% !TEX program = pdflatexmk
% !TEX parameter = -shell-escape
% Author: Izaak Neutelings (September 2024)
% Instructions: To compile via command line, run the following twice
%   pdflatex -shell-escape LQ.tex
\documentclass[11pt,border=2pt,multi=page,crop]{standalone}
\usepackage{feynmp-auto}

% DEFINE TEXT COLORS
\usepackage{xcolor}
\definecolor{colvtx}{rgb}{0,.1,1} % LQ vertex (blue)
\definecolor{colqcd}{rgb}{1,0,0} % strong vertex (red)

% 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 {colvtx,colqcd}{ % 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
\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{dash_len}{10} % dashes length
    \fmfset{wiggly_len}{12} % boson wavelength
    \fmfset{wiggly_slope}{65} % boson slope of waves
    \fmfcmd\MPcolors % define custom line colors in MetaPost
    \BODY % main code
  \end{fmffile}
  }
  \end{page}
}

\begin{document}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% SINGLE LQ PRODUCTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% SINGLE LQ PRODUCTION - s-channel
\begin{fmfpicture}{3,22}{13,15}{LQ_single_schan} % padding (LTRB)
  \begin{fmfgraph*}(130,80) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{8 up}{o1,o2}
    \fmfshift{18 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.22w,.50h)}{v1} % exact placement
    \fmfforce{(.62w,.50h)}{v2} % exact placement
    \fmfforce{(.78w,.86h)}{lq} % exact placement
    % incoming partons
    \fmf{gluon}{v1,i1}
    \fmf{fermion}{i2,v1}
    % s-channel
    \fmf{fermion,l.s=right,label=$q$}{v1,v2}
    % associated lepton
    \fmf{fermion}{v2,o3}
    % LQ -> lepton + quark
    \fmf{dashes,t=1.2,l.s=left,label=LQ}{v2,lq}
    \fmf{fermion}{o2,lq,o1}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-8}{v2}
    % labels
    \fmfv{l.a=155,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-155,l.d=4,l=$q$}{i2}
    \fmfv{l.a=25,l.d=4,l=$q$}{o1}
    \fmfv{l.a=-20,l.d=4,l=\vspace{-2pt}$\ell^+$}{o2}
    \fmfv{l.a=-25,l.d=3,l=$\ell^-$}{o3}
  \end{fmfgraph*}
\end{fmfpicture}

% SINGLE LQ PRODUCTION - s-channel
\begin{fmfpicture}{3,22}{13,13}{LQ_single_schan_btautau} % padding (LTRB)
  \begin{fmfgraph*}(130,80) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{8 up}{o1,o2}
    \fmfshift{18 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.22w,.50h)}{v1} % exact placement
    \fmfforce{(.62w,.50h)}{v2} % exact placement
    \fmfforce{(.78w,.86h)}{lq} % exact placement
    % incoming partons
    \fmf{gluon}{v1,i1}
    \fmf{fermion}{i2,v1}
    % s-channel
    \fmf{fermion,l.s=right,label=b}{v1,v2}
    % associated lepton
    \fmf{fermion}{v2,o3}
    % LQ -> lepton + quark
    \fmf{dashes,t=1.2,l.s=left,label=LQ}{v2,lq}
    \fmf{fermion}{o2,lq,o1}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-8}{v2}
    % labels
    \fmfv{l.a=155,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-155,l.d=4,l=b}{i2}
    \fmfv{l.a=25,l.d=4,l=b}{o1}
    \fmfv{l.a=-20,l.d=4,l=\vspace{-2pt}$\tau^+$}{o2}
    \fmfv{l.a=-20,l.d=5,l=\vspace{-2pt}$\tau^-$}{o3}
  \end{fmfgraph*}
\end{fmfpicture}

