MACRO results on atmospheric neutrinos
  We discuss the final results of the MACRO experiment on atmospheric neutrino oscillations. The data concern event topologies with average neutrino energies of ~3 and ~50 GeV. Multiple Coulomb Scattering of the high energy muons was used to estimate the neutrino energy event by event. The angular distributions, the L/E_nu distribution, the particle ratios and the absolute fluxes all favor nu_mu --> nu_tau oscillations with maximal mixing and Delta m^2 ~0.0023 eV^2. Emphasis is given to measured ratios which are not affected by Monte Carlo (MC) absolute normalization; a discussion is made on MC uncertainties. A preliminary search for possible Lorentz invariance violation contributions to atmospheric neutrino oscillations is presented and discussed. 
G. Giacomelli and A. Margiotta (Dipartimento di Fisica   dell'Universita' and Sezione INFN - Bologna, Italy)