Direct detection and CMB constraints on light DM scenario of top quark asymmetry and dijet excess at Tevatron

We study in detail the model by Isidori and Kamenik that is claimed to explain the top quark forward-backward asymmetry at Tevatron, provide GeV-scale dark matter (DM), and possibly improve the agreement between data and theory in Tevatron W+jj events. We compute the DM thermal relic density, the spin-independent DM-nucleon scattering cross section, and the cosmic microwave background constraints on both Dirac and Majorana neutralino DM in the parameter space that explains the top asymmetry. A stable light neutralino is not allowed unless the local DM density is 3-4 times smaller than expected, in which case Dirac DM with mass around 3 GeV may be possible, to be tested by the Planck mission. The model predicts a too broad excess in the dijet distribution and a strong modification of the missing E_T distribution in W+jj events.