Vacuum Cherenkov radiation for nonminimal dimension-5 Lorentz violation

Abstract

Vacuum Cherenkov radiation is investigated in the Lorentz-violating Standard-Model Extension for isotropic dim-5 operators $\hat{m}$ and $\hat{a}^{\mu}$ in the fermion sector. Both the kinematics and dynamics of this process are analyzed by analytical and numerical means, leading to its decay and radiated-energy rates as functions of the initial-fermion momentum. We adopt the point of view that vacuum Cherenkov radiation is actually a physical phenomenon expected to occur for a charged, massive fermion in the presence of Lorentz violation, when some additional requirements are satisfied. The absence of this effect in ultrahigh-energy cosmic rays detected on Earth allows us to infer stringent bounds on isotropic dim-5 Lorentz violation in protons, quarks, and electrons.