overline{\mathrm{L}}$}{o2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(2,13)(8,16){ % padding (L,T)(R,B)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{fermion}{i1,v1,i2} % incoming particles
\fmf{fermion,f=(0,,0,,1)}{o2,v2,o1} % outgoing particles
\fmf{boson,t=1.1,label=W$^\pm$,l.s=left,l.d=4}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=q}{i1}
\fmfv{l.d=5,l.a=-156,l=$\overline{\mathrm{q}}$}{i2}
\fmfv{l.d=5,l.a=25,l=\color{colVLL} N}{o1}
\fmfv{l.d=5,l.a=-25,l=\color{colVLL}$\overline{\mathrm{E}}$}{o2}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(3,14)(11,13){ % padding (L,T)(R,B)
\begin{fmfgraph*}(160,140) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d}
\fmfright{o6,o5,o4,o3,o2,o1}
\fmfshift{10 left}{o1,o6}
\fmfshift{5 down}{i1}
\fmfshift{5 up}{i2}
% qq -> W & skeleton
\fmf{fermion,t=1.5}{i1,v1,i2}
\fmf{boson,t=1.5,label=W$^\pm$,l.s=right,l.d=4}{v2,v1}
\fmf{fermion,t=0.7}{w1,o1} % top outgoing fermion
\fmf{fermion,t=0.7}{o6,w2} % bottom outgoing fermion
% W decay to heavy leptons
\fmf{fermion,t=1.1,f=(0,,0,,1),label=\color{colVLL} N,l.d=5,l.s=left}{v2,w1} % HNL
\fmf{fermion,t=1.1,f=(0,,0,,1),label=\color{colVLL} $\overline{\mathrm{E}}$,l.d=5,l.s=left}{w2,v2} % HNL
\fmffreeze
% HNL decay
\fmf{boson,t=1.2,label=$\mathrm{W}^\pm$,l.d=5,l.s=right}{w1,d1} % W boson
\fmf{fermion}{o2,d1,o3}
% HCL decay
\fmf{dashes,t=1.2,label=H,l.d=5,l.s=left}{w2,d2} % Higgs boson
\fmf{fermion}{o5,d2,o4}
% labels
\fmfv{l.d=4,l.a=155,l=q}{i1}
\fmfv{l.d=3,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=5,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=20,l=$\ell^\pm$}{o2}
\fmfv{l.d=5,l.a=-15,l=$\nu$}{o3}
\fmfv{l.d=5,l.a=20,l=b}{o4}
\fmfv{l.d=5,l.a=-15,l=$\overline{\mathrm{b}}$}{o5}
\fmfv{l.d=5,l.a=-25,l=$\overline{\nu}$}{o6}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(1,11)(13,14){ % padding (L,T)(R,B)
\begin{fmfgraph*}(160,140) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d}
\fmfright{o6,o5,o4,o3,o2,o1}
\fmfshift{10 left}{o1,o6}
\fmfshift{5 down}{i1}
\fmfshift{5 up}{i2}
% qq -> W & skeleton
\fmf{fermion,t=1.5}{i1,v1,i2}
\fmf{boson,t=1.5,label=Z/$\gamma^*$,l.s=right,l.d=4}{v2,v1}
\fmf{fermion,t=0.7}{w1,o1} % top outgoing fermion
\fmf{fermion,t=0.7}{o6,w2} % bottom outgoing fermion
% W decay to heavy leptons
\fmf{fermion,t=1.1,f=(0,,0,,1),label=\color{colVLL} E,l.d=5,l.s=left}{v2,w1} % HNL
\fmf{fermion,t=1.1,f=(0,,0,,1),label=\color{colVLL} $\overline{\mathrm{E}}$,l.d=5,l.s=left}{w2,v2} % HNL
\fmffreeze
% HNL decay
\fmf{boson,t=1.2,label=$\mathrm{W}^\pm$,l.d=5,l.s=right}{w1,d1} % W boson
\fmf{fermion}{o3,d1,o2}
% HCL decay
