Draw rotated self-energy of electron on an oblique line TikZ-Feynman

Question

I have to draw a diagram for radiative corrections on an external field, but I would like to make half-loops for self-energy of electron on the slanted fermionic lines (see figure and code). I tried this but it doesn't seem to have any effect. There is nothing on the documentation. Could anyone help me?

\begin{tikzpicture}
     \begin{feynman}
          \vertex (a) ;
          \vertex[below right= of a] (b);
          \vertex[above right= of b] (c);
          \vertex[crossed dot, below= of b] (d) {};
          \diagram* {
                (a) -- [fermion] (b) -- [fermion] (c);
                (b) -- [boson] (d);
          };
          \draw [boson, half left] ($(b)!0.2!(c)$) -- ($(b)!0.8!(c)$);
     \end{feynman}
\end{tikzpicture}

Is it possibile to add momentum for this half loop?

EDIT:

https://www.overleaf.com/8134191135krhdbksyvxpg

the idea is to draw these

Answer 1

Instead of using -- to draw a straight path, you could use the tikz arc path:

% !TeX TS-program = lualatex 

\documentclass{standalone}

\usepackage{tikz-feynman}

\begin{document}
\begin{tikzpicture}
     \begin{feynman}
          \vertex (a) ;
          \vertex[below right= of a] (b);
          \vertex[above right= of b] (c);
          \vertex[crossed dot, below= of b] (d) {};
          \diagram* {
                (a) -- [fermion] (b) -- [fermion] (c);
                (b) -- [boson] (d);
          };
          \draw [boson] ($(b)!0.2!(c)$) arc[start angle=235, end angle=35, radius=12pt] node[midway,above] {k} ($(b)!0.8!(c)$);
     \end{feynman}
\end{tikzpicture}
\end{document}