The Impact of Sidereal Variation on Time-Independent Probability Analysis in Neutrino Long-Baseline Experiments

Lorentz invariance is a well-known fundamental symmetry, serving as the pillar of widely accepted theories such as quantum field theory and Einstein theory of relativity, and has deep connections with the charge, parity, and time-reversal symmetry. The search for Lorentz invariance violation (LIV) is getting more attention in recent years due to many theories of beyond standard model (Stochastic space-time foam, quantum loop gravity, string theory, etc.) predicting LIV in high-energy physics. We adopt the non-isotropic model to study the LIV parameters. We compare the impact of LIV in different long-baseline neutrino experiments and shows how they are sensitivity depends on their position and orientation. We have also investigated the effect of the non-isotropic LIV parameter on disappearance channels in time-independent analysis.