\fmf{boson,t=1.2,label=Z,l.d=5,l.s=left}{w2,d2} % Z boson
\fmf{fermion}{o5,d2,o4}
% labels
\fmfv{l.d=4,l.a=155,l=q}{i1}
\fmfv{l.d=4,l.a=-155,l=$\overline{\mathrm{q}}$}{i2}
\fmfv{l.d=5,l.a=25,l=$\nu$}{o1}
\fmfv{l.d=5,l.a=20,l=q$''$}{o2}
\fmfv{l.d=5,l.a=-15,l=$\overline{\mathrm{q}}'''$}{o3}
\fmfv{l.d=5,l.a=20,l=$\ell^\mp$}{o4}
\fmfv{l.d=5,l.a=-15,l=$\ell^\pm$}{o5}
\fmfv{l.d=4,l.a=-25,l=$\ell^\pm$}{o6}
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colBSM}{rgb}{.96,.3,0} % BSM mediator (orange)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(3,13)(5,13){ % padding (L,T)(R,B)
\begin{fmfgraph*}(90,65) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfleft{d,i,d,d}
\fmfright{o3,m,o2,o1}
\fmftop{t} % for pulling
\fmfshift{9 down}{o2}
\fmfshift{4 left}{o3}
% main process
\fmf{fermion,f=(0,,0,,1),t=1.4}{i,v}
\fmf{phantom}{v,m}
\fmffreeze
\fmf{boson,f=(.96,,.3,,0),t=1.5,label=\color{colBSM} U,l.s=left,l.d=4}{v,w}
\fmf{fermion}{o2,w,o1}
\fmf{fermion}{v,o3}
\fmf{phantom,t=0.7}{w,t} % pull W decay vertex
% labels
\fmfv{l.d=5,l.a=180,l=\color{colVLL} E}{i}
\fmfv{l.d=5,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}$}{o2}
\fmfv{l.d=4,l.a=-25,l=b}{o3}
%\fmfv{l.d=8,l.a=180,l=U}{w} % for boson line
\end{fmfgraph*}
} % close \fmfframe
\end{fmffile}
\end{document}
\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\definecolor{colBSM}{rgb}{.96,.3,0} % BSM mediator (orange)
\begin{document}
\begin{fmffile}{feyngraph}
\fmfframe(4,13)(5,13){ % padding (L,T)(R,B)
\begin{fmfgraph*}(90,65) % canvas (W,H)
% line style
\fmfset{wiggly_len}{12} % boson wavelength
\fmfset{wiggly_slope}{65} % boson slope of waves
% external vertices
\fmfleft{d,i,d,d}
\fmfright{o3,m,o2,o1}
\fmftop{t} % for pulling
\fmfshift{9 down}{o2}
\fmfshift{4 left}{o3}
% main process
\fmf{fermion,f=(0,,0,,1),t=1.4}{i,v}
\fmf{phantom}{v,m}
\fmffreeze
\fmf{boson,t=1.5,f=(.96,,.3,,0),label=\color{colBSM} U,l.s=left,l.d=4}{v,w}
\fmf{fermion}{o2,w,o1}
\fmf{fermion}{v,o3}
\fmf{phantom,t=0.7}{w,t} % pull W decay vertex
% labels
\fmfv{l.d=5,l.a=180,l=\color{colVLL} N}{i}
\fmfv{l.d=5,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}$}{o2}
\fmfv{l.d=4,l.a=-25,l=t}{o3}
%\fmfv{l.d=8,l.a=180,l=U}{w} % for boson line
\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 (January 2024)
% Description: VLQ/VLL production & HNL in pp collisions
% Sources: https://cms-results.web.cern.ch/cms-results/public-results/publications/EXO-23-006
% Instructions: To compile via command line, run the following twice
% pdflatex -shell-escape VLQ_VLL.tex
\documentclass[10pt,border=2pt,multi=page,crop]{standalone}
\usepackage{feynmp-auto}