% SINGLE LQ PRODUCTION - s-channel, gluon-splitting
\begin{fmfpicture}{3,32}{13,13}{LQ_single_schan_gsplit} % padding (LTRB)
  \begin{fmfgraph*}(135,95) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o4,o3,o2,o1}
    \fmfshift{20 up}{o1,o2}
    \fmfshift{8 up}{o3}
    \fmfshift{6 left}{o3}
    \fmfshift{28 left}{o4}
    % internal vertices (exact placement)
    \fmfforce{(.25w,.31h)}{vg} % exact placement
    \fmfforce{(.25w,.69h)}{v1} % exact placement
    \fmfforce{(.62w,.69h)}{v2} % exact placement
    \fmfforce{(.78w,1.04h)}{lq} % exact placement
    % gluon splitting
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,vg}
    \fmf{fermion,l.s=left,label=b}{vg,v1}
    \fmf{fermion}{o4,vg}
    % s-channel
    \fmf{fermion,l.s=left,label=b}{v1,v2}
    % associated lepton
    \fmf{fermion}{v2,o3}
    % LQ -> lepton + quark
    \fmf{dashes,t=1.2,l.d=4,l.s=left,label=LQ}{v2,lq}
    \fmf{fermion}{o2,lq,o1}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-110}{v2}
    % labels
    \fmfv{l.a=155,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-155,l.d=4,l=b}{i2}
    \fmfv{l.a=25,l.d=4,l=b}{o1}
    \fmfv{l.a=-20,l.d=4,l=\vspace{-2pt}$\tau^+$}{o2}
    \fmfv{l.a=-20,l.d=5,l=\vspace{-2pt}$\tau^-$}{o3}
    \fmfv{l.a=-20,l.d=5,l=\vspace{-2pt}b}{o4}
  \end{fmfgraph*}
\end{fmfpicture}

% SINGLE LQ PRODUCTION - s-channel, gluon-splitting
\begin{fmfpicture}{-10,14}{12,11}{LQ_single_schan_gsplit2} % padding (LTRB)
  \begin{fmfgraph*}(130,90) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o4,o3,o2,o1}
    \fmfshift{12 down}{i1}
    \fmfshift{12 up}{i2}
    % gluon splitting
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,v2}
    \fmf{fermion,t=0.9,l.s=left,label=b}{v2,v1} % t-channel
    \fmf{phantom,t=0.6}{v1,o1,o4,v2}
    \fmffreeze
    % outgoing bottom quarks
    \fmf{fermion}{v1,lq1}
    \fmf{fermion,t=0.8}{lq1,o1}
    \fmf{fermion}{o4,v2}
    \fmffreeze
    % LQ -> btau
    \fmf{dashes,t=0.9,l.s=right,l.d=4,label=LQ}{lq1,lq2}
    \fmf{fermion,t=0.9}{o2,lq2,o3}
    \fmf{phantom,t=0.9}{v2,lq2}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=120}{lq1}
    % labels
    \fmfv{l.a=160,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-160,l.d=4,l=$g$}{i2}
    \fmfv{l.a=25,l.d=4,l=$\tau^-$}{o1}
    \fmfv{l.a=25,l.d=4,l=\vspace{-2pt}$\tau^+$}{o2}
    \fmfv{l.a=-20,l.d=5,l=b}{o3}
    \fmfv{l.a=-20,l.d=5,l=\vspace{-2pt}b}{o4}
  \end{fmfgraph*}
\end{fmfpicture}

