Vacuum Cherenkov radiation in spacelike Maxwell-Chern-Simons theory

A detailed analysis of vacuum Cherenkov radiation in spacelike Maxwell-Chern-Simons (MCS) theory is presented. A semiclassical treatment reproduces the leading terms of the tree-level result from quantum field theory. Moreover, certain quantum corrections turn out to be suppressed for large energies of the charged particle, for example, the quantum corrections to the classical MCS Cherenkov angle. It is argued that MCS-theory Cherenkov radiation may, in principle, lead to anisotropy effects for ultra-high-energy cosmic rays (UHECRs). In addition, a qualitative discussion of vacuum Cherenkov radiation from a modified-Maxwell term in the action is given, together with UHECR bounds on some of its dimensionless “coupling constants.”

Figure 1

Feynman diagram contributing to vacuum Cherenkov radiation from charged particles coupled to MCS photons.

Figure 2

Radiated energy rate $\mathrm{d}W/\mathrm{d}t$ from MCS-theory Cherenkov radiation, in units of $\alpha M^2$ and as a function of $|q_{\parallel }|/M$, for a charged scalar particle with mass $M$, electric charge $e\equiv \sqrt{4\pi \alpha }$, and parallel momentum component $q_{\parallel }$ as defined by (2.4). The radiated energy rate is calculated from (2.13, b1a), for a particular choice of the CS mass scale, $m={10}^{-10}M$. The curve for a charged Dirac particle hardly differs from the curve for a charged scalar particle shown here.