Gluon loop diagrams

Question

I am trying to draw a gluon loop with two-three and four external gluon legs attached to the gluon loop, but as you may see from the attached file these diagrams are not nice enough, could anybody help me to draw them in a nice and symmetric way please? here comes what I have tried:

\documentclass{article}
    \usepackage{feynmp}
    %\usepackage{feynmf}
\DeclareGraphicsRule{*}{mps}{*}{}
    \begin{document}
\begin{figure}[h]
\centering
\begin{eqnarray}
\non
 \begin{fmffile}{gluoncasediagrams}
\newenvironment{8p}{
            \begin{fmfgraph}(60,40)}
{\end{fmfgraph}}
\parbox{20mm}{
\begin{8p}
\fmfleft{i1,i2} \fmfright{o1,o2}
 \fmf{gluon,fore=blue}{i1,v3}
% \fmflabel{$p_3,a_3,\mu_3$}{i1}
\fmf{gluon,fore=black}{i2,v4}
%\fmflabel{$p_4,a_4,\mu_4$}{i2}
\fmf{gluon,fore=red}{v2,o1}
 %\fmflabel{$p_2,a_2,\mu_2$}{o1}
 \fmf{gluon,fore=green}{v1,o2}
 %\fmflabel{$p_1, a_1,\mu_1$}{o2}
\fmf{gluon,tension=0.1}{v1,v2}
 \fmf{gluon,tension=0.3}{v2,v3}
\fmf{gluon,tension=0.3}{v3,v4}
\fmf{gluon,tension=0.3}{v4,v1}
\end{8p}}
\qquad \hspace{0.2cm} \qquad
\parbox{20mm}{
\begin{8p}
\fmfleft{i1,i2} \fmfright{o1,o2}
 \fmf{gluon,fore=red}{i1,v1}
 %\fmflabel{$p_2,a_2$}{i1}
\fmf{gluon,fore=blue}{i2,v2}
%\fmflabel{$p_3,a_3$}{i2}
\fmf{gluon,tension=4,fore=green}{v3,o1}
 %\fmflabel{$p_1,a_1$}{o1}
\fmf{gluon,tension=4,fore=black}{v3,o2}
 %\fmflabel{$p_4,a_4$}{o2} 
 \fmf{gluon,tension=0.1}{v2,v1}
 \fmf{gluon,tension=0.3}{v1,v3}
\fmf{gluon,tension=0.3}{v3,v2}
\end{8p}}
\qquad \hspace{0.2cm}\qquad
\parbox{20mm}{
\begin{8p}
\fmfleft{i1,i2} \fmfright{o1,o2}
 \fmf{gluon,fore=red}{i1,v1}
% \fmflabel{$p_2,a_2$}{i1}
\fmf{gluon,fore=blue}{i2,v1}
%\fmflabel{$p_3,a_3$}{i2}
\fmf{gluon,fore=green}{v2,o1}
 %\fmflabel{$p_1,a_1$}{o1}
\fmf{gluon,fore=black}{v2,o2}
 %\fmflabel{$p_4,a_4$}{o2} 
\fmf{gluon,left,tension=.3}{v1,v2,v1}
\end{8p}}
\qquad \hspace{0.2cm}\qquad
\parbox{20mm}{
\begin{8p}
\fmfleft{i1,i2} \fmfright{o1,o2}
 \fmf{gluon,fore=red}{i1,v2}
% \fmflabel{$p_2,a_2$}{i1}
\fmf{gluon,fore=blue}{i2,v1}
%\fmflabel{$p_3,a_3$}{i2}
\fmf{gluon,fore=green}{v2,o1}
 %\fmflabel{$p_1,a_1$}{o1}
\fmf{gluon,fore=black}{v2,o2}
 %\fmflabel{$p_4,a_4$}{o2} 
\fmf{gluon,left,tension=.3}{v1,v2,v1}
\end{8p}}
\end{fmffile}
\end{eqnarray}
\end{figure}
\end{document}

