Leptoquark decay

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This posts shows code examples of Feynman diagrams of various leptoquark (LQ) decay. For LQ production diagrams, please have a look at this post.

Note that the charge of the LQ and the allowed LQ decays depends on the model. For more information on the different LQ models, you can have a look at this great summary by I. Doršner et al., and this graphical representation by myself.

Click on a diagram to jump to the code & download links below:
LQ_decay-001.png LQ_decay-002.png LQ_decay-003.png 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{colvtx}{rgb}{0,.1,1} % LQ vertex (blue)
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(14,14)(1,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(60,60) % dimensions (WH)
    % line style
    \fmfset{dash_len}{8} % dashes length
    % external vertices
    \fmfleft{i}
    \fmfright{q,l}
    \fmf{dashes,l.s=left,t=1.2}{i,v}
    % LQ -> ql
    \fmf{fermion}{v,q}
    \fmf{fermion}{v,l}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=(0,,.1,,1),
          l=\strut\color{colvtx}$\lambda$,l.d=6,l.a=-8}{v}
    % labels
    \fmfv{l=LQ}{i}
    \fmfv{l.a=-28,l=$q$}{q}
    \fmfv{l.a=28,l=$\ell$}{l}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex. 

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\usepackage{xcolor}
\definecolor{colvtx}{rgb}{0,.1,1} % LQ vertex (blue)
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(14,14)(2,14){ % padding (L,T)(R,B)
  \begin{fmfgraph*}(60,60) % dimensions (WH)
    % line style
    \fmfset{dash_len}{8} % dashes length
    % external vertices
    \fmfleft{i}
    \fmfright{q,l}
    \fmf{dashes,l.s=left,t=1.2}{i,v}
    % LQ -> ql
    \fmf{fermion}{v,q}
    \fmf{fermion}{v,l}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=(0,,.1,,1),
          l=\strut\color{colvtx}$\lambda$,l.d=6,l.a=-8}{v}
    % labels
    \fmfv{l=LQ}{i}
    \fmfv{l.a=-28,l=b}{q}
    \fmfv{l.a=28,l=$\tau$}{l}
  \end{fmfgraph*}
  } % close \fmfframe
\end{fmffile}
\end{document}
Download as .png, .pdf, or .tex.

LQ pair decay and different combinatorics for a LQ that decays to third-generation fermions (LQ → bτ, tν):

\documentclass[11pt,border=4pt]{standalone}
\usepackage{feynmp-auto}
\begin{document}
\begin{fmffile}{feyngraph}
  \fmfframe(-4,10)(43,10){ % padding (L,T)(R,B)
  \def\b#1{\makebox[16pt][l]{#1}} % macro to have horizontal alignment
  \begin{fmfgraph*}(60,90) % dimensions (WH)
    % line style
    \fmfset{dash_len}{8} % dashes length
    % external vertices
    \fmfstraight
    \fmfleft{t2,m,t1}
    \fmfright{o4,o3,o2,o1}
    % internal vertices (exact placement)
    \fmfforce{(.52w,.84h)}{v1} % exact placement
    \fmfforce{(.52w,.16h)}{v2} % exact placement
    % LQ pair
    \fmf{dashes,t=1.4,l.s=right,label=LQ}{v1,m}
    \fmf{dashes,t=1.4,l.s=right,label=$\overline{\mathrm{LQ}}$}{m,v2}
    % LQ decay
    \fmf{fermion,t=1.1}{v1,o1}
    \fmf{fermion,t=1.1}{v1,o2}
    \fmf{fermion,t=1.1}{v2,o3}
    \fmf{fermion,t=1.1}{v2,o4}
    % labels
    \fmfv{l=\b{$\tau$,,}\b{$\tau$,,}\b{$\nu$},l.d=8,l.a=0}{o1}
    \fmfv{l=\b{b,,}\b{b,,}\b{t},l.d=8,l.a=0}{o2}
    \fmfv{l=\b{$\tau$,,}\b{$\nu$,,}\b{$\nu$},l.d=8,l.a=0}{o3}
    \fmfv{l=\b{b,,}\b{t,,}\b{t},l.d=8,l.a=0}{o4}
  \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 (September 2024)
% Instructions: To compile via command line, run the following twice
%   pdflatex -shell-escape LQ_decay.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)

