Motivated by recent attempts to reconcile hints of direct dark matter detection by the CoGeNT and DAMA experiments, we construct simple particle physics models that can accommodate the constraints. We point out challenges for building reasonable models and identify the most promising scenarios for getting isospin violation and inelasticity, as indicated by some phenomenological studies. If inelastic scattering is demanded, we need two new light gauge bosons, one of which kinetically mixes with the standard model hypercharge and has mass $<2\mathrm{GeV}$, and another which couples to baryon number and has mass $6.8\pm \genfrac{}{}{0ex}{}{0.1}{0.2}\mathrm{GeV}$. Their interference gives the desired amount of isospin violation. The dark matter is nearly Dirac, but with small Majorana masses induced by spontaneous symmetry breaking, so that the gauge boson couplings become exactly off-diagonal in the mass basis, and the small mass splitting needed for inelasticity is simultaneously produced. If only elastic scattering is demanded, then an alternative model, with interference between the kinetically mixed gauge boson and a hidden sector scalar Higgs, is adequate to give the required isospin violation. In both cases, the light kinetically mixed gauge boson is in the range of interest for currently running fixed target experiments.

• Received 15 August 2011

DOI:https://doi.org/10.1103/PhysRevD.84.075003