enter image description here

Welcome to TeX SE. Note that you can format code by indenting it by 4 spaces or highlighting and using the {} button in the editing bar. — cfr, Jun 30 '14 at 02:39
What exactly do you mean by "nice and symmetric"? I assume you don't want any of the gluon paths to intersect in their loops (and they look pretty symmetric to me, unless you'r taking about which way the gluon paths curl). I don't use feynmf, but have you tried the TikZ package with the path decoration coil (on page 588 of the manual)? — Jānis Lazovskis, Jun 30 '14 at 06:04
I would like to have a nice loop where the external gluons attached to it in a nicer way not like what I have done here. As you said I do not want the gluon paths to intersect in their loop like these! and do you know how can I change the angle of the external gluons, my last diagram is really ugly!thanks — Hawi, Jul 01 '14 at 06:11

score 3 · Answer 1 · answered Feb 22 '17 at 13:26

Looking "nice" is a very subjective thing so is hard to do in a way everyone will agree on but I have a few options that may improve it.

Firstly if you really want diagrams this small you probably want to adjust the size of the gluon curl. This is done with the command \fmfset{curly_len}{1.5mm} which sets the length of one curl to 1.5mm.

Secondly to increase the symmetry I would make the diagrams actually be square i.e. make them so the height is the same as the width. This tends to produce nicer diagrams in my opinion even if the diagram isn't symmetric.

Thirdly the junctions tend to be neater if all the gluons curl on the same side. i.e. at any given vertex all the gluons curl to the clockwise direction. This can be done by writing all the lines being drawn in a consistent order which you will see I have done in my examples below.

Lastly for the most complex example to make nice the "massless bubble" I have done a few tweaks that I think improve the diagram. First is to make the curves on the loop not form a full circle but rather a lens shape by setting the amount of "left" to use to 0.7. I also chose to adjust where the end of the loop with three gluons is by making two of them be a straight line, freezing the location of the vertex at the end of the loop then adding the other gluons including the loop in extra.

Combining all of this gives the code:

\begin{fmffile}{diagram}
\fmfset{curly_len}{1.5mm}
\begin{figure}[h]
\centering
\begin{eqnarray}
\newenvironment{8p}{\begin{fmfgraph}(60,60)}{\end{fmfgraph}}
\parbox{20mm}{
\begin{8p}
\fmfsurround{_,i1,_,i2,_,i3,_,i4}
\fmf{gluon,fore=blue}{i1,v1}
\fmf{gluon,fore=black}{i2,v2}
\fmf{gluon,fore=green}{i3,v3}
\fmf{gluon,fore=red}{i4,v4}
\fmf{gluon,tension=0.6}{v1,v2,v3,v4,v1}
\end{8p}}
\qquad \hspace{0.2cm} \qquad
\parbox{20mm}{
\begin{8p}
\fmfsurround{_,i1,_,i2,_,i3,_,i4}
\fmf{gluon,fore=blue}{i1,v1}
\fmf{gluon,fore=black}{i2,v2}
\fmf{gluon,fore=green}{i3,v2}
\fmf{gluon,fore=red}{i4,v3}
\fmf{gluon,tension=0.6}{v1,v2,v3}
\fmf{gluon,tension=0.3}{v3,v1}
\end{8p}}
\qquad \hspace{0.2cm}\qquad
\parbox{20mm}{
\begin{8p}
\fmfsurround{_,i1,_,i2,_,i3,_,i4}
\fmf{gluon,fore=blue}{i1,v1}
\fmf{gluon,fore=black}{i2,v2}
\fmf{gluon,fore=green}{i3,v2}
\fmf{gluon,fore=red}{i4,v1}
\fmf{gluon,tension=0.3,left}{v1,v2,v1}
\end{8p}}
\qquad \hspace{0.2cm}\qquad
\parbox{20mm}{
\begin{8p}
\fmfsurround{_,i1,_,i2,_,i3,_,i4}
\fmf{gluon,fore=black}{i2,v2}
\fmf{gluon,fore=red}{v2,i4}
\fmffreeze
\fmf{gluon,fore=blue}{i1,v1}
\fmf{gluon,fore=green}{i3,v2}
\fmf{gluon,tension=0.3,left=0.8}{v1,v2,v1}
\end{8p}}
\end{eqnarray}
\end{figure}
\end{fmffile}

which gives the output:

Gluon loop diagrams

1 Answers1