Neutrino oscillations and Lorentz invariance violation in a Finslerian geometrical model

Neutrino oscillations are one of the first evidences of physics beyond the Standard Model (SM). Since Lorentz invariance is a SM fundamental symmetry, recently also neutrino physics has been explored to verify this symmetry eventual modification and its potential magnitude. In this work we study the Lorentz invariance violation (LIV) introduction consequences in the high energy neutrinos propagation and evaluate the impact of this eventual violation on the oscillations predictions. An effective theory explaining these physical effects is introduced via modified dispersion relations. This approach, originally introduced by Coleman and Glashow, corresponds in our model to a special relativity geometry modification. Moreover, this perspective generalization leads to the introduction of a maximum attainable velocity which is specific of the particle. This can be formalized in Finsler geometry, a more general theory of space-time. In the present paper the impact of this kind of LIV on neutrino phenomenology is studied, in particular by analyzing the corrections introduced in neutrino oscillation probabilities for different values of neutrino energies and baselines of experimental interest. The possibility of further improving the present constraints on CPT-even LIV coefficients by means of our analysis is also discussed.