  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.