\usepackage{amsmath}
% DEFINE TEXT COLORS
\usepackage{xcolor}
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\definecolor{colBSM}{rgb}{.96,.3,0} % BSM mediator (orange)
% DEFINE COLOR MACROS
% The following loops over the user color names and defines
% a handy \<colname> command to set text color, as well as
% defines colors in MetaPost of the same and value for lines
\usepackage{pgffor} % for \foreach
\def\MPcolors{} % MetaPost code importing xcolor names
\foreach \colname in {colVLQ,colVLL,colBSM}{ % create command & MetaPost code
\expandafter\xdef\csname\colname\endcsname{\noexpand\color{\colname}} % \newcommand\<colname>
\convertcolorspec{named}{\colname}{rgb}\tmprgb % get rgb code
\xdef\MPcolors{\MPcolors color \colname; \colname := (\tmprgb); } % add color name
}
% DEFINE fmfpicture ENVIRONMENT
% The following defines a custom picture environment that
% helps to create standalone pages with common settings,
% and correctly padding the diagram with \fmfframe
\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
\fmfcmd{ % custom line style: double arrows for Majorana neutrino
style_def majorana
expr p = cdraw p;
cfill (tarrow (p,0.18)); % shift arrow
cfill (tarrow (reverse(p),0.18)); % shift arrow
enddef;
}
\fmfcmd\MPcolors % define custom line colors in MetaPost
\BODY % main code
\end{fmffile}
}
\end{page}
}
% BRACES
\usepackage{scalerel}
\newcommand{\mylbrace}[2]{\vspace{#2pt}\hspace{4pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{\lbrace}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{.}}
\newcommand{\myrbrace}[2]{\vspace{#2pt}\scaleleftright[\dimexpr6pt+#1\dimexpr0.11pt]{.}{\rule[\dimexpr2pt-#1\dimexpr0.5pt]{-4pt}{#1pt}}{\rbrace}\hspace{2pt}}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% VLQ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% VLQ pair production - gluon fusion
\begin{fmfpicture}{3,16}{8,18}{vlq_qq-QQ} % padding (LT)(RB)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{quark}{i1,v1,i2} % incoming particles
\fmf{fermion,f=colVLQ}{o2,v2,o1} % outgoing particles
\fmf{gluon,t=1.1}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=q}{i1}
\fmfv{l.d=3,l.a=-156,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=5,l.a=25,l=\colVLQ Q}{o1}
\fmfv{l.d=5,l.a=-25,l=\colVLQ$\overline{\mathrm{Q}}$}{o2}
\end{fmfgraph*}
\end{fmfpicture}
% VLQ pair production - quark-antiquark annihilation
\begin{fmfpicture}{1,16}{8,18}{vlq_gg-QQ} % padding (LT)(RB)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{gluon}{i2,v1,i1} % incoming particles
\fmf{fermion,f=colVLQ}{o2,v2,o1} % outgoing particles