% SINGLE LQ PRODUCTION - t-channel
\begin{fmfpicture}{3,15}{13,11}{LQ_single_tchan} % padding (LTRB)
  \begin{fmfgraph*}(110,80) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{20 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.34w,.75h)}{v1} % exact placement
    \fmfforce{(.34w,.23h)}{v2} % exact placement
    \fmfforce{(.73w,.75h)}{lq} % exact placement
    \fmffreeze
    % gluon + quarks
    \fmf{gluon}{v1,i1}
    \fmf{fermion}{i2,v2,o3}
    % LQs
    \fmf{dashes,t=1.2,l.s=left,l.d=4,label=LQ}{v1,lq}
    \fmf{dashes,l.s=left,l.d=4,label=LQ}{v2,v1}
    % LQ -> lepton + quark
    \fmf{fermion}{o2,lq,o1}
    % vertex
    %\fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
    %      l=\colqcd$\alpha_\mathrm{s}$,l.d=5,l.a=-40}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=7,l.a=-90}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-160,l.d=4,l=b}{i2}
    \fmfv{l.a=-20,l.d=5,l=$\tau^-$}{o3}
    \fmfv{l.a=25,l.d=4,l=b}{o1}
    \fmfv{l.a=-20,l.d=5,l=$\tau^+$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% SINGLE LQ PRODUCTION - t-channel (photon-induced)
\begin{fmfpicture}{3,15}{13,11}{LQ_single_tchan_photon} % padding (LTRB)
  \begin{fmfgraph*}(110,80) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    \fmfshift{20 left}{o3}
    % internal vertices (exact placement)
    \fmfforce{(.34w,.75h)}{v1} % exact placement
    \fmfforce{(.34w,.23h)}{v2} % exact placement
    \fmfforce{(.73w,.75h)}{lq} % exact placement
    \fmffreeze
    % gluon + quarks
    \fmf{fermion}{i1,v1}
    \fmf{photon}{i2,v2} % photon
    \fmf{fermion}{v2,o3}
    % LQs
    \fmf{dashes,t=1.2,l.s=left,l.d=4,label=LQ}{v1,lq}
    \fmf{fermion,l.s=right,label=$\tau$}{v1,v2}
    % LQ -> lepton + quark
    \fmf{fermion}{o2,lq,o1}
    % vertex
    %\fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
    %      l=\colqcd$\alpha_\mathrm{s}$,l.d=5,l.a=-40}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=7,l.a=-90}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-160,l.d=4,l=$\gamma$}{i2}
    \fmfv{l.a=-20,l.d=5,l=$\tau^-$}{o3}
    \fmfv{l.a=25,l.d=4,l=b}{o1}
    \fmfv{l.a=-20,l.d=5,l=$\tau^+$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% LQ PAIR PRODUCTION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% LQ PAIR PRODUCTION - gluon fusion, s-channel
\begin{fmfpicture}{-8,16}{6,17}{LQ_pair_gg_schan} % padding (LTRB)
  \begin{fmfgraph*}(120,70) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % gg -> g
    \fmf{gluon}{i2,v1,i1}
    \fmf{gluon,t=1.1}{v1,v2} % s-channel
    % g -> LQ LQ
    \fmf{dashes,t=1.2}{o1,v2}
    \fmf{dashes,t=1.2}{o2,v2}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
          l=\strut\colqcd$\alpha_\mathrm{s}$,l.d=6,l.a=0}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-150,l.d=4,l=$g$}{i2}
    \fmfv{l.a=25,l.d=3,l=LQ}{o1}
    \fmfv{l.a=-25,l.d=4,l=$\overline{\mathrm{LQ}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR PRODUCTION - quark-antiquark annihilation
\begin{fmfpicture}{-10,16}{4,17}{LQ_pair_qq} % padding (LTRB)
  \begin{fmfgraph*}(120,70) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % gg -> g
    \fmf{fermion}{i1,v1,i2}
    \fmf{gluon,t=1.1}{v2,v1} % s-channel
    % g -> LQ LQ
    \fmf{dashes,t=1.2}{o1,v2}
    \fmf{dashes,t=1.2}{o2,v2}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
          l=\strut\colqcd$\alpha_\mathrm{s}$,l.d=6,l.a=0}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$q$}{i1}
    \fmfv{l.a=-150,l.d=4,l=$\overline{q}$}{i2}
    \fmfv{l.a=25,l.d=3,l=LQ}{o1}
    \fmfv{l.a=-25,l.d=4,l=$\overline{\mathrm{LQ}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR PRODUCTION - gluon-LQ fusion
\begin{fmfpicture}{-8,16}{6,17}{LQ_pair_ggLQ} % padding (LTRB)
  \begin{fmfgraph*}(80,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % gg -> g
    \fmf{gluon}{i2,v,i1}
    % g -> LQ LQ
    \fmf{dashes,t=1.2}{o1,v}
    \fmf{dashes,t=1.2}{o2,v}
    % vertex
    %\fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
    %      l=\strut\colqcd$\alpha_\mathrm{s}$,l.d=6,l.a=0}{v}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-150,l.d=4,l=$g$}{i2}
    \fmfv{l.a=25,l.d=4,l=LQ}{o1}
    \fmfv{l.a=-25,l.d=5,l=$\overline{\mathrm{LQ}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR PRODUCTION - gluon fusion, t-channel
\begin{fmfpicture}{-10,13}{4,13}{LQ_pair_gg_tchan} % padding (LTRB)
  \begin{fmfgraph*}(120,70) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % gg -> LQ LQ
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,v2}
    \fmf{dashes,t=0.8,l.s=right,label=LQ}{v1,v2} % t-channel
    % outgoing LQs
    \fmf{dashes}{o1,v1}
    \fmf{dashes}{o2,v2}
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
          l=\colqcd$\alpha_\mathrm{s}$,l.d=8,l.a=70}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
          l=\colqcd$\alpha_\mathrm{s}$,l.d=8,l.a=-70}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-150,l.d=4,l=$g$}{i2}
    \fmfv{l.a=20,l.d=5,l=LQ}{o1}
    \fmfv{l.a=-20,l.d=5,l=$\overline{\mathrm{LQ}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR PRODUCTION - quark-antiquark annihilation, t-channel
\begin{fmfpicture}{-10,11}{4,11}{LQ_pair_qq_tchan} % padding (LTRB)
  \begin{fmfgraph*}(120,70) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % qq -> LQ LQ
    \fmf{fermion}{i1,v1}
    \fmf{fermion}{v2,i2}
    \fmf{fermion,t=0.8,l.s=right,label=$\ell$}{v1,v2} % t-channel
    % outgoing LQs
    \fmf{dashes}{o1,v1}
    \fmf{dashes}{o2,v2}
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=7,l.a=90}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=7,l.a=-90}{v2}
    % labels
    \fmfv{l.a=160,l.d=4,l=$q$}{i1}
    \fmfv{l.a=-160,l.d=4,l=$\overline{q}$}{i2}
    \fmfv{l.a=20,l.d=4,l=LQ}{o1}
    \fmfv{l.a=-20,l.d=5,l=$\overline{\mathrm{LQ}}$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR PRODUCTION
\begin{fmfpicture}{3,14}{14,11}{LQ_pair_gg_decay} % padding (LTRB)
  \begin{fmfgraph*}(140,100) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o4,o3,o2,o1}
    \fmfshift{10 down}{i1}
    \fmfshift{10 up}{i2}
    % internal vertices (exact placement)
    \fmfforce{(.80w,.82h)}{lq1} % exact placement
    \fmfforce{(.80w,.18h)}{lq2} % exact placement
    % gg -> g
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,v1}
    \fmf{gluon,t=1.1}{v1,v2} % s-channel
    % g -> LQ LQ
    \fmf{dashes,t=1.2,l.s=left,label=LQ}{v2,lq1}
    \fmf{dashes,t=1.2,l.s=right,label=$\overline{\mathrm{LQ}}$}{v2,lq2}
    % LQ -> ql
    \fmf{fermion}{o2,lq1,o1}
    \fmf{fermion}{o3,lq2,o4}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
          l=\strut\colqcd$\alpha_\mathrm{s}$,l.d=6,l.a=0}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-150,l.d=4,l=$g$}{i2}
    \fmfv{l.a=25,l=$\tau^-$}{o1}
    \fmfv{l.a=-20,l=$\overline{\mathrm{b}}$}{o2}
    \fmfv{l.a=25,l=$\tau^+$}{o3}
    \fmfv{l.a=-20,l=\vspace{-2pt}b}{o4}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR PRODUCTION - round
\begin{fmfpicture}{-6,14}{14,11}{LQ_pair_gg_decay_round} % padding (LTRB)
  \begin{fmfgraph*}(150,120) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o4,o3,o2,o1}
    \fmfshift{12 down}{i1}
    \fmfshift{12 up}{i2}
    % internal vertices (exact placement)
    \fmfforce{(.80w,.75h)}{lq1} % exact placement
    \fmfforce{(.80w,.25h)}{lq2} % exact placement
    % gg -> g
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,v1}
    \fmf{gluon,t=1.1}{v1,v2} % s-channel
    % g -> LQ LQ
    \fmf{dashes,t=1.1,l.s=left,label=LQ}{v2,lq1}
    \fmf{dashes,t=1.1,l.s=right,label=$\overline{\mathrm{LQ}}$}{v2,lq2}
    % LQ -> ql
    \fmf{fermion}{o2,lq1,o1}
    \fmf{fermion}{o3,lq2,o4}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colqcd,
          l=\strut\colqcd$\alpha_\mathrm{s}$,l.d=6,l.a=0}{v2}
    % labels
    \fmfv{l.a=150,l.d=4,l=$g$}{i1}
    \fmfv{l.a=-150,l.d=4,l=$g$}{i2}
    \fmfv{l.a=25,l=$\tau^-$}{o1}
    \fmfv{l.a=-20,l=$\overline{\mathrm{b}}$}{o2}
    \fmfv{l.a=25,l=$\tau^+$}{o3}
    \fmfv{l.a=-20,l=\vspace{-2pt}b}{o4}
  \end{fmfgraph*}
\end{fmfpicture}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% NONRESONANT DILEPTON PRODUCTION %%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% NONRESONANT DILEPTON PRODUCTION - t-channel
\begin{fmfpicture}{-6,10}{3,10}{LQ_tchan} % padding (LTRB)
  \begin{fmfgraph*}(110,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main: qq -> ll
    \fmf{fermion}{i1,v1,o1}
    \fmf{fermion}{o2,v2,i2}
    \fmf{dashes,t=0.7,l.s=right,l.d=4,label=LQ}{v1,v2} % t-channel
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=90}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-90}{v2}
    % labels
    \fmfv{l.a=160,l=$q$}{i1}
    \fmfv{l.a=20,l=$\ell^-$}{o1}
    \fmfv{l.a=-170,l=$\overline{q}$}{i2}
    \fmfv{l.a=-10,l=$\ell^+$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% NONRESONANT DITAU PRODUCTION - t-channel
\begin{fmfpicture}{-6,10}{4,10}{LQ_tchan_bbtautau} % padding (LTRB)
  \begin{fmfgraph*}(110,60) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o2,o1}
    % main: qq -> ll
    \fmf{fermion}{i1,v1,o1}
    \fmf{fermion}{o2,v2,i2}
    \fmf{dashes,t=0.7,l.s=right,l.d=4,label=LQ}{v1,v2} % t-channel
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=90}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-90}{v2}
    % labels
    \fmfv{l.a=160,l=b}{i1}
    \fmfv{l.a=20,l=$\tau^-$}{o1}
    \fmfv{l.a=-170,l=$\overline{\mathrm{b}}$}{i2}
    \fmfv{l.a=-10,l=$\tau^+$}{o2}
  \end{fmfgraph*}
\end{fmfpicture}

