More tests, will possibly be split for a gallery view. Preamble settings/definitions could be moved to a separate file and uploaded to the online compiler.
% !TEX program = pdflatexmk
% !TEX parameter = -shell-escape
% Author: Izaak Neutelings (January 2024)
% Description: VLQs / VLLs / HNLs in pp collisions
% Sources: https://cms.cern.ch/iCMS/analysisadmin/cadilines?line=EXO-23-006
% Instructions: To compile via command line, run the following twice
% pdflatex -shell-escape VLQ_VLL_HNL.tex
\documentclass[10pt,border=2pt,multi=page,crop]{standalone}
\usepackage{feynmp-auto}
\usepackage{amsmath}
\usepackage{xcolor}
\usepackage{pgffor} % for \foreach
%\usepackage{graphicx}
% DEFINE TEXT COLORS
\definecolor{colVLQ}{rgb}{.5,0,.7} % VLQ (purple)
\definecolor{colVLL}{rgb}{0,0,1} % VLL (blue)
\definecolor{colHNL}{rgb}{.1,.5,.1} % HNL (green)
\definecolor{colBSM}{rgb}{.96,.3,0} % BSM mediator (orange)
\definecolor{colrd}{rgb}{.9,0,0} % red
%\definecolor{mybl}{rgb}{0,0,1} % blue
%\definecolor{mygr}{rgb}{.1,.7,.1} % green
%\definecolor{myor}{rgb}{1,0.5,0} % orange
\newcommand\colVLQ{\color{colVLQ}}
\newcommand\colVLL{\color{colVLL}}
\newcommand\colHNL{\color{colHNL}}
\newcommand\colBSM{\color{colBSM}}
\newcommand\colrd{\color{colrd}}
% DEFINE ENVIRONMENT
\usepackage{environ}
\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}{11} % 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{ % define custom line colors in MetaPost (does not work in \fmfv)
color colVLQ; colVLQ := (.5,0,.7); % VLQ (purple)
color colVLL; colVLL := (0,0,.8); % VLL (blue)
color colHNL; colHNL := (.1,.5,.1); % HNL (green)
color colBSM; colBSM := (.96,.3,0); % BSM mediator (orange)
color myrd; myrd := (.9,0,0); % red
%color mybl; mybl := (0,0,1); % blue
%color myrd; mygr := (.1,.7,.1); % green
%color myor; myor := (1,.5,0); % orange
%color black; black := (.1,.7,.1); % HNL (green)
}
\BODY % main code
\end{fmffile}
}
\end{page}
}
%% MACRO to expand macros in \fmf
%\newcommand{\efmf}[1]{%
% \begingroup\edef\x{\endgroup\noexpand\fmf{#1}}\x
%}
% 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}
\large % increase font size
%%%%%%%%%%%
% VLQ %
%%%%%%%%%%%
% VLQ pair production - gluon fusion
