Neutrino Mixing Angle and Neutrino Oscillation in Axion-Like Particles Matter

Neutrino oscillations in axion-like particle (ALP) matter are studied. It has been shown that in order to obtain a dependence of neutrino oscillations on the density of ALPs, it is necessary to use second-order perturbation theory. The majoron could contribute significantly to neutrino oscillations through the seesaw mechanism. If the majoron is considered a candidate for dark matter, this contribution may be negligible. Nevertheless, it could be observed in objects with high majoron densities, such as majoron stars, which are interesting from the perspective of majoron decay into neutrinos.