Testing Lorentz Invariance in Weak Decay Experiments

Violating the Lorentz invariance attracts theoretical interests, especially for building quantum gravitational theories. Also, it has been experimentally tested in many sectors; however, the testing precisions in the weak interaction are an order of magnitude worse than other interactions, e.g., electromagnetic interaction, etc. After trying to test lifetime variation synchronizing to the Earth's rotation of polarized Li-8 at TRIUMF, we performed a new experiment testing that of muon at J-PARC aiming 10-ppm precision. The status of the experiment and new technical developments to perform high statistics measurements will be presented.