Drawing a loop with two different line types using TikZ-Feynman

Question

I'm trying to draw a diagram for an interacting field theory. The diagram essentially just needs to consist of a loop connected to two external lines. The problem is that I need the loop to be made up of a dashed and solid line. So far, I have:

\documentclass{article}
\usepackage{tikz}
\usepackage[compat=1.1.0]{tikz-feynman}
\begin{document}
\feynmandiagram [horizontal=a to b, layered layout] {
  a -- [scalar] b [dot] -- [out=125, in=55, loop, min distance=2cm] b -- c,
};
\end{document}

which yields

I need the right-half of the loop to be dashed. Is this possible?

Answer 1

You can superimpose another dash pattern over the scalar option (which is equivalent to dashed. You need to adjust the pattern, however, in order to have exactly the left half of the loop drawn:

\documentclass{article}
\usepackage[compat=1.1.0]{tikz-feynman}
\begin{document}
\feynmandiagram [horizontal=a to b, layered layout] {
  a -- [scalar] b [dot] -- [out=125, in=55, loop, min distance=2cm, scalar, postaction={draw, dash pattern=on 1.5cm off 1.5cm}] b -- c,
};
\end{document}

---

A maybe more elegant approach would be to use decorations to re-draw the first half of the loop path:

\documentclass{article}
\usepackage[compat=1.1.0]{tikz-feynman}
\pgfdeclaremetadecoration{draw first half}{initial}{
    \state{initial}[width={\pgfmetadecoratedpathlength/2}, next state=final]{
        \decoration{curveto}
    }
    \state{final}{}
}
\begin{document}
\feynmandiagram [horizontal=a to b, layered layout] {
  a -- [scalar] b [dot] -- [out=125, in=55, loop, min distance=2cm, scalar, postaction={decorate, draw, decoration={draw first half}}] b -- c,
};
\end{document}

A variation of this approach would be to include the dash pattern in the decoration:

\documentclass{article}
\usepackage[compat=1.1.0]{tikz-feynman}
\pgfdeclaremetadecoration{half dashed}{initial}{
    \state{initial}[width={\pgfmetadecoratedpathlength/2}, next state=final]{
        \decoration{curveto}
        \afterdecoration{
            \pgfusepath{stroke}
        }
    }
    \state{final}{
        \beforedecoration{
            \pgfsetdash{{3pt}{3pt}}{0pt}
        }
        \decoration{curveto}
    }
}
\begin{document}
\feynmandiagram [horizontal=a to b, layered layout] {
  a -- [scalar] b [dot] -- [out=125, in=55, loop, min distance=2cm, decorate, decoration={half dashed}] b -- c,
};
\end{document}

The output of these two code snippets look the same as above.

Answer 2

1. A dirty (?) trick to use \pgfpathcurvebetweentime which I recently used in a different context but I don't want to mess with the to paths that handle the whole out and in stuff.

   \pgfpathcurvebetweentime uses \pgfpathcurveto internally which is why we need to restore it right away again.

   This also draws the path twice, one for the first half and another time for the second half but we need to specify it twice in the code (which is why I defined a key for the loop above a node).

2. Same as 2. but with its own graphs key that may help remove redundancy.

Code

\documentclass{article}
\usepackage[compat=1.1.0]{tikz-feynman}
\makeatletter
\let\pgfpathcurveto@orig\pgfpathcurveto
\tikzset{
  curve from/.code args={#1 to #2}{%
    \let\pgfpathcurveto@orig\pgfpathcurveto
    \def\pgfpathcurveto{\let\pgfpathcurveto\pgfpathcurveto@orig
      \pgfpathcurvebetweentime{#1}{#2}{\tikz@timer@start}}}}
\makeatother
\begin{document}
\feynmandiagram [horizontal=a to b, layered layout,
  la/.style={out=125, in=55, loop, min distance=2cm}]{
  a -- [scalar] b [dot]
  -- [la, curve from=0 to .5] b
  -- [la, curve from=.5 to 1, scalar] b
  -- c,
};
\feynmandiagram [horizontal=a to b, layered layout,
  la/.style={out=125, in=55, loop, min distance=2cm}][
  /tikz/graphs/halfsies/.style n args={6}{% #1 = start, #2 = target,
    % #3 = common, #4 = "half"way point, #5 = first half, #6 = second half
    parse={#1 -- [#3,curve from=0 to #4, #5] #2;
           #1 -- [#3,curve from=#4 to 1, #6] #2;}}]{
  a -- [scalar] b [dot] -- c,
  {[halfsies=bb{la}{.5}{}{scalar}]};
};
\end{document}

Output

Answer 3

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{decorations.pathmorphing}
\usepackage[compat=1.1.0]{tikz-feynman}
\begin{document}
\tikzset{
half dashed/.style={
draw=none,
postaction={draw, dashed, decoration={curveto, post=moveto, post length=1/2*\pgfmetadecoratedpathlength}, decorate},
postaction={draw, decoration={curveto, pre=moveto, pre length=1/2*\pgfmetadecoratedpathlength}, decorate},
},
}
\feynmandiagram [horizontal=a to b, layered layout] {
  a -- [scalar] b [dot] -- [out=125, in=55, loop, min distance=2cm, half dashed] b -- c,
};
\end{document}