in flavor basis (heff)ab in the diagonal form (where the indices a, b = e, μ, τ and a′, b′ =1, 2, 3 denote the flavor and diagonal basis, respectively), then we can write the oscillation probability from a flavor state to as where are the eigenvalues. For the conventional massive model . In the SME formalism, the neutrino sector is described by a 6-component vector with three active left-handed neutrinos and three right-handed antineutrinos. The effective Lorentz-violating Hamiltonian is a 6 × 6 matrix that takes the explicit form where flavor indices have been suppressed for simplicity. The widehat on the elements of the last term indicates that these effective coefficients for Lorentz violation are associated to operators of arbitrary dimension. These elements are in general functions of the energy, neutrino direction of propagation, and coefficients for Lorentz violation. Each block corresponds to a 3 × 3 matrix. The 3 × 3 diagonal blocks describe neutrino–neutrino and antineutrino–antineutrino mixing, respectively. The 3 × 3 off-diagonal blocks lead to neutrino–antineutrino oscillations. This hamiltonian contains the information of propagation and oscillations of neutrinos. In particular, the speed of propagation relevant for time-of-flight measurements can be written that corresponds to oscillation-free approximation of the hamiltonian above. In this expression the neutrino speed has been spherically decomposed by using the standard spherical harmonics. This expression shows how neutrino speed can depend on energy and direction of propagation. In general, this speed can also depend on neutrino flavor. The index d denotes the dimension of the operator that breaks Lorentz symmetry. The form of neutrino speed shows that faster-than-light neutrinos can naturally be described by the SME. During the last decade, studies have mainly focused on the minimal sector of the general theory, in which case the hamiltonian above takes the explicit form The indices of this effective Hamiltonian take the six values A, B = e, μ, τ, , , , for neutrinos and antineutrinos. The lowercase indices indicate neutrinos (a, b = e, μ, τ), and the barred lowercase indices indicate antineutrinos (, = , , ). Notice that the ultrarelativistic approximation has been used. The first term is diagonal and can be removed because it does not contribute to oscillations; however, it can play an important role in the stability of the theory. The second term is the standard massive-neutrino Hamiltonian. The third term is the Lorentz-violating contribution. It involves four