The discovery of the phenomena of neutrino oscillations suggests that neutrinos have non-zero masses, providing solid experimental evidence for physics beyond SM (BSM). To explain the non-zero masses of neutrinos, SM needs an extension. We use the Standard Model Extension (SME) framework to analyze Lorentz Invariance Violation (LIV), wherein the LIV effects are treated as a perturbative effect on the standard Lagrangian. Lorentz invariance is a space-time symmetry in physics that states that all physical laws are invariant under Lorentz transformations, such as boost and rotation. The LIV effect considered here is inherent in nature, and its effects will be noticeable even in a vacuum. In the presence of LIV parameters, the modified Hamiltonian can be used to investigate the indication of Lorentz Invariance Violation. The potential of probing LIV by measuring neutrino oscillation probability is intriguing.
In the present work, we investigate how the presence of LIV terms affects the probability of neutrino oscillation in the matter. We have also explored the sensitivity of various long-baseline experiments to the presence of LIV parameters in neutrino oscillation probability.