what is the kinematics of a particle with complex mass?

Question

• particles with real-mass have time-like kinematics ($ds^2 > 0$).
• particles with zero-mass have light-like kinematics ($ds^2 = 0$).
• particles with imaginary-mass have space-like kinematics ($ds^2 < 0$) (tachyons).

So the question is pretty simple:

What would be the kinematics of a particle with both non-zero real and imaginary parts?

Answer 1

I think the question has no meaningful answer, at least in our universe. If you look at $$E^2 - p^2 = m^2$$ then if $m$ is complex with non-zero real and imaginary components, then $m^2$ is also complex with non-zero real and imaginary components and therefore either $E$ or $p$ (or both) must also be complex with non-zero real and imaginary components. I don't think there is any meaningful description of the kinematics of a particle with complex energy or momentum.

Answer 2

In AWT (dense aether model) all particles have complex mass terms due the quantum fluctuations. A the case of photons and neutrinos the complex mass becomes pronounced. With respect to high density of atom nuclei the mesons are have complex mass too. These particles are doing tachyonic "jumps" in space-time and they undergo quantum decoherence and oscillations.