\begin{fmfpicture}{4,14}{8,16}{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=5,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}{4,14}{8,16}{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}{2,-5}{47,-4}{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}{24,12}{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}{4,14}{8,16}{vlq-qq-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}{3,12}{8,14}{vll-qq-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}{3,12}{10,14}{vll-qq-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}{4,15}{14,16}{vll-qq-w-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=4,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}{2,15}{14,16}{vll-qq-z-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}{3,12}{7,13}{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}{3,12}{7,13}{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}
%%%%%%%%%%%
% HNL %
%%%%%%%%%%%
% HNL single production without W/Z decay
\begin{fmfpicture}{4,-8}{16,3}{hnl-qq-llV} % padding (LT)(RB)
\begin{fmfgraph*}(130,105) % canvas (W,H)
% external vertices
%\fmfstraight
\fmfleft{d,i2,d,i1,d} % incoming vertices
\fmfright{o3,o2,o1} % outgoing vertices
\fmfshift{10 left}{o2}
%\fmfshift{5 up}{o2}
%\fmfshift{5 up}{o3}
% skeleton
\fmf{fermion,t=1.0}{i1,v1,i2} % incoming particles
\fmf{phantom,t=0.38}{o3,v2,o1} % outgoing particles (pull)
\fmf{boson,t=0.9,label=W$^\pm$/Z,l.s=right,l.d=3}{v2,v1} % s-channel
\fmffreeze
% HNL + SM lepton
\fmf{fermion}{n1,v2} % SM lepton
\fmf{fermion,f=colHNL,label=\colHNL N,l.s=right,l.d=4}{v2,n2} % HNL
\fmf{phantom,t=1.2}{n1,o1} % pull SM lepton
\fmf{phantom,t=1.0,f=colHNL}{n2,o3} % pull HNL
\fmffreeze
% HNL decay
\fmf{fermion}{n2,o2} % outgoing particles
\fmf{boson,t=1.0,label=W$^\pm$/Z,l.s=right,l.d=3}{n2,o3} % W/Z boson
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=2,l.a=40,l=$\ell^\pm/\nu$}{n1}
\fmfv{l.d=2,l.a=26,l=$\ell'^\mp/\overline{\nu}'$}{o2}
\end{fmfgraph*}
\end{fmfpicture}
% HNL single production with W_R decay
\begin{fmfpicture}{5,-18}{10,10}{hnl-qq-llqq-WR} % padding (LT)(RB)
\begin{fmfgraph*}(140,120) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d} % incoming vertices
\fmfright{o4,o3,o2,d,o1} % outgoing vertices
\fmfshift{10 left}{o2}
\fmfshift{5 up}{o2}
\fmfshift{5 up}{o3}
% skeleton
\fmf{fermion,t=1.0}{i1,v1,i2} % incoming particles
\fmf{phantom,t=0.35}{o4,v2,o1} % outgoing particles (pull)
\fmf{boson,t=1.1,f=colBSM,label=\colBSM W$_\mathrm{R}^\pm$,l.s=right,l.d=4}{v2,v1} % s-channel
\fmffreeze
% HNL + SM lepton
\fmf{fermion}{n1,v2} % SM lepton
\fmf{majorana,f=colHNL,label=\colHNL N$_\ell$,l.s=right,l.d=4}{v2,n2} % HNL
\fmf{phantom,t=0.9}{n1,o1} % pull SM lepton
\fmf{phantom,t=0.6}{n2,o4} % pull HNL
\fmffreeze
% HNL decay
\fmf{fermion}{n2,o2} % outgoing particles
\fmf{boson,t=1,f=colBSM,label=\colBSM W$_\mathrm{R}^\pm$,l.s=right,l.d=3}{n2,v3} % W/Z boson
\fmf{fermion}{o4,v3} % outgoing particles
\fmffreeze