% NONRESONANT DITAU PRODUCTION - t-channel, gluon splitting
\begin{fmfpicture}{-6,12}{15,14}{LQ_tchan_bbtautau_gsplit} % padding (LTRB)
  \begin{fmfgraph*}(110,80) % dimensions (WH)
    % external vertices
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    % incoming
    \fmf{fermion,t=1.7}{i1,v1}
    \fmf{gluon,t=1.7}{i2,v2}
    % t-channel
    \fmf{dashes,l.s=left,l.d=4,label=LQ}{v,v1} % t-channel
    \fmf{fermion}{v,v2} % t-channel
    % outgoing
    \fmf{fermion}{v1,o1}
    \fmf{fermion}{v2,o3}
    \fmf{fermion}{o2,v}
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=90}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx\strut$\lambda$,l.d=4,l.a=-65}{v}
    % labels
    \fmfv{l.d=6,l.a=158,l=q}{i1}
    \fmfv{l.d=6,l.a=-152,l=$g$}{i2}
    \fmfv{l.d=6,l.a=22,l=$\tau^-$}{o1}
    \fmfv{l.d=6,l.a=0,l=$\tau^+$}{o2}
    \fmfv{l.d=6,l.a=-20,l=b}{o3}
  \end{fmfgraph*}
\end{fmfpicture}

