Bremsstrahlung in chiral medium: Anomalous magnetic contribution to the Bethe-Heitler formula

Abstract

We investigate photon bremsstrahlung in chiral media. The chiral medium response to the magnetic field is described by the chiral magnetic current $\mathbit{j}={b}_{0}\mathbit{B}$, where ${b}_{0}$ is the chiral magnetic conductivity. This current modifies the photon dispersion relation producing a resonance in the scattering amplitude. We show that the resonant contribution is proportional to the magnetic moment $\ensuremath{\mu}$ of the target nucleus. We analytically compute the corresponding cross section. We argue that the anomalous contribution is enhanced by a factor ${b}_{0}^{2}/{\mathrm{\ensuremath{\Gamma}}}^{2}$, where $\mathrm{\ensuremath{\Gamma}}$ is a width of the resonance related to the chiral magnetic instability of the electromagnetic field. The most conspicuous feature of the anomalous contribution to the photon spectrum is the emergence of the kneelike structure at photon energies proportional to ${b}_{0}$. We argue that the phenomenological significance of the anomalous terms depends on the magnitude of the ratio of ${b}_{0}$ to the projectile fermion mass.