The current work focuses on the process of vacuum Cherenkov radiation for Lorentz-violating fermions that are described by the minimal standard-model extension (SME). To date, most considerations of this important hypothetical process have been restricted to Lorentz-violating photons, as the necessary theoretical tools for the SME fermion sector have not been available. With their development in a very recent paper, we are now in a position to compute the decay rates based on a modified Dirac theory. Two realizations of the Cherenkov process are studied. In the first scenario, the spin projection of the incoming fermion is assumed to be conserved, and in the second, the spin projection is allowed to flip. The first type of process is shown to be still forbidden for the dimensionful $a$ and $b$ coefficients where there are strong indications that it is energetically disallowed for the $H$ coefficients, as well. However, it is rendered possible for the dimensionless $c$, $d$, $e$, $f$, and $g$ coefficients. For large initial fermion energies, the decay rates for the $c$ and $d$ coefficients were found to grow linearly with momentum and to be linearly suppressed by the smallness of the Lorentz-violating coefficient where for the $e$, $f$, and $g$ coefficients this suppression is even quadratic. The decay rates vanish in the vicinity of the threshold, as expected. The decay including a fermion spin-flip plays a role for the spin-nondegenerate operators and it was found to occur for the dimensionful $b$ and $H$ coefficients as well as for the dimensionless $d$ and $g$. The characteristics of this process differ much from the properties of the spin-conserving one, e.g., there is no threshold. Based on experimental data of ultra-high-energy cosmic rays, new constraints on Lorentz violation in the quark sector are obtained from the thresholds. However, it does not seem to be possible to derive bounds from the spin-flip decays. This work reveals the usefulness of the quantum field theoretic methods recently developed to study the phenomenology of high-energy fermions within the framework of the SME.

• Received 6 March 2017

DOI:https://doi.org/10.1103/PhysRevD.96.095026