The detection of cosmic neutrino background with helicity-changing decays

In this talk, we present the investigation of the invisible decays of a heavy massive neutrino into a lighter neutrino and a massless Nambu-Goldstone boson, i.e., ${\nu }_i^{}\to {\nu }_j^{}+\phi$. The total decay rates are calculated in the most general case, where the individual helicities of both parent and daughter neutrinos are specified. We then examine the evolution of the number densities of cosmological relic neutrinos throughout the expansion of the Universe, and explore the consequent impacts on the capture rates in PTOLEMY-like experiments. The total event rates can be significantly modified compared to those in the scenario of stable neutrinos, with helicity-changing decays playing an especially important role in the Dirac neutrino case.