Unitarity limits on the mass and radius of dark-matter particles

Abstract

Using partial-wave unitarity and the observed density of the Universe, we show that a stable elementary particle which was once in thermal equilibrium cannot have a mass greater than 340 TeV. An extended object which was once in thermal equilibrium cannot have a radius less than 7.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}7}$ fm. A lower limit to the relic abundance of such particles is also found.