\fmf{gluon,t=1.1}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=g}{i1}
\fmfv{l.d=5,l.a=-156,l=g}{i2}
\fmfv{l.d=5,l.a=25,l=\colVLQ Q}{o1}
\fmfv{l.d=5,l.a=-25,l=\colVLQ$\overline{\mathrm{Q}}$}{o2}
\end{fmfgraph*}
\end{fmfpicture}
% VLQ pair production + decay
\begin{fmfpicture}{1,-4}{46,-5}{vlq_gg-TT_decay} % padding (LT)(RB)
\begin{fmfgraph*}(130,120) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d}
\fmfright{o4,o3,o2,o1}
\fmftop{t}
\fmfbottom{b}
% gluons
\fmf{gluon,t=1.6}{i2,v1,i1}
\fmf{gluon,t=1.8}{v1,v2}
\fmf{fermion,t=1.3,f=colVLQ,label=\colVLQ T,l.s=left}{v2,d1}
\fmf{fermion,t=1.3,f=colVLQ,label=\colVLQ$\overline{\mathrm{T}}$,l.s=left}{d2,v2}
% decay products
\fmfshift{16 down}{o1}
\fmfshift{ 8 down}{o2}
\fmfshift{ 8 up}{o3}
\fmfshift{16 up}{o4}
\fmf{fermion,t=1.8}{o1,d1} % decay on top
\fmf{dashes,t=1.8}{d1,o2} % decay on top
\fmf{boson,t=1.8}{d2,o3} % decay on bottom
\fmf{fermion,t=1.8}{o4,d2} % decay on bottom
\fmf{phantom,t=0.8}{t,d1} % pull decay vertex
\fmf{phantom,t=0.8}{d2,b} % pull decay vertex
% labels
\fmfv{l.d=4,l.a=156,l=g}{i1}
\fmfv{l.d=4,l.a=-156,l=g}{i2}
\fmfv{l.d=5,l.a=24,l=t}{o1}
\fmfv{l.d=4,l.a=-20,l=H}{o2}
\fmfv{l.d=4,l.a=20,l=W$^-$/H/Z}{o3}
\fmfv{l.d=5,l.a=-20,l=$\overline{\mathrm{b}}$/$\overline{\mathrm{t}}$/$\overline{\mathrm{t}}$}{o4}
\end{fmfgraph*}
\end{fmfpicture}
% VLQ single production
\begin{fmfpicture}{-10,12}{23,11}{vlq_qg-qbT} % padding (LT)(RB)
\begin{fmfgraph*}(130,85) % canvas (W,H)
\fmfleft{i2,i1}
\fmfright{o3,o2,o1}
% main
\fmf{fermion}{i1,v1}
\fmf{fermion}{v1,o1}
\fmf{gluon}{i2,v2}
\fmf{fermion}{o3,v2}
\fmf{fermion,t=1}{v2,v} % t-channel
\fmf{boson,t=1,l.s=left,l.d=5,label=W/Z}{v,v1} % t-channel
\fmffreeze
\fmf{fermion,f=colVLQ}{v,o2} % top out
% labels
\fmfv{l.d=6,l.a=160,l=q}{i1}
\fmfv{l.d=6,l.a=-160,l=g}{i2}
\fmfv{l.d=6,l.a=22,l=q$'$/q}{o1}
\fmfv{l.d=6,l.a=0,l=\colVLQ T/B}{o2}
\fmfv{l.d=6,l.a=-20,l=$\overline{\mathrm{b}}$}{o3}
\end{fmfgraph*}
\end{fmfpicture}
% VLQ single production - quark-antiquark annihilation, new mediator
\begin{fmfpicture}{2,14}{8,16}{vlq_qq-w-bT} % padding (LT)(RB)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{gluon}{i2,v1,i1} % incoming particles
\fmf{fermion,f=colVLQ}{v2,o1} % outgoing particles
\fmf{fermion}{o2,v2} % outgoing particles
\fmf{boson,t=1.1,f=colBSM,label=\colBSM W$'$,l.s=left,l.d=4}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=g}{i1}
\fmfv{l.d=5,l.a=-156,l=g}{i2}
\fmfv{l.d=5,l.a=25,l=\colVLQ T}{o1}
\fmfv{l.d=5,l.a=-25,l=$\overline{\mathrm{b}}$}{o2}
\end{fmfgraph*}
\end{fmfpicture}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% VLL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% VLL pair production
