Apparent CPT Violation in Neutrino Oscillation from Dark Non-Standard Interactions

A natural realization of CPT violation in neutrino oscillation can arise due to the coupling to a light scalar or vector dark matter (DM). The dark non-standard interaction (NSI) is associated with the $\gamma_0$ matrix in neutrino's effective propagator and hence corrects the neutrino Hamiltonian as dark matter potential, in the same way as the ordinary matter effect. The effect is, however, inversely proportional to the neutrino energy and hence appears as a correction to the neutrino mass squared. Due to a sign difference in the corrections for neutrino and anti-neutrino modes, the neutrino oscillation receives CPT violation from the dark NSI. Seeing difference in the neutrino and anti-neutrino mass squared differences not necessarily leads to the conclusion of CPT symmetry breaking in the fundamental Lagrangian but can indicate light DM and its coupling with neutrinos.