% NONRESONANT DITAU PRODUCTION - t-channel, gluon splitting (straight)
\begin{fmfpicture}{6,18}{16,12}{LQ_tchan_bbtautau_gsplit_straight} % padding (LTRB)
  \begin{fmfgraph*}(100,75) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{o3,o2,o1}
    % main
    \fmf{fermion}{i1,v1}
    \fmf{fermion}{v1,o1}
    \fmf{gluon}{i2,v2}
    \fmf{fermion}{v2,o3}
    \fmffreeze
    \fmf{fermion}{v,v2} % t-channel
    \fmf{dashes,l.s=left,l.d=5,label=LQ}{v,v1} % t-channel
    \fmf{fermion,t=0}{o2,v} % tau out
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=90}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx\strut$\lambda$,l.d=6,l.a=-160}{v}
    % labels
    \fmfv{l.d=6,l.a=170,l=q}{i1}
    \fmfv{l.d=6,l.a=-170,l=$g$}{i2}
    \fmfv{l.d=6,l.a=10,l=$\tau^-$}{o1}
    \fmfv{l.d=6,l.a=0,l=\strut$\tau^+$}{o2}
    \fmfv{l.d=6,l.a=-10,l=b}{o3}
  \end{fmfgraph*}
\end{fmfpicture}

