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Thank you for the responses.

I don't understand why I can't sum to zero when calculating the matrix elements using QED-like axial-vector theory. The only thing which is relevant for the unitarity is the internal structure of the gauge group, which in my toy-like case is just the direct product of the abelian gauge groups. In my initial question, the 1- GA5 coupling from the toy example corresponds to Z-boson which longitudinal degree of freedom decouples for low energies, so I again can make the replacement of the sum over the polarizations by -g_\mu\nu (in my question, the sum over the polarizations appears in the Z propagator).

Also, this doesn't tell nothing about why the unitarity is restored just under changing of the sign of the mp term in the propagators nominator of my two examples, without any other changes.

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