Shadowing Neutrino Mass Hierarchy with Lorentz Invariance Violation

The effects of Lorentz Invariance Violation(LIV) operators up to dimension 6 in long baseline neutrino experiments are discussed, in specific for DUNE and T2K. A phenomenological Lagrangian is proposed followed by a computation of the effective Hamiltonian of neutrino propagation in matter for mass eigenstates. It is shown that the simplest dimension 4 Lorentz violation parameter can decrease DUNE sensitivity to neutrino mass hierarchy. Also, a ${\chi }^2$ analysis is performed to obtain the expected long-baseline constraints to the LIV operators up to dimension 6.