Thermal abundance of semirelativistic relics

Approximate analytical solutions of the Boltzmann equation for particles that are either extremely relativistic or nonrelativistic when they decouple from the thermal bath are well established. However, no analytical formula for the relic density of particles that are semirelativistic at decoupling is yet known. We propose a new ansatz for the thermal average of the annihilation cross sections for such particles, and find a semianalytical treatment for calculating their relic densities. As examples, we consider Majorana- and Dirac-type neutrinos. We show that such semirelativistic relics cannot be good cold dark matter candidates. However, late decays of metastable semirelativistic relics might have released a large amount of entropy, thereby diluting the density of other, unwanted relics.