Self-Interacting Dark Matter with Naturally Light Mediator

A promising proposal for resolving the cusp-core anomaly in the density profile of dwarf galaxies is to allow dark matter to interact with itself through a light mediator of mass much less than a GeV. The theoretical challenge is to have a complete renormalizable theory where this happens naturally even though dark matter itself may be of the electroweak scale, i.e. 100 GeV to 1 TeV. I propose here such a model, with just two neutral complex scalar singlets under a softly broken dark global U(1) symmetry.