\fmf{fermion}{v3,o3} % outgoing particles
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=2,l.a=40,l=$\ell^\pm$}{n1}
\fmfv{l.d=3,l.a=26,l=$\ell'^\mp$}{o2}
\fmfv{l.d=4,l.a=24,l=q$'$}{o3}
\fmfv{l.d=5,l.a=-20,l=$\overline{\mathrm{q}}''$}{o4}
\end{fmfgraph*}
\end{fmfpicture}
% HNL single production with W/Z decay
\begin{fmfpicture}{5,-15}{53,10}{hnl-qq-llqq} % padding (LT)(RB)
\begin{fmfgraph*}(140,120) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d} % incoming vertices
\fmfright{o4,o3,o2,d,o1} % outgoing vertices
\fmfshift{10 left}{o2}
\fmfshift{5 up}{o2}
\fmfshift{5 up}{o3}
% skeleton
\fmf{fermion,t=1.0}{i1,v1,i2} % incoming particles
\fmf{phantom,t=0.35}{o4,v2,o1} % outgoing particles (pull)
\fmf{boson,t=1.1,label=W$^\pm$/Z,l.s=right,l.d=4}{v2,v1} % s-channel
\fmffreeze
% HNL + SM lepton
\fmf{fermion}{n1,v2} % SM lepton
\fmf{fermion,f=colHNL,label=\colHNL N,l.s=right,l.d=4}{v2,n2} % HNL
\fmf{phantom,t=0.9}{n1,o1} % pull SM lepton
\fmf{phantom,t=0.6}{n2,o4} % pull HNL
\fmffreeze
% HNL decay
\fmf{fermion}{n2,o2} % outgoing particles
\fmf{boson,t=1.0,label=W$^\pm$/Z,l.s=right,l.d=3}{n2,v3} % W/Z boson
\fmf{fermion}{o4,v3} % outgoing particles
\fmffreeze
\fmf{fermion}{v3,o3} % outgoing particles
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=2,l.a=40,l=$\ell^\pm/\nu$}{n1}
\fmfv{l.d=3,l.a=26,l=$\ell'^\mp/\overline{\nu}'$}{o2}
\fmfv{l.d=4,l.a=24,l=$q''/\ell''^\mp/\nu''$}{o3}
\fmfv{l.d=5,l.a=-20,l=$\overline{\mathrm{q}}'''/\ell''^\pm/\overline{\nu}''$}{o4}
\end{fmfgraph*}
\end{fmfpicture}
% HNL single production through Wgamma
\begin{fmfpicture}{2,-11}{11,10}{hnl-gW-llqqq} % padding (LT)(RB)
\begin{fmfgraph*}(150,140) % canvas (W,H)
% external vertices
\fmfstraight
\fmfleft{d,i2,d,i1,d} % incoming vertices
\fmfright{o5,o4,o3,o2,o1} % outgoing vertices
\fmfshift{7 down}{o2,o3}
\fmfshift{5 down}{o4}
% skeleton
\fmf{fermion,t=2.5}{i1,v1} % top incoming particle
\fmf{boson,t=2.5}{i2,v2} % bottom incoming particle (photon)
\fmf{fermion,t=2}{v1,p1} % top outgoing particle (quark)
\fmf{phantom,t=2}{p1,o1} % top outgoing particle (to pull quark)
\fmf{phantom,t=2}{v2,p2,o5} % bottom outgoing particle
\fmf{boson,t=2.8,label=W$^\pm$,l.s=right,l.d=3}{v1,v2} % t-channel W boson
\fmffreeze
% HNL decay
\fmf{boson,label=W$^\pm$\!,l.s=right,l.d=4}{v2,N1} % fused W boson
\fmf{majorana,f=colHNL,label=\colHNL N,l.s=right,l.d=4}{N1,N2} % HNL
\fmf{boson,label=W$^\pm$\!,l.s=right,l.d=4}{N2,w} % W boson from HNL decay
\fmf{fermion}{o5,w} % quark from W decay
\fmffreeze
% outgoing leptons
\fmf{fermion}{l1,N1} % lepton from W decay