% NONRESONANT DITAU PRODUCTION - t-channel, double gluon splitting
\begin{fmfpicture}{3,9}{13,9}{LQ_tchan_bbtautau_gsplit2} % padding (LTRB)
  \begin{fmfgraph*}(115,135) % dimensions (WH)
    % external vertices
    \fmfleft{d,i2,i1,d}
    \fmfright{b2,o2,o1,b1}
    \fmfshift{8 down}{b1}
    \fmfshift{8 up}{b2}
    % gluon splitting
    \fmf{gluon}{g1,i1}
    \fmf{gluon}{i2,g2}
    \fmf{phantom,t=0.62}{g1,o1,o2,g2} % pull gluons straight right
    \fmffreeze
    % main: qq -> ll
    \fmf{fermion}{g1,v1,o1}
    \fmf{fermion}{o2,v2,g2}
    \fmf{fermion}{b1,g1}
    \fmf{fermion}{g2,b2}
    \fmf{dashes,t=0.6,l.s=right,label=LQ}{v1,v2} % t-channel
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=90}{v1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-90}{v2}
    % labels
    \fmfv{l.a=160,l=$g$}{i1}
    \fmfv{l.a=-170,l=$g$}{i2}
    \fmfv{l.a=20,l=$\tau^-$}{o1}
    \fmfv{l.a=-10,l=$\tau^+$}{o2}
    \fmfv{l.a=25,l.d=4,l=\vspace{-2pt}$\overline{\mathrm{b}}$}{b1}
    \fmfv{l.a=-25,l.d=4,l=b}{b2}
  \end{fmfgraph*}
\end{fmfpicture}

