Low-energy phenomenology of scalarless standard-model extensions with high-energy Lorentz violation

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-Nc 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.