Diagrams for nucleon scattering

[carllacan]

According to Tong there are two Feynman diagrams for nucleon-nucleon scattering in the interaction of the complex and real scalar fields, but I can draw another diagram where the p1 and p2 particles enter a vertex and the p1' and p2' particles go out of another vertex (linked to the first one by a dotted real-field line, of course). Why is this diagram impossible?

I think it is because the interaction term is ψ*ψΦ, so every vertex requires a real field particle plus either a particle going in and an antiparticle going out or an antiparticle-particle pair both going out or going in. Is that so?

 

[vanhees71]

The vertex consists of a dotted line, representing the meson and in incoming and an outgoing fermion line (representing $\psi$ and $\bar{\psi}$). Now connecting two points stands for contractions. The contraction of two $\psi$'s or two $\bar{\psi}$'s gives 0. So you can connect fermions only in the proper sense of the arrows. So there are indeed only two diagrams at tree level (consisting of two vertices). So your assumption is correct.

 

[carllacan]

The vertex consists of a dotted line, representing the meson and in incoming and an outgoing fermion line (representing $\psi$ and $\bar{\psi}$). Now connecting two points stands for contractions. The contraction of two $\psi$'s or two $\bar{\psi}$'s gives 0. So you can connect fermions only in the proper sense of the arrows. So there are indeed only two diagrams at tree level (consisting of two vertices). So your assumption is correct.

Thanks for your answer. Just a little doubt: I don't understand why are you talking about fermions. I thought fermions were the particles of the Dirac field. Did you think I was talking about Yukawa theory or are complex field particles also called fermions?

 

[vanhees71]

Well, I thought you talk about nucleons, i.e., protons and neutrons. A particle's name includes all its properties, and nucleons are Dirac fermions in the effective theory described in your source.