\begin{fmfpicture}{2,14}{7,16}{vll_qq-z-LL} % padding (LT)(RB)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{fermion}{i1,v1,i2} % incoming particles
\fmf{fermion,f=colVLL}{o2,v2,o1} % outgoing particles
\fmf{boson,t=1.1,label=Z/$\gamma^*$,l.s=left,l.d=5}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=q}{i1}
\fmfv{l.d=5,l.a=-156,l=$\overline{\mathrm{q}}$}{i2}
\fmfv{l.d=5,l.a=25,l=\colVLL L}{o1}
\fmfv{l.d=5,l.a=-25,l=\colVLL$\overline{\mathrm{L}}$}{o2}
\end{fmfgraph*}
\end{fmfpicture}
% VLL pair production
\begin{fmfpicture}{2,13}{8,16}{vll_qq-w-EN} % padding (LT)(RB)
\begin{fmfgraph*}(110,75) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{i2,i1} % incoming vertices
\fmfright{o2,o1} % outgoing vertices
% main process
\fmf{fermion}{i1,v1,i2} % incoming particles
\fmf{fermion,f=colVLL}{o2,v2,o1} % outgoing particles
\fmf{boson,t=1.1,label=W$^\pm$,l.s=left,l.d=4}{v2,v1} % s-channel
% labels
\fmfv{l.d=5,l.a=156,l=q}{i1}
\fmfv{l.d=5,l.a=-156,l=$\overline{\mathrm{q}}$}{i2}
\fmfv{l.d=5,l.a=25,l=\colVLL N}{o1}
\fmfv{l.d=5,l.a=-25,l=\colVLL$\overline{\mathrm{E}}$}{o2}
\end{fmfgraph*}
\end{fmfpicture}
% VLL pair production through W + decay
\begin{fmfpicture}{3,14}{11,13}{vll_qq-w-NE_decay} % padding (LT)(RB)
\begin{fmfgraph*}(160,140) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d}
\fmfright{o6,o5,o4,o3,o2,o1}
\fmfshift{10 left}{o1,o6}
\fmfshift{5 down}{i1}
\fmfshift{5 up}{i2}
% qq -> W & skeleton
\fmf{fermion,t=1.5}{i1,v1,i2}
\fmf{boson,t=1.5,label=W$^\pm$,l.s=right,l.d=4}{v2,v1}
\fmf{fermion,t=0.7}{w1,o1} % top outgoing fermion
\fmf{fermion,t=0.7}{o6,w2} % bottom outgoing fermion
% W decay to heavy leptons
\fmf{fermion,t=1.1,f=colVLL,label=\colVLL N,l.d=5,l.s=left}{v2,w1} % HNL
\fmf{fermion,t=1.1,f=colVLL,label=\colVLL $\overline{\mathrm{E}}$,l.d=5,l.s=left}{w2,v2} % HNL
\fmffreeze
% HNL decay
\fmf{boson,t=1.2,label=$\mathrm{W}^\pm$,l.d=5,l.s=right}{w1,d1} % W boson
\fmf{fermion}{o2,d1,o3}
% HCL decay
\fmf{dashes,t=1.2,label=H,l.d=5,l.s=left}{w2,d2} % Higgs boson
\fmf{fermion}{o5,d2,o4}
% labels
\fmfv{l.d=4,l.a=155,l=q}{i1}
\fmfv{l.d=3,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=5,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=20,l=$\ell^\pm$}{o2}
\fmfv{l.d=5,l.a=-15,l=$\nu$}{o3}
\fmfv{l.d=5,l.a=20,l=b}{o4}
\fmfv{l.d=5,l.a=-15,l=$\overline{\mathrm{b}}$}{o5}
\fmfv{l.d=5,l.a=-25,l=$\overline{\nu}$}{o6}
\end{fmfgraph*}
\end{fmfpicture}
% VLL pair production through Z/gamma + decay
\begin{fmfpicture}{1,11}{13,14}{vll_qq-z-EE_decay} % padding (LT)(RB)
\begin{fmfgraph*}(160,140) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d}
