# Drawing appropriate Feynman graphs

I have learned to compute the corresponding mathematical expressions for a Feynman graph, however, I am yet to conceive the idea of drawing them properly for example

describes the nucleon-antinucleon annihilation/meson creation (that's what(meson creation is written in his book))process. (Picture taken from the lecture notes of Sidney Coleman. )However, I didn't look up the diagram first, instead, I thought about coming up with one. I don't know how to draw Feynman Graphs here, but I can share what came to my mind, I had a Nucleon and an Anti-Nucleon being annihilated at a vertex, a virtual meson emerging out of the vertex and then at another vertex giving rise to 2 mesons. I then thought they (nucleon antinucleon)wouldn't be annihilated if they had different four-momentum, but then I remembered Coleman describing the Nucleon-Antinucleon Scattering process where both had different four-momentum but got annihilated at a vertex giving rise to a virtual meson of momentum as the sum of the two which would then at another vertex give a nucleon and an antinucleon. I want to know what's wrong with my Idea and how to come up with Feynman Graphs.

I am not sure I understand entirely the point of the question, but I will attempt to write an answer and if it is not what you are looking for, you can always comment and I can always edit my answer.

Each Feynman diagram is comprised of internal and external lines, as well as vertices. The internal lines are associated with the kinetic terms of the Lagrangian describing the theory, whereas the vertices are derived from the interaction terms of the respective Lagrangian.

The interaction terms can be such that the vertex has three prongs (three particles meeting at the vertex at hand), or they can be such that the vertex has four prongs (four particles meeting at the vertex at hand). In the $$N+\bar{N}\rightarrow \phi+\phi$$ example you give, there is a three point vertex. We usually use different kind of lines for different species of particles (i.e. wavy line for the photon, straight line with an arrow on the middle of it for the fermion etc). So, from what I can see, I would guess that the straight lines with the arrow correspond to the nucleus (the arrow pointing to the reverse direction is the antinucleus), and the straight lines without the arrows are the mesons $$\phi$$. The must not be charged, since there is no distinction betwee particle and antiparticle (by including an arrow on the respective lines).

I hope this helps.

EDIT: You see, the building blocks are the ones I described. So, if you know the process, I take it you mean that you know the initial and final particles. So, draw one external line for each of those. In addition, those have to somehow interact. Therefore, you have to draw a vertex or multiple vertices in all possible ways such that the external particles are connected to the vertices. This is it. In the figure you have there are two such ways, hence two such (distinct) diagrams.

• Respectfully, I am not asking for an interpretation of the given diagram. I am saying given a process, say the one I have asked, how to sketch the graphs? Commented Nov 8, 2023 at 8:09
• I think I am answering that. You see, the building blocks are the ones I described. So, if you know the process, I take it you mean that you know the initial and final particles. So, draw one external line for each of those. In addition, those have to somehow interact. Therefore, you have to draw a vertex or multiple vertices in all possible ways such that the external particles are connected to the vertices. This is it. In the figure you have there are two such ways, hence two such (distinct) diagrams. Commented Nov 8, 2023 at 12:00
• Ok, I did not ask a precise question here. Apologies. In the given diagram the interaction is done through a virtual nucleon. Is this the only unique way? I thought of a virtual nucleon doing that. I apologise if I am being sloppy again. Commented Nov 8, 2023 at 12:22
• Sorry, I am not sure I understand your comment... Yes, the interaction is "mediated" through a virtual nucleon. Or at least, this is what it appears to be the case. And, indeed, these two ways are the only possible ways of this $2\rightarrow2$ interaction. So, if you are asking if some other particle can be the mediator while keeping the external particles as they are, it appears that this is impossible (otherwise you would have more diagrams) Commented Nov 8, 2023 at 16:01
• Yes , that was helpful, thank you Commented Nov 8, 2023 at 18:39