\fmf{fermion}{N2,l2} % lepton from HNL decay
% outgoing quark
\fmf{fermion}{w,o4} % quark from W decay
\fmf{phantom,t=1.7}{l1,o2} % pull
\fmf{phantom,t=2.4}{l2,o3} % pull
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\gamma$}{i2}
\fmfv{l.d=5,l.a=26,l=$\ell^\pm$}{l1}
\fmfv{l.d=5,l.a=26,l=$\ell^\pm$}{l2}
\fmfv{l.d=5,l.a=23,l=q$'$}{p1}
\fmfv{l.d=5,l.a=23,l=q$''$}{o4}
\fmfv{l.d=5,l.a=-20,l=$\overline{\mathrm{q}}'''$}{o5}
\end{fmfgraph*}
\end{fmfpicture}
% HNL from B decay
% https://wiki.physik.uzh.ch/cms/latex:feynman#neutron_beta_decay_with_spectator_quarks
\begin{fmfpicture}{14,16}{35,20}{hnl-B-decay} % padding (LT)(RB)
\begin{fmfgraph*}(160,80) % canvas (W,H)
% external vertices
\fmfstraight
\fmftop{t1,t2,t3} % top vertices
\fmfbottom{b1,b2,d,b3} % bottom vertices
\fmfright{o2,o1,d,d}
\fmfshift{10 right}{o1,o2}
\fmfshift{6 right}{b2} % make quark line longer
\fmfshift{3 right}{t2} % move outgoing (primary) lepton
% skeleton
\fmf{phantom,t=1.3}{v1,t1} % pull
\fmf{phantom,t=1}{v1,b1} % pull
\fmf{fermion,t=1.2,f=colHNL,label=\colHNL N$_\ell$,l.s=right,l.d=6}{v1,v2} % HNL s-channel
\fmf{fermion,t=1.3}{v2,t3} % outgoing lepton
\fmf{phantom,t=1}{v2,b3} % pull
\fmffreeze
% B decay
\fmf{boson,t=1.5,label=W$^{\pm*}$,l.s=left,l.d=4}{d1,v1} % left W boson
\fmf{fermion,t=2}{b2,d1,b1} % B meson top quark lines
\fmf{phantom,t=0.6}{b1,d1} % pull left W decay vertex to left
% B decay spectator quarks
\fmffreeze % before using \fmfi
\fmf{phantom,t=0}{d1,b2} % hack to reverse arrowhead
\fmfi{fermion}{vpath (__b1,__d1) shifted (0,-13)} % incoming spectator quark
\fmfi{fermion}{vpath (__d1,__b2) shifted (0,-13)} % outgoing spectator quark
\fmfv{l=\parbox{6pt}{B}\mylbrace{21}{-12},l.d=8,l.a=180}{b1} % left brace
\fmfv{l=\myrbrace{21}{-12}\parbox{2pt}{$X$},l.d=8,l.a=0}{b2} % right brace
% HNL decay
\fmf{fermion,t=1.1}{t2,v1} % outgoing (primary) lepton
\fmf{boson,t=2,label=W$^{\pm*}$,l.s=left,l.d=4}{d2,v2}
\fmf{fermion,t=2}{o1,d2,o2} % right W decay
\fmf{phantom,t=1.4}{b2,d2} % pull right W decay vertex to left
\fmf{phantom,t=1.4}{o2,d2} % pull right W decay vertex to right
\fmfv{l=\myrbrace{34}{-26}\parbox{2pt}{$\pi^\pm$},l.d=8,l.a=0}{o1} % right brace
% labels
\fmfv{l.d=3,l.a=25,l=$\ell^\pm_\mathrm{P}$}{t2}
\fmfv{l.d=4,l.a=60,l=$\ell^\mp$}{t3}
%\fmfv{d.sh=circle,d.si=3,f=(.9,,0,,0),l.d=3,l.a=113,
% l=\normalsize\colrd$V_{\ell N}$}{v1} % neutrino
%\fmfv{d.sh=circle,d.si=3,f=(.9,,0,,0),l.d=3,l.a=113,
% l=\normalsize\colrd$V_{\ell N}$}{v2} % neutrino
\end{fmfgraph*}
\end{fmfpicture}
% HNL from B decay with explicit mixing
