Study on $\nu_{\mu}$, $\nu_{\tau}$ Decays and CP-Non Invariance at Early Epoch of the Universe

Abstract

We study the $\nu_{\mu}$ and $\nu_{\tau}$ decays in the early epoch of the universe. If $m_{\nu_{\tau}}>2m_e$, there would be a CP asymmetry between $\nu_{\tau}\rightarrow e^++e^-+\nu_e$ and $\bar{\nu}_{\tau} \rightarrow e^++e^-+\bar{\nu}_e$. The resultant CP non-invariance is a function of temperature and density and can reach $10^{-7}$ for a reasonable temperature range, but it is noticed that if $m_{\nu_{\tau}}>2m_{\mu}\sim 200$ MeV, the CP non-invariance can be much larger.