# Interaction Lagrangian for specific channels

I'm trying to build an interaction Lagrangian ($${\cal L}_{int}$$) with 2 fields, a complex $$\varphi$$ and another $$\chi$$ that can be real or complex. The key is to do it granting $$U(1)$$ symmetry and in such a way that the process $$\varphi + \varphi \rightarrow \varphi + \varphi$$ is purely s-channel and $$\varphi + \bar\varphi \rightarrow \varphi + \bar\varphi$$ has no s-channel ($$\bar\varphi$$ is the antiparticle created by $$\varphi$$).

In the first case, vertex s-channel leads to a charged particle, so $$\chi$$ has to be complex due to charge conservation. For this reason, t, u-channels aren't allowed. For the second case, we need to fix $$\chi$$ as complex again due to s-diagram would lead to a non-charged particle, this is, scalar field.

So, ok, we know how $$\chi$$ should be but if I want $$U(1)$$ symmetry I would need $${\cal L}_{int}$$ constructed by products of the form $$g\chi^\dagger\chi\varphi^\dagger\varphi$$, but at $$\mathcal{O}(g^2)$$ I get a loop of $$\chi$$ particles, not the propagator of just one.

Therefore, this Lagrangian doesn't work. How do I fix it?