% https://wiki.physik.uzh.ch/cms/latex:feynman#neutron_beta_decay_with_spectator_quarks
\begin{fmfpicture}{14,16}{35,20}{hnl-B-decay-mix} % padding (LT)(RB)
\begin{fmfgraph*}(180,80) % canvas (W,H)
% external vertices
\fmfstraight
\fmftop{t1,t2,t3} % top vertices
\fmfbottom{b1,b2,d,b3} % bottom vertices
\fmfright{o2,o1,d,d}
\fmfshift{10 right}{o1,o2}
\fmfshift{6 right}{b2} % make quark line longer
\fmfshift{3 right}{t2} % move outgoing (primary) lepton
% skeleton
\fmf{phantom,t=1.3}{v1,t1} % pull
\fmf{phantom,t=1}{v1,b1} % pull
\fmf{phantom,t=1.2}{v1,v2}
\fmf{fermion,t=1.3}{v2,t3} % outgoing lepton
\fmf{phantom,t=1}{v2,b3} % pull
\fmffreeze
% B decay
\fmf{boson,t=1.5,label=W$^{\pm*}$,l.s=left,l.d=4}{d1,v1} % left W boson
\fmf{fermion,t=2}{b2,d1,b1} % B meson top quark lines
\fmf{phantom,t=0.6}{b1,d1} % pull left W decay vertex to left
% B decay spectator quarks
\fmffreeze % before using \fmfi
\fmf{phantom,t=0}{d1,b2} % hack to reverse arrowhead
\fmfi{fermion}{vpath (__b1,__d1) shifted (0,-13)} % incoming spectator quark
\fmfi{fermion}{vpath (__d1,__b2) shifted (0,-13)} % outgoing spectator quark
\fmfv{l=\parbox{6pt}{B}\mylbrace{21}{-12},l.d=8,l.a=180}{b1} % left brace
\fmfv{l=\myrbrace{21}{-12}\parbox{2pt}{$X$},l.d=8,l.a=0}{b2} % right brace
% s-channel
\fmf{plain,t=2,label=$\nu_{\ell_\mathrm{P}}$,l.s=right,l.d=4}{v1,n1} % neutrino s-channel
\fmf{plain,t=2,label=$\nu_\ell$,l.s=right,l.d=4}{n2,v2} % neutrino s-channel
\fmf{fermion,f=colHNL,label=\colHNL N$_\ell$,l.s=right,l.d=6}{n1,n2} % HNL s-channel
\fmfv{decor.shape=cross,decor.size=8}{n1,n2} % t-channel neutrino
% HNL decay
\fmf{fermion,t=1.1}{t2,v1} % outgoing (primary) lepton
\fmf{boson,t=2,label=W$^{\pm*}$,l.s=right,l.d=3}{d2,v2}
\fmf{fermion,t=2}{o1,d2,o2} % right W decay
\fmf{phantom,t=1.4}{b2,d2} % pull right W decay vertex to left
\fmf{phantom,t=1.4}{o2,d2} % pull right W decay vertex to right
\fmfv{l=\myrbrace{34}{-26}\parbox{2pt}{$\pi^\pm$},l.d=8,l.a=0}{o1} % right brace
% labels
\fmfv{l.d=3,l.a=25,l=$\ell^\pm_\mathrm{P}$}{t2}
\fmfv{l.d=4,l.a=60,l=$\ell^\mp$}{t3}
\end{fmfgraph*}
\end{fmfpicture}
% WEINBERG operator - t-channel
\begin{fmfpicture}{-8,10}{10,14}{hnl-vbf-ll-wein} % padding (LT)(RB)
\begin{fmfgraph*}(120,100) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o4,o3,o2,o1}
\fmfshift{1 up}{o2}
\fmfshift{1 down}{o3}
% VBF process
\fmf{fermion,t=1.7}{i1,v1} % top incoming quark
\fmf{fermion,t=1.7}{i2,v2} % bottom incoming quark
\fmf{phantom,t=0.4}{v1,v2} % t-channel
\fmf{fermion}{v1,o1} % top outgoing quark
\fmf{fermion}{o4,v2} % bottom outgoing quark
\fmffreeze
% main process
