Cherenkov-like emission of Z bosons

We study CPT and Lorentz violation in the electroweak gauge sector of the Standard Model in the context of the Standard-Model Extension (SME). In particular, we show that any non-zero value of a certain relevant Lorentz violation parameter that is thus far unbounded by experiment would imply that for sufficiently large energies one of the helicity modes of the Z boson should propagate with spacelike four-momentum and become stable against decay in vacullin. In this scenario, Cherenkov-hike radiation of Z bosons by ultra-highenergy cosmic-ray protons becomes possible. We deduce a bound on the Lorentz violation parameter from the observational data on ultra-high energy cosmic rays.Portuguese Fundacao para a Ciencia e a Tecnologia (FCT) [SFRH/BPD/101403/2014]; program POPH/FS