Upper bounds on asymmetric dark matter self annihilation cross sections

Most models for asymmetric dark matter allow for dark matter self annihilation processes, which can wash out the asymmetry at temperatures near and below the dark matter mass. We study the coupled set of Boltzmann equations for the symmetric and antisymmetric dark matter number densities, and derive conditions applicable to a large class of models for the absence of a significant wash-out of an asymmetry. These constraints are applied to various existing scenarios. In the case of left- or right-handed sneutrinos, very large electroweak gaugino masses, or very small mixing angles are required.