Draw OPE diagram

[Turgon-Aran-Gondolin]

How to draw a textbook operator product expansion diagram like this? In another word, how to make lines to have some kind of angle between each other and how to separate two points only a little bit?

[JP-Ellis]

The easiest in this case will be start using the more explicit syntax which requires you to place the position of the start and end points explicitly:

\begin{tikzpicture}
  \begin{feynman}
    % code goes here
  \end{feynman}
\end{tikzpicture}

There are examples of this in the documentation.

So for the little half-loop in the middle diagram, you'll be better of asking this on TeX StackExchange.