Lawrence Berkeley National Laboratory

Some extensions of the Standard Model of particle physics allow for Lorentz invariance and charge-parity-time invariance violations. In the neutrino sector strong constraints have been set by neutrino-oscillation and time-of-flight experiments. However, some Lorentz-invariance-violating parameters are not accessible via these probes. In this work, we focus on the parameters (aof(3))00, (aof(3))10, and (aof(3))11 which would manifest themselves in a nonisotropic β-decaying source as a sidereal oscillation and an overall shift of the spectral endpoint. Based on the data of the first scientific run of the KATRIN experiment, we set the first 90% confidence-level limit on |(aof(3))11| of <0.9×10-6 GeV to 3.7×10-6 GeV, depending on the phase. Moreover, we derive new constraints on (aof(3))00 and (aof(3))10.