\fmf{fermion,t=1}{l1,o2} % outgoing lepton
\fmf{fermion,t=1}{l2,o3} % outgoing lepton
%\fmf{plain,t=1.5,label=\strut$\nu_\ell$,l.s=left,l.d=3}{l2,x} % t-channel
%\fmf{plain,t=1.5,label=$\overline{\nu}_\ell$,l.s=left,l.d=3}{x,l1} % t-channel
\fmf{plain,t=1.5}{l2,x,l1} % t-channel
\fmfv{decor.shape=cross,decor.size=8}{x} % t-channel neutrino
\fmf{boson,t=1.3,label=W$^\pm$,l.s=left,l.d=3}{l1,v1} % boson
\fmf{boson,t=1.3,label=W$^\pm$,l.s=right,l.d=3}{l2,v2} % boson
% labels
\fmfv{l.d=5,l.a=160,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=q$'$}{i2}
\fmfv{l.d=5,l.a=22,l=q$''$}{o1}
\fmfv{l.d=5,l.a=10,l=$\ell^\pm$}{o2}
\fmfv{l.d=5,l.a=-10,l=$\ell^\pm$}{o3}
\fmfv{l.d=5,l.a=-23,l=q$''''$}{o4}
\fmfv{l.d=5,l.a=-120,l=$\nu_\ell$}{l1} % neutrino
\fmfv{l.d=5,l.a=120,l=$\overline{\nu}_\ell$}{l2} % neutrino
\end{fmfgraph*}
\end{fmfpicture}
% HNL (Majorana) - t-channel
\begin{fmfpicture}{-8,10}{10,14}{hnl-vbf-ll-majo} % padding (LT)(RB)
\begin{fmfgraph*}(120,100) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o4,o3,o2,o1}
\fmfshift{1 up}{o2}
\fmfshift{1 down}{o3}
% VBF process
\fmf{fermion,t=1.7}{i1,v1} % top incoming quark
\fmf{fermion,t=1.7}{i2,v2} % bottom incoming quark
\fmf{phantom,t=0.4}{v1,v2} % t-channel
\fmf{fermion}{v1,o1} % top outgoing quark
\fmf{fermion}{v2,o4} % bottom outgoing quark
\fmffreeze
% main process
\fmf{fermion,t=1}{l1,o2} % outgoing lepton
\fmf{fermion,t=1}{l2,o3} % outgoing lepton
%\fmf{fermion,t=0.75,f=colHNL,label=\colHNL N,l.d=4}{l2,l1} % t-channel Majorana
%\fmf{fermion,t=0.00,f=colHNL}{l1,l2} % t-channel Majorana
\fmf{majorana,t=0.75,f=colHNL,label=\colHNL N$_\ell$,l.s=left,l.d=4}{l2,l1} % t-channel Majorana
\fmf{boson,t=1.3,label=W$^\pm$,l.s=left,l.d=2}{l1,v1} % boson
\fmf{boson,t=1.3,label=W$^\pm$,l.s=right,l.d=1}{l2,v2} % boson
% vertices highlights
\fmfv{d.sh=circle,d.si=3,f=(.9,,0,,0),l.d=4,l.a=-50,
l=\normalsize\colrd$V_{\ell N}$}{l1} % neutrino
\fmfv{d.sh=circle,d.si=3,f=(.9,,0,,0),l.d=4,l.a=50,
l=\normalsize\colrd$V_{\ell N}$}{l2} % neutrino
% labels
\fmfv{l.d=5,l.a=160,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=q$'$}{i2}
\fmfv{l.d=5,l.a=22,l=q$''$}{o1}
\fmfv{l.d=5,l.a=10,l=$\ell^\pm$}{o2}
\fmfv{l.d=5,l.a=-10,l=$\ell^\pm$}{o3}
\fmfv{l.d=5,l.a=-23,l=q$''''$}{o4}
\end{fmfgraph*}
\end{fmfpicture}
% HNL (Type-III Seesaw) pair production through W*
\begin{fmfpicture}{4,15}{14,16}{hnl-qq-w-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=colHNL,label=\colHNL $\Sigma^0$,l.d=3,l.s=left}{v2,w1} % HNL