% NONRESONANT DITAU PRODUCTION - t-channel, double gluon splitting (straight)
\begin{fmfpicture}{1,4}{15,4}{LQ_tchan_bbtautau_gsplit2_straight} % padding (LTRB)
  \begin{fmfgraph*}(120,125) % dimensions (WH)
    % external vertices
    \fmfleft{d,i2,m2,m1,i1,d} % add dummies 'd' for spacing
    \fmfright{b2,p2,o2,o1,p1,b1} % add dummies 'd' for spacing
    \fmfshift{3 down}{i1,p1}
    \fmfshift{3 up}{i2,p2}
    \fmfshift{7 down}{b1,o2}
    \fmfshift{7 up}{b2,o1}
    % incoming
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,v2}
    \fmf{phantom,t=0.6}{v1,p1,p2,v2} % pull gluons straight right
    \fmffreeze
    %%%% outgoing tau leptons
    %%%\fmf{fermion}{lq1,o1} % tau out
    %%%\fmf{fermion}{o2,lq2} % tau out
    %%%\fmf{phantom,t=0.5}{lq1,m1,m2,lq2} % pull taus straight left
    %%%\fmffreeze
    %%% outgoing b quarks from gluon splitting
    \fmf{fermion}{b1,v1}
    \fmf{fermion}{v2,b2}
    % t-channel
    \fmf{fermion}{v1,lq1} % t-channel
    \fmf{dashes,t=0.8,l.s=right,l.d=5,label=LQ}{lq1,lq2} % t-channel
    \fmf{fermion}{lq2,v2} % t-channel
    % outgoing tau leptons
    \fmf{fermion,t=0.9}{lq1,o1} % tau out
    \fmf{fermion,t=0.9}{o2,lq2} % tau out
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=90}{lq1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=6,l.a=-90}{lq2}
    % labels
    \fmfv{l.d=6,l.a=170,l=$g$}{i1}
    \fmfv{l.d=6,l.a=-170,l=$g$}{i2}
    \fmfv{l.d=6,l.a=10,l=$\tau^-$}{o1}
    \fmfv{l.d=6,l.a=0,l=\strut$\tau^+$}{o2}
    \fmfv{l.d=6,l.a=20,l=$\overline{\mathrm{b}}$}{b1}
    \fmfv{l.d=6,l.a=-20,l=b}{b2}
  \end{fmfgraph*}
\end{fmfpicture}

% NONRESONANT DITAU PRODUCTION - t-channel, double gluon splitting (square)
\begin{fmfpicture}{6,12}{16,12}{LQ_tchan_bbtautau_gsplit2_square} % padding (LTRB)
  \begin{fmfgraph*}(100,90) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{i2,i1}
    \fmfright{b2,o2,o1,b1}
    % incoming
    \fmf{gluon}{v1,i1}
    \fmf{gluon}{i2,v2}
    % outgoing b quarks from gluon splitting
    \fmf{fermion}{b1,v1}
    \fmf{fermion}{v2,b2}
    \fmffreeze
    % t-channel
    \fmf{fermion}{v1,lq1} % t-channel
    \fmf{dashes,l.s=right,l.d=5,label=LQ}{lq1,lq2} % t-channel
    \fmf{fermion}{lq2,v2} % t-channel
    \fmffreeze
    % outgoing tau leptons
    \fmf{fermion}{lq1,o1} % tau out
    \fmf{fermion}{o2,lq2} % tau out
    % vertices
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx$\lambda$,l.d=5,l.a=140}{lq1}
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\colvtx\vspace{-2pt}$\lambda$,l.d=5,l.a=-160}{lq2}
    % labels
    \fmfv{l.d=6,l.a=170,l=$g$}{i1}
    \fmfv{l.d=6,l.a=-170,l=$g$}{i2}
    \fmfv{l.d=6,l.a=10,l=$\tau^-$}{o1}
    \fmfv{l.d=6,l.a=0,l=\strut$\tau^+$}{o2}
    \fmfv{l.d=6,l.a=10,l=$\overline{\mathrm{b}}$}{b1}
    \fmfv{l.d=6,l.a=-10,l=b}{b2}
  \end{fmfgraph*}
\end{fmfpicture}

\end{document}