What Are the Feynman Rules for Bremsstrahlung with Vector Particle Production?

[Maurice7510]

So this isn't a homework problem really, but based on the posting rules for the HEP section this seems to fit better here. My issue is that I'm trying to use a Feynman diagram to represent a Bremsstrahlung process in which a vector particle is produced: $$ Z + e^- \rightarrow Z + e^- + v. $$ If I make the lowest order Feynman diagrams of the situation, you get the two in the PDF I attached on here. The problems I have are twofold -- the first is: can I ignore the proton here are just have an incoming photon, thus reducing these diagrams to looking just like the two for Compton scattering (except with outgoing v instead of a photon)? If I can't, how do I find the amplitude from a diagram that looks like this? The second problem is this: regardless of whether or not I can draw this without the proton, what's the vertex factor for $$e^- \rightarrow \e^- + v $$ and what is the external line factor associated ith a vector particle? I've looked all around and can't seem to find the information I need, so any help would be great. Thanks!

 

[BigJDubs]

A:The two diagrams in the PDF represent the two possible ways of producing a vector particle in a Bremsstrahlung process. The first diagram (the one with the 'e' and the 'Z' crossed) represents the process of photon emission from an electron which is scattered off the Z boson. The second diagram (the one with the 'e' and the 'Z' not crossed) represents the process of photon emission from a Z boson which is scattered off the electron. In order to calculate the amplitude from these diagrams, you need to use the Feynman rules. For the vertex factor, you will need to use the Standard Model couplings for the electron and the Z boson. For the external line factor, you will need to use the propagator for the vector particle. Once you have all of these pieces, you can then calculate the amplitude from the diagrams. Hope this helps!