10 GeV dark matter candidates and cosmic-ray antiprotons

Recent measurements performed with some direct dark matter detection experiments, e.g. CDMS-II and CoGENT (after DAMA/LIBRA), have unveiled a few events compatible with weakly interacting massive particles. The preferred mass range is around 10 GeV, with a quite large spin-independent cross section of $10^{-43}$-$10^{-41}\,{\rm cm^2}$. In this paper, we recall that a light dark matter particle with dominant couplings to quarks should also generate cosmic-ray antiprotons. Taking advantage of recent works constraining the Galactic dark matter mass profile on the one hand and on cosmic-ray propagation on the other hand, we point out that considering a thermal annihilation cross section for such low mass candidates very likely results in an antiproton flux in tension with the current data, which should be taken into account in subsequent studies.