\fmf{fermion,t=1.1,f=colHNL,label=\colHNL $\Sigma^\pm$,l.d=4,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{boson,t=1.2,label=$\mathrm{W}^\pm$,l.d=5,l.s=left}{w2,d2} % W 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=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=20,l=$\overline{\nu}$}{o2}
\fmfv{l.d=5,l.a=-15,l=$\ell^\pm$}{o3}
\fmfv{l.d=5,l.a=15,l=$\nu$}{o4}
\fmfv{l.d=5,l.a=-15,l=$\ell^\pm$}{o5}
\fmfv{l.d=5,l.a=-25,l=$\overline{\nu}$}{o6}
\end{fmfgraph*}
\end{fmfpicture}
% HNL (Type-III Seesaw) pair production through Z
\begin{fmfpicture}{2,15}{14,15}{hnl-qq-z-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 -> Z & 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=colHNL,label=\colHNL $\Sigma^\mp$,l.d=3,l.s=left}{v2,w1} % HNL
\fmf{fermion,t=1.1,f=colHNL,label=\colHNL $\Sigma^\pm$,l.d=4,l.s=left}{w2,v2} % HNL
\fmffreeze
% HNL decay
\fmf{boson,t=1.2,label=Z,l.d=5,l.s=right}{w1,d1} % Z boson
\fmf{fermion}{o2,d1,o3}
% 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=$\ell^\mp$}{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=15,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}
% HNL pair production through Z'
\begin{fmfpicture}{2,15}{14,15}{hnl-qq-zp-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 -> Z' & skeleton
\fmf{fermion,t=1.5}{i1,v1,i2}
\fmf{boson,t=1.5,f=colBSM,label=\colBSM Z$'$,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
% Z' decay to heavy leptons
\fmf{majorana,t=1.1,f=colHNL,label=\colHNL N$_\ell$,l.d=4,l.s=left}{v2,w1} % HNL
\fmf{majorana,t=1.1,f=colHNL,label=\colHNL N$_\ell$,l.d=4,l.s=left}{w2,v2} % HNL
\fmffreeze
% HNL decay on top
\fmf{boson,t=1.2,f=colBSM,label=\colBSM W$_\mathrm{R}^{\pm*}$,l.d=4,l.s=right}{w1,d1} % W boson
\fmf{fermion}{o3,d1,o2}
% HCL decay on bottom
\fmf{boson,t=1.2,f=colBSM,label=\colBSM W$_\mathrm{R}^{\mp*}$,l.d=4,l.s=left}{w2,d2} % W 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=$\ell^\mp$}{o1}
\fmfv{l.d=5,l.a=21,l=q$'$}{o2}
\fmfv{l.d=5,l.a=-21,l=$\overline{\mathrm{q}}''$}{o3}
\fmfv{l.d=5,l.a=21,l=q$'''$}{o4}
\fmfv{l.d=5,l.a=-22,l=$\overline{\mathrm{q}}''''$}{o5}
\fmfv{l.d=4,l.a=-25,l=$\ell^\pm$}{o6}
\end{fmfgraph*}
\end{fmfpicture}
% HLN four-fermion interaction
\begin{fmfpicture}{-6,11}{-14,13}{hnl-four-fermion} % padding (LT)(RB)
\parbox{110pt}{\begin{fmfgraph*}(90,70) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% main process
\fmf{fermion}{i1,v,i2} % incoming particles
\fmf{fermion}{v,o1} % outgoing particle
\fmf{majorana,f=colHNL}{o2,v} % outgoing particle
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=4,l.a=25,l=$\ell^\mp$}{o1}
\fmfv{l.d=4,l.a=-25,l=\colHNL N$_\ell$}{o2}