\fmfright{o6,o5,o4,o3,o2,o1}
\fmfshift{10 left}{o1,o6}
\fmfshift{5 down}{i1}
\fmfshift{5 up}{i2}
% qq -> W & skeleton
\fmf{fermion,t=1.5}{i1,v1,i2}
\fmf{boson,t=1.5,label=Z/$\gamma^*$,l.s=right,l.d=4}{v2,v1}
\fmf{fermion,t=0.7}{w1,o1} % top outgoing fermion
\fmf{fermion,t=0.7}{o6,w2} % bottom outgoing fermion
% W decay to heavy leptons
\fmf{fermion,t=1.1,f=colVLL,label=\colVLL E,l.d=5,l.s=left}{v2,w1} % HNL
\fmf{fermion,t=1.1,f=colVLL,label=\colVLL $\overline{\mathrm{E}}$,l.d=5,l.s=left}{w2,v2} % HNL
\fmffreeze
% HNL decay
\fmf{boson,t=1.2,label=$\mathrm{W}^\pm$,l.d=5,l.s=right}{w1,d1} % W boson
\fmf{fermion}{o3,d1,o2}
% HCL decay
\fmf{boson,t=1.2,label=Z,l.d=5,l.s=left}{w2,d2} % Z boson
\fmf{fermion}{o5,d2,o4}
% labels
\fmfv{l.d=4,l.a=155,l=q}{i1}
\fmfv{l.d=4,l.a=-155,l=$\overline{\mathrm{q}}$}{i2}
\fmfv{l.d=5,l.a=25,l=$\nu$}{o1}
\fmfv{l.d=5,l.a=20,l=q$''$}{o2}
\fmfv{l.d=5,l.a=-15,l=$\overline{\mathrm{q}}'''$}{o3}
\fmfv{l.d=5,l.a=20,l=$\ell^\mp$}{o4}
\fmfv{l.d=5,l.a=-15,l=$\ell^\pm$}{o5}
\fmfv{l.d=4,l.a=-25,l=$\ell^\pm$}{o6}
\end{fmfgraph*}
\end{fmfpicture}
% VLL E -> bql decay
\begin{fmfpicture}{3,13}{5,13}{vll_bql_decay} % padding (LT)(RB)
\begin{fmfgraph*}(90,65) % canvas (W,H)
% external vertices
\fmfleft{d,i,d,d}
\fmfright{o3,m,o2,o1}
\fmftop{t} % for pulling
\fmfshift{9 down}{o2}
\fmfshift{4 left}{o3}
% main process
\fmf{fermion,f=colVLL,t=1.4}{i,v}
\fmf{phantom}{v,m}
\fmffreeze
\fmf{boson,f=colBSM,t=1.5,label=\colBSM U,l.s=left,l.d=4}{v,w}
\fmf{fermion}{o2,w,o1}
\fmf{fermion}{v,o3}
\fmf{phantom,t=0.7}{w,t} % pull W decay vertex
% labels
\fmfv{l.d=5,l.a=180,l=\colVLL E}{i}
\fmfv{l.d=5,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}$}{o2}
\fmfv{l.d=4,l.a=-25,l=b}{o3}
%\fmfv{l.d=8,l.a=180,l=U}{w} % for boson line
\end{fmfgraph*}
\end{fmfpicture}
% VLL N -> tql decay
\begin{fmfpicture}{4,13}{5,13}{vll_tql_decay} % padding (LT)(RB)
\begin{fmfgraph*}(90,65) % canvas (W,H)
% external vertices
\fmfleft{d,i,d,d}
\fmfright{o3,m,o2,o1}
\fmftop{t} % for pulling
\fmfshift{9 down}{o2}
\fmfshift{4 left}{o3}
% main process
\fmf{fermion,f=colVLL,t=1.4}{i,v}
\fmf{phantom}{v,m}
\fmffreeze
\fmf{boson,t=1.5,f=colBSM,label=\colBSM U,l.s=left,l.d=4}{v,w}
\fmf{fermion}{o2,w,o1}
\fmf{fermion}{v,o3}
\fmf{phantom,t=0.7}{w,t} % pull W decay vertex
% labels
\fmfv{l.d=5,l.a=180,l=\colVLL N}{i}
\fmfv{l.d=5,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}$}{o2}
\fmfv{l.d=4,l.a=-25,l=t}{o3}
%\fmfv{l.d=8,l.a=180,l=U}{w} % for boson line
\end{fmfgraph*}
\end{fmfpicture}
\end{document}Click to download: VLQ_VLL.tex • VLQ_VLL.pdf
Open in Overleaf: VLQ_VLL.tex
