Confronting the direct search of low mass dark matter from CoGeNT data with antiproton PAMELA data

If the excess events from the CoGeNT experiment arise from elastic scatterings of a light dark matter off the nuclei, crossing symmetry implies nonvanishing annihilation cross sections of the light dark matter into hadronic final states inside the Galactic halo, which we confront with the antiproton spectrum measured by the PAMELA Collaboration. We consider two types of effective interactions between the dark matter and the quarks: (1) contact interactions from integrating out heavy particles and (2) long-range interactions due to the electromagnetic properties of the dark matter. The lack of excess in the antiproton spectrum results in tensions for a scalar and, to a lesser extent, vector dark matter interacting with the quarks through the Higgs portal.