\fmfblob{20}{v}
\end{fmfgraph*}}
=\quad
\parbox{120pt}{\begin{fmfgraph*}(110,65) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% main process
\fmf{fermion}{i1,v1,i2} % incoming particles
\fmf{boson,t=1,label=W$^\pm$,l.s=left}{v1,w2} % s-channel
\fmf{fermion}{w2,o1} % outgoing particle
\fmf{majorana,f=colHNL}{o2,w2} % outgoing particle
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=4,l.a=25,l=$\ell^\pm$}{o1}
\fmfv{l.d=4,l.a=-25,l=\colHNL N$_\ell$}{o2}
\fmfdot{w2}
\end{fmfgraph*}}
+\quad
\parbox{110pt}{\begin{fmfgraph*}(90,65) % canvas (W,H)
% external vertices
\fmfleft{i2,i1}
\fmfright{o2,o1}
% main process
\fmf{fermion}{i1,v,i2} % incoming particles
\fmf{fermion}{v,o1} % outgoing particle
\fmf{majorana,f=colHNL}{o2,v} % outgoing particle
% labels
\fmfv{l.d=5,l.a=155,l=q}{i1}
\fmfv{l.d=5,l.a=-155,l=$\overline{\mathrm{q}}'$}{i2}
\fmfv{l.d=4,l.a=25,l=$\ell^\pm$}{o1}
\fmfv{l.d=4,l.a=-25,l=\colHNL N$_\ell$}{o2}
\fmfdot{v}
\end{fmfgraph*}}
\end{fmfpicture}
% HLN decay
\begin{fmfpicture}{-7,13}{-10,14}{hnl-decay-blob} % padding (LT)(RB)
\parbox{120pt}{\begin{fmfgraph*}(100,70) % canvas (W,H)
% external vertices
\fmfleft{i1}
\fmfright{o3,o2,o1}
% main process
\fmf{majorana,f=colHNL,t=1,label=\colHNL N$_\ell$,l.s=left}{i1,v}
\fmf{fermion}{o2,v}
\fmffreeze
\fmf{fermion}{v,o1}
\fmf{fermion}{v,o3}
% labels
\fmfv{l.d=5,l.a=25,l=q}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}'$}{o2}
\fmfv{l.d=4,l.a=-25,l=$\ell^\mp$}{o3}
\fmfblob{20}{v}
\end{fmfgraph*}}
=\quad
\parbox{120pt}{\begin{fmfgraph*}(100,70) % canvas (W,H)
% external vertices
\fmfleft{i1}
\fmfright{o3,d,m,o2,o1}
\fmftop{t} % for pulling
\fmfshift{9 down}{o2}
\fmfshift{4 left}{o3}
% main process
\fmf{majorana,f=colHNL,t=1.2,label=\colHNL N$_\ell$,l.s=left}{i1,v}
\fmf{phantom,t=1.1}{v,m}
\fmffreeze
%\fmf{boson,t=1.5,label=W$^\pm$,l.d=1,l.s=left}{v,w}
\fmf{boson,t=1.5}{v,w}
\fmf{fermion}{o2,w,o1}
\fmf{fermion}{v,o3}
\fmf{phantom,t=0.4}{w,t}
% labels
\fmfv{l.d=5,l.a=25,l=q}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}'$}{o2}
\fmfv{l.d=4,l.a=-25,l=$\ell^\mp$}{o3}
\fmfv{l.d=8,l.a=180,l=W$^\pm$}{w} % for boson line
\end{fmfgraph*}}
+\quad
\parbox{110pt}{\begin{fmfgraph*}(90,65) % canvas (W,H)
% external vertices
\fmfleft{i1}
\fmfright{o3,o2,o1}
\fmf{majorana,f=colHNL,t=1,label=\colHNL N$_\ell$,l.s=left}{i1,v}
\fmf{fermion}{o2,v}
\fmffreeze
\fmf{fermion}{v,o1}
\fmf{fermion}{v,o3}
% labels
\fmfv{l.d=5,l.a=25,l=q}{o1}
\fmfv{l.d=5,l.a=0,l=$\overline{\mathrm{q}}'$}{o2}
\fmfv{l.d=4,l.a=-25,l=$\ell^\mp$}{o3}
\fmfdot{v}
\end{fmfgraph*}}
\end{fmfpicture}
\end{document}