Chiral Cherenkov radiation in the presence of a time-dependent chiral chemical potential

The photon production process $f\to f+\gamma$ in the presence of a time-dependent chiral chemical potential ${\mu }_5$ is studied. The validity of the adiabatic approximation is demonstrated in the ultra-relativistic limit. Analytical expressions for the photon spectrum are derived for two models of the chiral magnetic conductivity $b_0\propto {\mu }_5$: (i) $b_0(t)=A_1+B_1\tanh (t\mathrm{/}\tau )$ and (ii) $b_0(t)=A_2(t\mathrm{/}\tau )\mathrm{/}(1+t^2\mathrm{/}{\tau }^2)$. It is known that for constant $b_0$, photon emission may exhibit a resonance for one photon polarization depending on the sign of $b_0$. It is shown that in model (i), up to two resonances may occur, depending on the sign of the asymptotic values $b_0(\mathrm{\infty })$ and $b_0(-\mathrm{\infty })$. No resonances are observed in model (ii). Numerical calculations are performed using parameters relevant to quark-gluon plasma, and the universality of the results is discussed.