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latex:feynman

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Phantoms, freezing and tension

How can you have more control over the line length and vertex positions? Consider making a diagram of a Higgs boson decaying into two W bosons (H → WW → 4f) without the use of tension:

\begin{fmffile}{feyngraph}
  \begin{fmfgraph}(150,150)
    \fmfleft{i1}
    \fmfright{o1,o2,o3,o4}
    \fmf{dashes}{i1,v1}
    \fmf{boson}{v1,v21}
    \fmf{boson}{v1,v22}
    \fmf{fermion}{o1,v21,o2}
    \fmf{fermion}{o3,v22,o4}
  \end{fmfgraph}
\end{fmffile}

This was pretty straightforward, but perhaps you prefer the fermion lines to be equal in length. This can be achieved by drawing help lines, which pull back the vertices of the W boson decays. Normally you would use the invisible phantom lines, but let's start with the visible dashes:

Notice the endpoints of the outgoing fermion lines are not horizontally aligned. This is solved by including the command \fmfstraight:

Use \fmffreeze to freeze this part of the diagram. This will prevent the next lines we add from ruining this balance. Now put back the rest (H → WW).

Now simple use phantom to make the help lines invisible. Note the use of tension, which needs to be fine-tuned:

\begin{fmffile}{feyngraph}
  \begin{fmfgraph}(150,150)
    \fmfstraight
    \fmfleft{i0,i1,i2}
    \fmfright{o1,o2,o3,o4}
    % fermions
    \fmf{fermion}{o1,v21,o2}
    \fmf{fermion}{o3,v22,o4}
    % phantoms to pull back fermion lines
    \fmf{phantom}{i0,v21}
    \fmf{phantom,tension=0.5}{v21,v22}
    \fmf{phantom}{i2,v22}
    \fmffreeze
    % HWW
    \fmf{dashes,tension=1.5}{i1,v1}
    \fmf{boson}{v1,v21}
    \fmf{boson}{v1,v22}
  \end{fmfgraph}
\end{fmffile}






Forcing vertices at desired (x,y) positions

If you do not like puzzling with phantom lines and tension, you could force the vertex at an exact location using \fmfforce{(0.4w,0.7h)}{v}, which places the vertex v at the x position that is 40% of the width from the left, and at the y position that is 70% of the height from the bottom.

\begin{fmffile}{feyngraph}
  \begin{fmfgraph}(150,150)
    \fmfstraight
    \fmfleft{i}
    \fmfright{o1,o2,o3,o4}
    % force vertex locations
    \fmfforce{(0.40w,0.50h)}{v}
    \fmfforce{(0.68w,0.20h)}{v1}
    \fmfforce{(0.68w,0.80h)}{v2}
    % H -> WW
    \fmf{dashes,tension=1.5}{i,v}
    \fmf{boson}{v,v1}
    \fmf{boson}{v,v2}
    % outgoing fermions
    \fmf{fermion}{o1,v1,o2}
    \fmf{fermion}{o3,v2,o4}
  \end{fmfgraph}
\end{fmffile}






latex/feynman.1721287559.txt.gz · Last modified: 2024/07/18 09:25 by iwn