types of coefficients for Lorentz violation. The coefficients and are of dimension one and zero, respectively. These coefficients are responsible for the mixing of left-handed neutrinos, leading to Lorentz-violating neutrino–neutrino oscillations. Similarly, the coefficients and mix right-handed antineutrinos, leading to Lorentz-violating antineutrino–antineutrino oscillations. Notice that these coefficients are 3 × 3 matrices having both spacetime (Greek) and flavor indices (Roman). The off-diagonal block involves the dimension-zero coefficients, , and the dimension-one coefficients, . These lead to neutrino–antineutrino oscillations. All spacetime indices are properly contracted forming observer Lorentz scalars. The four-momentum shows explicitly that the direction of propagation couples to the mSME coefficients, generating the periodic variations and compass asymmetries described in the previous section. Finally, note that coefficients with an odd number of spacetime indices are contracted with operators that break CPT. It follows that the a- and g-type coefficients are CPT-odd. By similar reasoning, the c- and H-type coefficients are CPT-even. Applying the theory to experiments Negligible-mass description For most short baseline neutrino experiments, the ratio of experimental baseline to neutrino energy, L/E, is small, and neutrino masses can be neglected because they are not responsible for oscillations. In these cases, the possibility exists of attributing observed oscillations to Lorentz violation, even if the neutrinos are massive. This limit of the theory is sometimes called the short-baseline approximation. Caution is necessary in this point, because, in short-baseline experiments, masses can become relevant if the energies are sufficiently low. An analysis of this limit, presenting experimentally accessible coefficients for Lorentz violation, first appeared in a 2004 publication. Neglecting neutrino masses, the neutrino Hamiltonian becomes In appropriate cases, the oscillation amplitude can be expanded in the form This approximation is valid if the baseline L is short compared to the oscillation length given by heff. Since heff varies with energy, the term short baseline really depends on both L and E. At leading order, the oscillation probability becomes Remarkably, this mSME framework for short-baseline neutrino experiments, when applied to the LSND anomaly, leads to values of order for and for . These numbers are in the range of what one might expect from quantum-gravity effects. Data analysis has been performed using the LSND, MINOS, MiniBooNE, and IceCube experiments to set limits on the coefficients and . These results, along with experimental results in other sectors of the SME, are summarized in the Data Tables for Lorentz and CPT violation. Perturbative Lorentz-violating