% 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}{ % 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}{8} % dashes length
    \fmfcmd\MPcolors % define custom line colors in MetaPost
    \BODY % main code
  \end{fmffile}
  }
  \end{page}
}

\begin{document}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% LQ DECAY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% LQ DECAY
\begin{fmfpicture}{14,14}{1,14}{LQ_decay_ql} % padding (LTRB)
  \begin{fmfgraph*}(60,60) % dimensions (WH)
    % external vertices
    \fmfleft{i}
    \fmfright{q,l}
    \fmf{dashes,l.s=left,t=1.2}{i,v}
    % LQ -> ql
    \fmf{fermion}{v,q}
    \fmf{fermion}{v,l}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\strut\colvtx$\lambda$,l.d=6,l.a=-8}{v}
    % labels
    \fmfv{l=LQ}{i}
    \fmfv{l.a=-28,l=$q$}{q}
    \fmfv{l.a=28,l=$\ell$}{l}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ DECAY
\begin{fmfpicture}{14,14}{2,14}{LQ_decay_btau} % padding (LTRB)
  \begin{fmfgraph*}(60,60) % dimensions (WH)
    % external vertices
    \fmfleft{i}
    \fmfright{q,l}
    \fmf{dashes,l.s=left,t=1.2}{i,v}
    % LQ -> ql
    \fmf{fermion}{v,q}
    \fmf{fermion}{v,l}
    % vertex
    \fmfv{d.sh=circle,d.f=full,d.si=4,f=colvtx,
          l=\strut\colvtx$\lambda$,l.d=6,l.a=-8}{v}
    % labels
    \fmfv{l=LQ}{i}
    \fmfv{l.a=-28,l=b}{q}
    \fmfv{l.a=28,l=$\tau$}{l}
  \end{fmfgraph*}
\end{fmfpicture}

% LQ PAIR DECAY - combinatorics
\begin{fmfpicture}{-4,10}{43,10}{LQ_decay_pair} % padding (LTRB)
  \def\b#1{\makebox[16pt][l]{#1}} % macro to have horizontal alignment
  \begin{fmfgraph*}(60,90) % dimensions (WH)
    % external vertices
    \fmfstraight
    \fmfleft{t2,m,t1}
    \fmfright{o4,o3,o2,o1}
    % internal vertices (exact placement)
    \fmfforce{(.52w,.84h)}{v1} % exact placement
    \fmfforce{(.52w,.16h)}{v2} % exact placement
    % LQ pair
    \fmf{dashes,t=1.4,l.s=right,label=LQ}{v1,m}
    \fmf{dashes,t=1.4,l.s=right,label=$\overline{\mathrm{LQ}}$}{m,v2}
    % LQ decay
    \fmf{fermion,t=1.1}{v1,o1}
    \fmf{fermion,t=1.1}{v1,o2}
    \fmf{fermion,t=1.1}{v2,o3}
    \fmf{fermion,t=1.1}{v2,o4}
    % labels
    \fmfv{l=\b{$\tau$,,}\b{$\tau$,,}\b{$\nu$},l.d=8,l.a=0}{o1}
    \fmfv{l=\b{b,,}\b{b,,}\b{t},l.d=8,l.a=0}{o2}
    \fmfv{l=\b{$\tau$,,}\b{$\nu$,,}\b{$\nu$},l.d=8,l.a=0}{o3}
    \fmfv{l=\b{b,,}\b{t,,}\b{t},l.d=8,l.a=0}{o4}
  \end{fmfgraph*}
\end{fmfpicture}


\end{document}

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


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