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I am trying to create a tadpole diagram that is a photon that is vertical with a scalar loop attached to the top that has some momentum $l$. Here is what I have so far:

\documentclass[11pt,a4paper]{article}
\usepackage[compat=1.1.0]{tikz-feynman}
\begin{equation}
\feynmandiagram [baseline=(a.base), vertical=b to a] {
% Photon propagator
a -- [photon] b,
% Scalar loop on top
b -- [scalar, dashed, half left, momentum=\(l\)] c,
c -- [scalar,dashed, half left,]b
};
\end{equation}

which looks crooked almost to the right? It may be a visual issue since I can not figure out how to get the loop-arrow at the top of the loop.

My main question is then: how do I put the arrow of the momentum at the top of the loop, and then how would I instead place a large dot where the loop is? (It also looks crooked to me, but that may be a visual trick).

I also want to make a similar diagram but instead of a loop at the end (on top) of the photon propagator, instead I want to put a large black dot (these two diagram correspond to a particular renormalization of a constant in the theory where the loop is the correction or $\delta m^2$ and the one diagram with just a large black dot is the "bare" term $m_0^2$).

Any suggestions are welcomed and appreciated.

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  • Can you try to come up with a less generic question title which describes which problem you have, so future uses with the same problem will be able to find it? Feb 12 at 20:09
  • @samcarter_is_at_topanswers.xyz Yep!
    – MathZilla
    Feb 12 at 20:33
  • 3
    It may help if you add a drawing (maybe by hand) how the expected result should look like.
    – gernot
    Feb 12 at 22:22
  • An idea from another question: tex.stackexchange.com/q/708213/47927 Feb 13 at 7:34

1 Answer 1

2

I'm not a particle physicist, nor am I an expert in tikz-feynman, but using TikZ, we can use create a custom node called tadpole which has the attributes you want. I also agreed that the default half left produced a diagram that looked a little asymmetrical, so I used a circle for my tadpoles. The momentum is specified with tadpole = $l$, and you can include these tadpoles as one part of a larger Feynman diagram (example on the left) or completely on their own (example on the right).

Some weird looking Feynman diagrams. The one on the left has one central node connected to three outlying vertices, and the one on the right has only two vertices. On the left, there is a circular node drawn with a dashed line, and a clockwise arrow labeled with the letter "l" appears above it. On the right, there is a circular node with a clockwise arrow, also labeled with the letter "l".

\documentclass[11pt]{standalone}
\usepackage[compat=1.1.0]{tikz-feynman}

\tikzfeynmanset{
  tadpole/.style={
    /tikz/.cd,
    shape = circle,
    graphs/as = {},
    draw,
    minimum size = 1cm,
    append after command = {
      \pgfextra{%
        \draw[-stealth] (\tikzlastnode.center) ++ (135:7mm) arc (135:45:7mm)
        node [pos=0.5,anchor=south] {#1};
      }
    }
  }
}

\begin{document}

\feynmandiagram [vertical=b to a] {
  a -- [photon] b [tadpole = $l$, dashed] c,
  a -- d,
  a -- e
};
\qquad
\feynmandiagram [vertical=b to a] {
  a -- [photon] b [tadpole = $l$, fill=black] 
};

\end{document}
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  • 1
    +1 for the lot of efforts.
    – Sebastiano
    Feb 13 at 13:23

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