Effect of Relic Neutrino on Neutrino Pair Emission from Metastable Atoms

Abstract

A possiblity of measuring the cosmic neutrino temperature $\sim 1.9 K$ and other important quantities such as the chemical potential $\mu$ and the decoupling temperature $T_d$ is discussed, using the recently proposed process of photon irradiated neutrino pair emission from metastable atoms. The Pauli blocking effect of relic neutrinos reduces the rate by a large factor $\approx (1 + m_1/T_d)/4$ at the threshold of the lightest neutrino pair (of mass $2m_1$). Correction of linear order in $\mu$ near the mass thresholds can be used to improve the constraint on the lepton asymmetry.