Direct detection of dark matter in models with a light Z'

We discuss the direct detection signatures of dark matter interacting with nuclei via a new neutral gauge boson Z', focussing on the case where both the dark matter and the Z' have mass of a few GeV. Isospin violation (i.e. different couplings to protons and neutrons) arises naturally in this scenario. In particular it is possible to reconcile the preferred parameter regions inferred from the observed DAMA and CoGeNT modulations with the bounds from XENON100, which requires f _n /f _p ≃ - 0 .7. Moreover, the Z' mediator can also yield a large spin-dependent cross-section which could contribute to the DAMA signal, while the spin-independent cross-section is adequate to explain the CoGeNT signal.