Cosmic-ray fermion decay by emission of on-shell W bosons with C P T violation

We study CPT and Lorentz violation in the electroweak gauge sector of the Standard Model in the context of the Standard-Model Extension. In particular, we consider the Lorentz-violating and CPT-odd Chern-Simons like parameter for the W boson, which is thus far unbounded by experiment. We demonstrate that any non-zero value of this parameter implies that, for sufficiently large energies, one of the polarization modes of the W boson propagates with spacelike four-momentum. In this scenario, emission of W bosons by ultra-high-energy cosmic rays is possible. We calculate the induced fermion energy-loss rate and we deduce the first limit on the pertinent Lorentz- and CPT-violating parameter that couples to the W boson. Consistency between the quantum description in various reference frames is preserved by using a recently formulated covariant quantization procedure for massive photons and applying it to the W bosons.