Time-evolution of parity-odd cascades in homogeneous Abelian and non-Abelian media with chiral imbalance

We study radiation by a fast particle in a medium with a finite chiral chemical potential. The medium's anomalous response encompasses the chiral magnetic effect, enabling novel chiral Cherenkov and pair production processes. The kinematics of the corresponding cascades is fundamentally different from conventional cascades. Notably, it is not dominated by the strong ordering of momenta. Employing the effective Chern-Simons extensions of QED and QCD to incorporate the chiral magnetic effect, we derive and solve the evolution equations describing the cascades in a chiral medium, presuming that the anomalous contributions are dominant.