Undergrad Calc Ampl & Cross Sec: Electron + Positron to Photon + Z Boson

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The discussion focuses on calculating the amplitude and cross section for the annihilation process of an electron and positron into a photon and a Z boson. Key challenges include managing the polarization states of the Z boson, which has three degrees of freedom, and addressing the Lorentz gauge concerning the Z field. Participants are seeking guidance on techniques and methodologies for these calculations. The conversation emphasizes the importance of understanding particle interactions in quantum field theory. Clarification on these points will aid in accurately determining the process's characteristics.
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Process of electron and positron annihilation to photon and Z boson
Looking to calculate the amplitude and cross section of the process: electron + positron to photon + Z boson.

Basically the annihilation resulting in Z + gamma rather than gamma +gamma.

My question is mainly about how to deal with the polarization states with the Z boson, since there are 3 and how to handle to the Lorentz gauge wrt to the Z field. Any help will be appreciated.
 

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