  We consider renormalizable Standard-Model extensions that violate Lorentz
symmetry at high energies, but preserve CPT, and do not contain elementary
scalar fields. A Nambu--Jona-Lasinio mechanism gives masses to fermions and
gauge bosons, and generates composite Higgs fields at low energies. We study
the effective potential at the leading order of the large-N_{c} expansion,
prove that there exists a broken phase and study the phase space. In general,
the minimum may break invariance under boosts, rotations and CPT, but we give
evidence that there exists a Lorentz invariant phase. We study the spectrum of
composite bosons and the low-energy theory in the Lorentz phase. Our approach
predicts relations among the parameters of the low-energy theory. We find that
such relations are compatible with the experimental data, within theoretical
errors. We also study the mixing among generations, the emergence of the CKM
matrix and neutrino oscillations.
